The density-matrix renormalization group: a short introduction.

PubMed

Schollwöck, Ulrich

2011-07-13

The density-matrix renormalization group (DMRG) method has established itself over the last decade as the leading method for the simulation of the statics and dynamics of one-dimensional strongly correlated quantum lattice systems. The DMRG is a method that shares features of a renormalization group procedure (which here generates a flow in the space of reduced density operators) and of a variational method that operates on a highly interesting class of quantum states, so-called matrix product states (MPSs). The DMRG method is presented here entirely in the MPS language. While the DMRG generally fails in larger two-dimensional systems, the MPS picture suggests a straightforward generalization to higher dimensions in the framework of tensor network states. The resulting algorithms, however, suffer from difficulties absent in one dimension, apart from a much more unfavourable efficiency, such that their ultimate success remains far from clear at the moment.

Extending the range of real time density matrix renormalization group simulations

NASA Astrophysics Data System (ADS)

Kennes, D. M.; Karrasch, C.

2016-03-01

We discuss a few simple modifications to time-dependent density matrix renormalization group (DMRG) algorithms which allow to access larger time scales. We specifically aim at beginners and present practical aspects of how to implement these modifications within any standard matrix product state (MPS) based formulation of the method. Most importantly, we show how to 'combine' the Schrödinger and Heisenberg time evolutions of arbitrary pure states | ψ 〉 and operators A in the evaluation of 〈A〉ψ(t) = 〈 ψ | A(t) | ψ 〉 . This includes quantum quenches. The generalization to (non-)thermal mixed state dynamics 〈A〉ρ(t) =Tr [ ρA(t) ] induced by an initial density matrix ρ is straightforward. In the context of linear response (ground state or finite temperature T > 0) correlation functions, one can extend the simulation time by a factor of two by 'exploiting time translation invariance', which is efficiently implementable within MPS DMRG. We present a simple analytic argument for why a recently-introduced disentangler succeeds in reducing the effort of time-dependent simulations at T > 0. Finally, we advocate the python programming language as an elegant option for beginners to set up a DMRG code.

Description of quantum states using in free space optic communication

NASA Astrophysics Data System (ADS)

Kučera, Petr

2017-11-01

In the article we concentrate our attention on the quantum description of states which are prepared by light sources. The main goal of the article is the determination of density matrix of background radiation source. It is shown that these matrix elements satisfy Geometric distribution in the number state representation.

The Feynman-Vernon Influence Functional Approach in QED

NASA Astrophysics Data System (ADS)

Biryukov, Alexander; Shleenkov, Mark

2016-10-01

In the path integral approach we describe evolution of interacting electromagnetic and fermionic fields by the use of density matrix formalism. The equation for density matrix and transitions probability for fermionic field is obtained as average of electromagnetic field influence functional. We obtain a formula for electromagnetic field influence functional calculating for its various initial and final state. We derive electromagnetic field influence functional when its initial and final states are vacuum. We present Lagrangian for relativistic fermionic field under influence of electromagnetic field vacuum.

Electron paramagnetic resonance g-tensors from state interaction spin-orbit coupling density matrix renormalization group

NASA Astrophysics Data System (ADS)

Sayfutyarova, Elvira R.; Chan, Garnet Kin-Lic

2018-05-01

We present a state interaction spin-orbit coupling method to calculate electron paramagnetic resonance g-tensors from density matrix renormalization group wavefunctions. We apply the technique to compute g-tensors for the TiF3 and CuCl42 - complexes, a [2Fe-2S] model of the active center of ferredoxins, and a Mn4CaO5 model of the S2 state of the oxygen evolving complex. These calculations raise the prospects of determining g-tensors in multireference calculations with a large number of open shells.

Density-matrix description of heteronuclear decoupling in A mX n systems

NASA Astrophysics Data System (ADS)

McClung, R. E. D.; John, Boban K.

A detailed investigation of the effects of ordinary noise decoupling and spherical randomization decoupling on the elements of the density matrix for A mX n spin systems is presented. The elements are shown to reach steady-state values in the rotating frame of the decoupled nuclei when the decoupling field is strong and is applied for a sufficient time interval. The steady-state values are found to be linear combinations of the density-matrix elements at the beginning of the decoupling period, and often involve mixing of populations with multiple-quantum coherences, and mixing of the perpendicular components of the magnetization with higher coherences. This description of decoupling is shown to account for the "illusions" of spin decoupling in 2D gated-decoupler 13C J-resolved spectra reported by Levitt et al.

Transferring elements of a density matrix

DOE Office of Scientific and Technical Information (OSTI.GOV)

Allahverdyan, Armen E.; Hovhannisyan, Karen V.; Yerevan State University, A. Manoogian Street 1, Yerevan

2010-01-15

We study restrictions imposed by quantum mechanics on the process of matrix-element transfer. This problem is at the core of quantum measurements and state transfer. Given two systems A and B with initial density matrices lambda and r, respectively, we consider interactions that lead to transferring certain matrix elements of unknown lambda into those of the final state r-tilde of B. We find that this process eliminates the memory on the transferred (or certain other) matrix elements from the final state of A. If one diagonal matrix element is transferred, r(tilde sign){sub aa}=lambda{sub aa}, the memory on each nondiagonal elementmore » lambda{sub an}ot ={sub b} is completely eliminated from the final density operator of A. Consider the following three quantities, Relambda{sub an}ot ={sub b}, Imlambda{sub an}ot ={sub b}, and lambda{sub aa}-lambda{sub bb} (the real and imaginary part of a nondiagonal element and the corresponding difference between diagonal elements). Transferring one of them, e.g., Rer(tilde sign){sub an}ot ={sub b}=Relambda{sub an}ot ={sub b}, erases the memory on two others from the final state of A. Generalization of these setups to a finite-accuracy transfer brings in a trade-off between the accuracy and the amount of preserved memory. This trade-off is expressed via system-independent uncertainty relations that account for local aspects of the accuracy-disturbance trade-off in quantum measurements. Thus, the general aspect of state disturbance in quantum measurements is elimination of memory on non-diagonal elements, rather than diagonalization.« less

The difference between two random mixed quantum states: exact and asymptotic spectral analysis

NASA Astrophysics Data System (ADS)

Mejía, José; Zapata, Camilo; Botero, Alonso

2017-01-01

We investigate the spectral statistics of the difference of two density matrices, each of which is independently obtained by partially tracing a random bipartite pure quantum state. We first show how a closed-form expression for the exact joint eigenvalue probability density function for arbitrary dimensions can be obtained from the joint probability density function of the diagonal elements of the difference matrix, which is straightforward to compute. Subsequently, we use standard results from free probability theory to derive a relatively simple analytic expression for the asymptotic eigenvalue density (AED) of the difference matrix ensemble, and using Carlson’s theorem, we obtain an expression for its absolute moments. These results allow us to quantify the typical asymptotic distance between the two random mixed states using various distance measures; in particular, we obtain the almost sure asymptotic behavior of the operator norm distance and the trace distance.

Partially coherent electron transport in terahertz quantum cascade lasers based on a Markovian master equation for the density matrix

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jonasson, O.; Karimi, F.; Knezevic, I.

2016-08-01

We derive a Markovian master equation for the single-electron density matrix, applicable to quantum cascade lasers (QCLs). The equation conserves the positivity of the density matrix, includes off-diagonal elements (coherences) as well as in-plane dynamics, and accounts for electron scattering with phonons and impurities. We use the model to simulate a terahertz-frequency QCL, and compare the results with both experiment and simulation via nonequilibrium Green's functions (NEGF). We obtain very good agreement with both experiment and NEGF when the QCL is biased for optimal lasing. For the considered device, we show that the magnitude of coherences can be a significantmore » fraction of the diagonal matrix elements, which demonstrates their importance when describing THz QCLs. We show that the in-plane energy distribution can deviate far from a heated Maxwellian distribution, which suggests that the assumption of thermalized subbands in simplified density-matrix models is inadequate. As a result, we also show that the current density and subband occupations relax towards their steady-state values on very different time scales.« less

Density matrix approach to the hot-electron stimulated photodesorption

NASA Astrophysics Data System (ADS)

Kühn, Oliver; May, Volkhard

1996-07-01

The dissipative dynamics of the laser-induced nonthermal desorption of small molecules from a metal surface is investigated here. Based on the density matrix formalism a multi-state model is introduced which explicitly takes into account the continuum of electronic states in the metal. Various relaxation mechanisms for the electronic degrees of freedom are shown to govern the desorption dynamics and hence the desorption probability. Particular attention is paid to the modeling of the time dependence of the electron energy distribution in the metal which reflects different excitation conditions.

Calculations with off-shell matrix elements, TMD parton densities and TMD parton showers

NASA Astrophysics Data System (ADS)

Bury, Marcin; van Hameren, Andreas; Jung, Hannes; Kutak, Krzysztof; Sapeta, Sebastian; Serino, Mirko

2018-02-01

A new calculation using off-shell matrix elements with TMD parton densities supplemented with a newly developed initial state TMD parton shower is described. The calculation is based on the KaTie package for an automated calculation of the partonic process in high-energy factorization, making use of TMD parton densities implemented in TMDlib. The partonic events are stored in an LHE file, similar to the conventional LHE files, but now containing the transverse momenta of the initial partons. The LHE files are read in by the Cascade package for the full TMD parton shower, final state shower and hadronization from Pythia where events in HEPMC format are produced. We have determined a full set of TMD parton densities and developed an initial state TMD parton shower, including all flavors following the TMD distribution. As an example of application we have calculated the azimuthal de-correlation of high p_t dijets as measured at the LHC and found very good agreement with the measurement when including initial state TMD parton showers together with conventional final state parton showers and hadronization.

Calculations with off-shell matrix elements, TMD parton densities and TMD parton showers.

PubMed

Bury, Marcin; van Hameren, Andreas; Jung, Hannes; Kutak, Krzysztof; Sapeta, Sebastian; Serino, Mirko

2018-01-01

A new calculation using off-shell matrix elements with TMD parton densities supplemented with a newly developed initial state TMD parton shower is described. The calculation is based on the KaTie package for an automated calculation of the partonic process in high-energy factorization, making use of TMD parton densities implemented in TMDlib. The partonic events are stored in an LHE file, similar to the conventional LHE files, but now containing the transverse momenta of the initial partons. The LHE files are read in by the Cascade package for the full TMD parton shower, final state shower and hadronization from Pythia where events in HEPMC format are produced. We have determined a full set of TMD parton densities and developed an initial state TMD parton shower, including all flavors following the TMD distribution. As an example of application we have calculated the azimuthal de-correlation of high [Formula: see text] dijets as measured at the LHC and found very good agreement with the measurement when including initial state TMD parton showers together with conventional final state parton showers and hadronization.

Quantum Entanglement and Reduced Density Matrices

NASA Astrophysics Data System (ADS)

Purwanto, Agus; Sukamto, Heru; Yuwana, Lila

2018-05-01

We investigate entanglement and separability criteria of multipartite (n-partite) state by examining ranks of its reduced density matrices. Firstly, we construct the general formula to determine the criterion. A rank of origin density matrix always equals one, meanwhile ranks of reduced matrices have various ranks. Next, separability and entanglement criterion of multipartite is determined by calculating ranks of reduced density matrices. In this article we diversify multipartite state criteria into completely entangled state, completely separable state, and compound state, i.e. sub-entangled state and sub-entangledseparable state. Furthermore, we also shorten the calculation proposed by the previous research to determine separability of multipartite state and expand the methods to be able to differ multipartite state based on criteria above.

On the non-linear spectroscopy including saturated absorption and four-wave mixing in two and multi-level atoms: a computational study

NASA Astrophysics Data System (ADS)

Patel, M.; De Jager, G.; Nkosi, Z.; Wyngaard, A.; Govender, K.

2017-10-01

In this paper we report on the study of two and multi-level atoms interacting with multiple laser beams. The semi-classical approach is used to describe the system in which the atoms are treated quantum mechanically via the density matrix operator, while the laser beams are treated classically using Maxwells equations. We present results of a two level atom interacting with single and multiple laser beams and demonstrate Rabi oscillations between the levels. The effects of laser modulation on the dynamics of the atom (atomic populations and coherences) are examined by solving the optical Bloch equations. Plots of the density matrix elements as a function of time are presented for various parameters such as laser intensity, detuning, modulation etc. In addition, phase-space plots and Fourier analysis of the density matrix elements are provided. The atomic polarization, estimated from the coherence terms of the density matrix elements, is used in the numerical solution of Maxwells equations to determine the behaviour of the laser beams as they propagate through the atomic ensemble. The effects of saturation and hole-burning are demonstrated in the case of two counter propagating beams with one being a strong beam and the other being very weak. The above work is extended to include four-wave mixing in four level atoms in a diamond configuration. Two co-propagating beams of different wavelengths drive the atoms from a ground state |1〉 to an excited state |3〉 via an intermediate state |2〉. The atoms then move back to the ground state via another intermediate state |4〉, resulting in the generation of two additional correlated photon beams. The characteristics of these additional photons are studied.

Global quantum discord and matrix product density operators

NASA Astrophysics Data System (ADS)

Huang, Hai-Lin; Cheng, Hong-Guang; Guo, Xiao; Zhang, Duo; Wu, Yuyin; Xu, Jian; Sun, Zhao-Yu

2018-06-01

In a previous study, we have proposed a procedure to study global quantum discord in 1D chains whose ground states are described by matrix product states [Z.-Y. Sun et al., Ann. Phys. 359, 115 (2015)]. In this paper, we show that with a very simple generalization, the procedure can be used to investigate quantum mixed states described by matrix product density operators, such as quantum chains at finite temperatures and 1D subchains in high-dimensional lattices. As an example, we study the global discord in the ground state of a 2D transverse-field Ising lattice, and pay our attention to the scaling behavior of global discord in 1D sub-chains of the lattice. We find that, for any strength of the magnetic field, global discord always shows a linear scaling behavior as the increase of the length of the sub-chains. In addition, global discord and the so-called "discord density" can be used to indicate the quantum phase transition in the model. Furthermore, based upon our numerical results, we make some reliable predictions about the scaling of global discord defined on the n × n sub-squares in the lattice.

Inner Space Perturbation Theory in Matrix Product States: Replacing Expensive Iterative Diagonalization.

PubMed

Ren, Jiajun; Yi, Yuanping; Shuai, Zhigang

2016-10-11

We propose an inner space perturbation theory (isPT) to replace the expensive iterative diagonalization in the standard density matrix renormalization group theory (DMRG). The retained reduced density matrix eigenstates are partitioned into the active and secondary space. The first-order wave function and the second- and third-order energies are easily computed by using one step Davidson iteration. Our formulation has several advantages including (i) keeping a balance between the efficiency and accuracy, (ii) capturing more entanglement with the same amount of computational time, (iii) recovery of the standard DMRG when all the basis states belong to the active space. Numerical examples for the polyacenes and periacene show that the efficiency gain is considerable and the accuracy loss due to the perturbation treatment is very small, when half of the total basis states belong to the active space. Moreover, the perturbation calculations converge in all our numerical examples.

Separability and Entanglement in the Hilbert Space Reference Frames Related Through the Generic Unitary Transform for Four Level System

NASA Astrophysics Data System (ADS)

Man'ko, V. I.; Markovich, L. A.

2018-02-01

Quantum correlations in the state of four-level atom are investigated by using generic unitary transforms of the classical (diagonal) density matrix. Partial cases of pure state, X-state, Werner state are studied in details. The geometrical meaning of unitary Hilbert reference-frame rotations generating entanglement in the initially separable state is discussed. Characteristics of the entanglement in terms of concurrence, entropy and negativity are obtained as functions of the unitary matrix rotating the reference frame.

The multifacet graphically contracted function method. I. Formulation and implementation

NASA Astrophysics Data System (ADS)

Shepard, Ron; Gidofalvi, Gergely; Brozell, Scott R.

2014-08-01

The basic formulation for the multifacet generalization of the graphically contracted function (MFGCF) electronic structure method is presented. The analysis includes the discussion of linear dependency and redundancy of the arc factor parameters, the computation of reduced density matrices, Hamiltonian matrix construction, spin-density matrix construction, the computation of optimization gradients for single-state and state-averaged calculations, graphical wave function analysis, and the efficient computation of configuration state function and Slater determinant expansion coefficients. Timings are given for Hamiltonian matrix element and analytic optimization gradient computations for a range of model problems for full-CI Shavitt graphs, and it is observed that both the energy and the gradient computation scale as O(N2n4) for N electrons and n orbitals. The important arithmetic operations are within dense matrix-matrix product computational kernels, resulting in a computationally efficient procedure. An initial implementation of the method is used to present applications to several challenging chemical systems, including N2 dissociation, cubic H8 dissociation, the symmetric dissociation of H2O, and the insertion of Be into H2. The results are compared to the exact full-CI values and also to those of the previous single-facet GCF expansion form.

The multifacet graphically contracted function method. I. Formulation and implementation.

PubMed

Shepard, Ron; Gidofalvi, Gergely; Brozell, Scott R

2014-08-14

The basic formulation for the multifacet generalization of the graphically contracted function (MFGCF) electronic structure method is presented. The analysis includes the discussion of linear dependency and redundancy of the arc factor parameters, the computation of reduced density matrices, Hamiltonian matrix construction, spin-density matrix construction, the computation of optimization gradients for single-state and state-averaged calculations, graphical wave function analysis, and the efficient computation of configuration state function and Slater determinant expansion coefficients. Timings are given for Hamiltonian matrix element and analytic optimization gradient computations for a range of model problems for full-CI Shavitt graphs, and it is observed that both the energy and the gradient computation scale as O(N(2)n(4)) for N electrons and n orbitals. The important arithmetic operations are within dense matrix-matrix product computational kernels, resulting in a computationally efficient procedure. An initial implementation of the method is used to present applications to several challenging chemical systems, including N2 dissociation, cubic H8 dissociation, the symmetric dissociation of H2O, and the insertion of Be into H2. The results are compared to the exact full-CI values and also to those of the previous single-facet GCF expansion form.

Separable decompositions of bipartite mixed states

NASA Astrophysics Data System (ADS)

Li, Jun-Li; Qiao, Cong-Feng

2018-04-01

We present a practical scheme for the decomposition of a bipartite mixed state into a sum of direct products of local density matrices, using the technique developed in Li and Qiao (Sci. Rep. 8:1442, 2018). In the scheme, the correlation matrix which characterizes the bipartite entanglement is first decomposed into two matrices composed of the Bloch vectors of local states. Then, we show that the symmetries of Bloch vectors are consistent with that of the correlation matrix, and the magnitudes of the local Bloch vectors are lower bounded by the correlation matrix. Concrete examples for the separable decompositions of bipartite mixed states are presented for illustration.

Invertibility of retarded response functions for Laplace transformable potentials: Application to one-body reduced density matrix functional theory.

PubMed

Giesbertz, K J H

2015-08-07

A theorem for the invertibility of arbitrary response functions is presented under the following conditions: the time dependence of the potentials should be Laplace transformable and the initial state should be a ground state, though it might be degenerate. This theorem provides a rigorous foundation for all density-functional-like theories in the time-dependent linear response regime. Especially for time-dependent one-body reduced density matrix (1RDM) functional theory, this is an important step forward, since a solid foundation has currently been lacking. The theorem is equally valid for static response functions in the non-degenerate case, so can be used to characterize the uniqueness of the potential in the ground state version of the corresponding density-functional-like theory. Such a classification of the uniqueness of the non-local potential in ground state 1RDM functional theory has been lacking for decades. With the aid of presented invertibility theorem presented here, a complete classification of the non-uniqueness of the non-local potential in 1RDM functional theory can be given for the first time.

Matrix-product-operator approach to the nonequilibrium steady state of driven-dissipative quantum arrays

NASA Astrophysics Data System (ADS)

Mascarenhas, Eduardo; Flayac, Hugo; Savona, Vincenzo

2015-08-01

We develop a numerical procedure to efficiently model the nonequilibrium steady state of one-dimensional arrays of open quantum systems based on a matrix-product operator ansatz for the density matrix. The procedure searches for the null eigenvalue of the Liouvillian superoperator by sweeping along the system while carrying out a partial diagonalization of the single-site stationary problem. It bears full analogy to the density-matrix renormalization-group approach to the ground state of isolated systems, and its numerical complexity scales as a power law with the bond dimension. The method brings considerable advantage when compared to the integration of the time-dependent problem via Trotter decomposition, as it can address arbitrarily long-ranged couplings. Additionally, it ensures numerical stability in the case of weakly dissipative systems thanks to a slow tuning of the dissipation rates along the sweeps. We have tested the method on a driven-dissipative spin chain, under various assumptions for the Hamiltonian, drive, and dissipation parameters, and compared the results to those obtained both by Trotter dynamics and Monte Carlo wave function methods. Accurate and numerically stable convergence was always achieved when applying the method to systems with a gapped Liouvillian and a nondegenerate steady state.

Matrix product density operators: Renormalization fixed points and boundary theories

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cirac, J.I.; Pérez-García, D., E-mail: dperezga@ucm.es; ICMAT, Nicolas Cabrera, Campus de Cantoblanco, 28049 Madrid

We consider the tensors generating matrix product states and density operators in a spin chain. For pure states, we revise the renormalization procedure introduced in (Verstraete et al., 2005) and characterize the tensors corresponding to the fixed points. We relate them to the states possessing zero correlation length, saturation of the area law, as well as to those which generate ground states of local and commuting Hamiltonians. For mixed states, we introduce the concept of renormalization fixed points and characterize the corresponding tensors. We also relate them to concepts like finite correlation length, saturation of the area law, as well asmore » to those which generate Gibbs states of local and commuting Hamiltonians. One of the main result of this work is that the resulting fixed points can be associated to the boundary theories of two-dimensional topological states, through the bulk-boundary correspondence introduced in (Cirac et al., 2011).« less

The Dielectric Permittivity of Crystals in the Reduced Hartree-Fock Approximation

NASA Astrophysics Data System (ADS)

Cancès, Éric; Lewin, Mathieu

2010-07-01

In a recent article (Cancès et al. in Commun Math Phys 281:129-177, 2008), we have rigorously derived, by means of bulk limit arguments, a new variational model to describe the electronic ground state of insulating or semiconducting crystals in the presence of local defects. In this so-called reduced Hartree-Fock model, the ground state electronic density matrix is decomposed as {γ = γ^0_per + Q_{ν,\\varepsilon_F}}, where {γ^0_per} is the ground state density matrix of the host crystal and {Q_{ν,\\varepsilon_F}} the modification of the electronic density matrix generated by a modification ν of the nuclear charge of the host crystal, the Fermi level ɛ F being kept fixed. The purpose of the present article is twofold. First, we study in more detail the mathematical properties of the density matrix {Q_{ν,\\varepsilon_F}} (which is known to be a self-adjoint Hilbert-Schmidt operator on {L^2(mathbb{R}^3)}). We show in particular that if {int_{mathbb{R}^3} ν neq 0, Q_{ν,\\varepsilon_F}} is not trace-class. Moreover, the associated density of charge is not in {L^1(mathbb{R}^3)} if the crystal exhibits anisotropic dielectric properties. These results are obtained by analyzing, for a small defect ν, the linear and nonlinear terms of the resolvent expansion of {Q_{ν,\\varepsilon_F}}. Second, we show that, after an appropriate rescaling, the potential generated by the microscopic total charge (nuclear plus electronic contributions) of the crystal in the presence of the defect converges to a homogenized electrostatic potential solution to a Poisson equation involving the macroscopic dielectric permittivity of the crystal. This provides an alternative (and rigorous) derivation of the Adler-Wiser formula.

Mixed state dynamical quantum phase transitions

NASA Astrophysics Data System (ADS)

Bhattacharya, Utso; Bandyopadhyay, Souvik; Dutta, Amit

2017-11-01

Preparing an integrable system in a mixed state described by a thermal density matrix, we subject it to a sudden quench and explore the subsequent unitary dynamics. To address the question of whether the nonanalyticities, namely, the dynamical quantum phase transitions (DQPTs), persist when the initial state is mixed, we consider two versions of the generalized Loschmidt overlap amplitude (GLOA). Our study shows that the GLOA constructed using the Uhlmann approach does not show any signature of DQPTs at any nonzero initial temperature. On the other hand, a GLOA defined in the interferometric phase approach through the purifications of the time-evolved density matrix, indeed shows that nonanalyiticies in the corresponding "dynamical free-energy density" persist, thereby establishing the existence of mixed state dynamical quantum phase transitions (MSDQPTs). Our work provides a framework that perfectly reproduces both the nonanalyticities and also the emergent topological structure in the pure state limit. These claims are corroborated by analyzing the nonequilibrium dynamics of a transverse Ising chain initially prepared in a thermal state and subjected to a sudden quench of the transverse field.

Exact and approximate many-body dynamics with stochastic one-body density matrix evolution

NASA Astrophysics Data System (ADS)

Lacroix, Denis

2005-06-01

We show that the dynamics of interacting fermions can be exactly replaced by a quantum jump theory in the many-body density matrix space. In this theory, jumps occur between densities formed of pairs of Slater determinants, Dab=|Φa><Φb|, where each state evolves according to the stochastic Schrödinger equation given by O. Juillet and Ph. Chomaz [Phys. Rev. Lett. 88, 142503 (2002)]. A stochastic Liouville-von Neumann equation is derived as well as the associated. Bogolyubov-Born-Green-Kirwood-Yvon hierarchy. Due to the specific form of the many-body density along the path, the presented theory is equivalent to a stochastic theory in one-body density matrix space, in which each density matrix evolves according to its own mean-field augmented by a one-body noise. Guided by the exact reformulation, a stochastic mean-field dynamics valid in the weak coupling approximation is proposed. This theory leads to an approximate treatment of two-body effects similar to the extended time-dependent Hartree-Fock scheme. In this stochastic mean-field dynamics, statistical mixing can be directly considered and jumps occur on a coarse-grained time scale. Accordingly, numerical effort is expected to be significantly reduced for applications.

The multifacet graphically contracted function method. I. Formulation and implementation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Shepard, Ron; Brozell, Scott R.; Gidofalvi, Gergely

2014-08-14

The basic formulation for the multifacet generalization of the graphically contracted function (MFGCF) electronic structure method is presented. The analysis includes the discussion of linear dependency and redundancy of the arc factor parameters, the computation of reduced density matrices, Hamiltonian matrix construction, spin-density matrix construction, the computation of optimization gradients for single-state and state-averaged calculations, graphical wave function analysis, and the efficient computation of configuration state function and Slater determinant expansion coefficients. Timings are given for Hamiltonian matrix element and analytic optimization gradient computations for a range of model problems for full-CI Shavitt graphs, and it is observed that bothmore » the energy and the gradient computation scale as O(N{sup 2}n{sup 4}) for N electrons and n orbitals. The important arithmetic operations are within dense matrix-matrix product computational kernels, resulting in a computationally efficient procedure. An initial implementation of the method is used to present applications to several challenging chemical systems, including N{sub 2} dissociation, cubic H{sub 8} dissociation, the symmetric dissociation of H{sub 2}O, and the insertion of Be into H{sub 2}. The results are compared to the exact full-CI values and also to those of the previous single-facet GCF expansion form.« less

Encoding the structure of many-body localization with matrix product operators

NASA Astrophysics Data System (ADS)

Pekker, David; Clark, Bryan K.

2017-01-01

Anderson insulators are noninteracting disordered systems which have localized single-particle eigenstates. The interacting analog of Anderson insulators are the many-body localized (MBL) phases. The spectrum of the many-body eigenstates of an Anderson insulator is efficiently represented as a set of product states over the single-particle modes. We show that product states over matrix product operators of small bond dimension is the corresponding efficient description of the spectrum of an MBL insulator. In this language all of the many-body eigenstates are encoded by matrix product states (i.e., density matrix renormalization group wave functions) consisting of only two sets of low bond dimension matrices per site: the Gi matrices corresponding to the local ground state on site i and the Ei matrices corresponding to the local excited state. All 2n eigenstates can be generated from all possible combinations of these sets of matrices.

Electronic Absorption Spectra of Neutral Perylene (C20H12), Terrylene (C30H16), and Quaterrylene (C40H20) and their Positive and Negative Ions: Ne Matrix-Isolation Spectroscopy and Time Dependent Density Functional Theory Calculations

NASA Technical Reports Server (NTRS)

Halasinski, Thomas M.; Weisman, Jennifer L.; Lee, Timothy J.; Salama, Farid; Head-Gordon, Martin; Kwak, Dochan (Technical Monitor)

2002-01-01

We present a full experimental and theoretical study of an interesting series of polycyclic aromatic hydrocarbons, the oligorylenes. The absorption spectra of perylene, terrylene and quaterrylene in neutral, cationic and anionic charge states are obtained by matrix-isolation spectroscopy in Ne. The experimental spectra are dominated by a bright state that red shifts with growing molecular size. Excitation energies and state symmetry assignments are supported by calculations using time dependent density functional theory methods. These calculations also provide new insight into the observed trends in oscillator strength and excitation energy for the bright states: the oscillator strength per unit mass of carbon increases along the series.

Linear-response time-dependent density-functional theory with pairing fields.

PubMed

Peng, Degao; van Aggelen, Helen; Yang, Yang; Yang, Weitao

2014-05-14

Recent development in particle-particle random phase approximation (pp-RPA) broadens the perspective on ground state correlation energies [H. van Aggelen, Y. Yang, and W. Yang, Phys. Rev. A 88, 030501 (2013), Y. Yang, H. van Aggelen, S. N. Steinmann, D. Peng, and W. Yang, J. Chem. Phys. 139, 174110 (2013); D. Peng, S. N. Steinmann, H. van Aggelen, and W. Yang, J. Chem. Phys. 139, 104112 (2013)] and N ± 2 excitation energies [Y. Yang, H. van Aggelen, and W. Yang, J. Chem. Phys. 139, 224105 (2013)]. So far Hartree-Fock and approximated density-functional orbitals have been utilized to evaluate the pp-RPA equation. In this paper, to further explore the fundamentals and the potential use of pairing matrix dependent functionals, we present the linear-response time-dependent density-functional theory with pairing fields with both adiabatic and frequency-dependent kernels. This theory is related to the density-functional theory and time-dependent density-functional theory for superconductors, but is applied to normal non-superconducting systems for our purpose. Due to the lack of the proof of the one-to-one mapping between the pairing matrix and the pairing field for time-dependent systems, the linear-response theory is established based on the representability assumption of the pairing matrix. The linear response theory justifies the use of approximated density-functionals in the pp-RPA equation. This work sets the fundamentals for future density-functional development to enhance the description of ground state correlation energies and N ± 2 excitation energies.

Spin-polarized density-matrix functional theory of the single-impurity Anderson model

NASA Astrophysics Data System (ADS)

Töws, W.; Pastor, G. M.

2012-12-01

Lattice density functional theory (LDFT) is used to investigate spin excitations in the single-impurity Anderson model. In this method, the single-particle density matrix γijσ with respect to the lattice sites replaces the wave function as the basic variable of the many-body problem. A recently developed two-level approximation (TLA) to the interaction-energy functional W[γ] is extended to systems having spin-polarized density distributions and bond orders. This allows us to investigate the effect of external magnetic fields and, in particular, the important singlet-triplet gap ΔE, which determines the Kondo temperature. Applications to finite Anderson rings and square lattices show that the gap ΔE as well as other ground-state and excited-state properties are very accurately reproduced. One concludes that the spin-polarized TLA is reliable in all interaction regimes, from weak to strong correlations, for different hybridization strengths and for all considered impurity valence states. In this way the efficiency of LDFT to account for challenging electron-correlation effects is demonstrated.

Spectroscopic accuracy directly from quantum chemistry: application to ground and excited states of beryllium dimer.

PubMed

Sharma, Sandeep; Yanai, Takeshi; Booth, George H; Umrigar, C J; Chan, Garnet Kin-Lic

2014-03-14

We combine explicit correlation via the canonical transcorrelation approach with the density matrix renormalization group and initiator full configuration interaction quantum Monte Carlo methods to compute a near-exact beryllium dimer curve, without the use of composite methods. In particular, our direct density matrix renormalization group calculations produce a well-depth of D(e) = 931.2 cm(-1) which agrees very well with recent experimentally derived estimates D(e) = 929.7±2 cm(-1) [J. M. Merritt, V. E. Bondybey, and M. C. Heaven, Science 324, 1548 (2009)] and D(e) = 934.6 cm(-1) [K. Patkowski, V. Špirko, and K. Szalewicz, Science 326, 1382 (2009)], as well the best composite theoretical estimates, D(e) = 938±15 cm(-1) [K. Patkowski, R. Podeszwa, and K. Szalewicz, J. Phys. Chem. A 111, 12822 (2007)] and D(e) = 935.1±10 cm(-1) [J. Koput, Phys. Chem. Chem. Phys. 13, 20311 (2011)]. Our results suggest possible inaccuracies in the functional form of the potential used at shorter bond lengths to fit the experimental data [J. M. Merritt, V. E. Bondybey, and M. C. Heaven, Science 324, 1548 (2009)]. With the density matrix renormalization group we also compute near-exact vertical excitation energies at the equilibrium geometry. These provide non-trivial benchmarks for quantum chemical methods for excited states, and illustrate the surprisingly large error that remains for 1 ¹Σ(g)⁻ state with approximate multi-reference configuration interaction and equation-of-motion coupled cluster methods. Overall, we demonstrate that explicitly correlated density matrix renormalization group and initiator full configuration interaction quantum Monte Carlo methods allow us to fully converge to the basis set and correlation limit of the non-relativistic Schrödinger equation in small molecules.

Direct calculation of liquid-vapor phase equilibria from transition matrix Monte Carlo simulation

NASA Astrophysics Data System (ADS)

Errington, Jeffrey R.

2003-06-01

An approach for directly determining the liquid-vapor phase equilibrium of a model system at any temperature along the coexistence line is described. The method relies on transition matrix Monte Carlo ideas developed by Fitzgerald, Picard, and Silver [Europhys. Lett. 46, 282 (1999)]. During a Monte Carlo simulation attempted transitions between states along the Markov chain are monitored as opposed to tracking the number of times the chain visits a given state as is done in conventional simulations. Data collection is highly efficient and very precise results are obtained. The method is implemented in both the grand canonical and isothermal-isobaric ensemble. The main result from a simulation conducted at a given temperature is a density probability distribution for a range of densities that includes both liquid and vapor states. Vapor pressures and coexisting densities are calculated in a straightforward manner from the probability distribution. The approach is demonstrated with the Lennard-Jones fluid. Coexistence properties are directly calculated at temperatures spanning from the triple point to the critical point.

Density-matrix based determination of low-energy model Hamiltonians from ab initio wavefunctions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Changlani, Hitesh J.; Zheng, Huihuo; Wagner, Lucas K.

2015-09-14

We propose a way of obtaining effective low energy Hubbard-like model Hamiltonians from ab initio quantum Monte Carlo calculations for molecular and extended systems. The Hamiltonian parameters are fit to best match the ab initio two-body density matrices and energies of the ground and excited states, and thus we refer to the method as ab initio density matrix based downfolding. For benzene (a finite system), we find good agreement with experimentally available energy gaps without using any experimental inputs. For graphene, a two dimensional solid (extended system) with periodic boundary conditions, we find the effective on-site Hubbard U{sup ∗}/t tomore » be 1.3 ± 0.2, comparable to a recent estimate based on the constrained random phase approximation. For molecules, such parameterizations enable calculation of excited states that are usually not accessible within ground state approaches. For solids, the effective Hamiltonian enables large-scale calculations using techniques designed for lattice models.« less

Symmetry properties of the electron density and following from it limits on the KS-DFT applications

NASA Astrophysics Data System (ADS)

Kaplan, Ilya G.

2018-03-01

At present, the Density Functional Theory (DFT) approach elaborated by Kohn with co-authors more than 50 years ago became the most widely used method for study molecules and solids. Using modern computation facilities, it can be applied to systems with million atoms. In the atmosphere of such great popularity, it is particularly important to know the limits of the applicability of DFT methods. In this report, I will discuss two cases when the conventional DFT approaches, using only electron density ρ and its gradients, cannot be applied (I will not consider the Ψ-versions of DFT). The first case is quite evident. In the degenerated states, the electron density may not be defined, since electronic and nuclear motions cannot be separated, the vibronic interaction mixed them. The second case is related to the spin of the state. As it was rigorously proved by group theoretical methods at the theorem level, the electron density does not depend on the total spin S of the arbitrary N-electron state. It means that the Kohn-Sham equations have the same form for states with different S. The critical survey of elaborated DFT procedures, taking into account spin, shows that they modified only exchange functionals, the correlation functionals do not correspond to the spin of the state. The point is that the conception of spin cannot be defined in the framework of the electron density formalism, which corresponds to the one-particle reduced density matrix. This is the main reason of the problems arising in the study by DFT of magnetic properties of the transition metals. The possible way of resolving these problems can be found in the two-particle reduced density matrix formulation of DFT.

Efficient method for computing the maximum-likelihood quantum state from measurements with additive Gaussian noise.

PubMed

Smolin, John A; Gambetta, Jay M; Smith, Graeme

2012-02-17

We provide an efficient method for computing the maximum-likelihood mixed quantum state (with density matrix ρ) given a set of measurement outcomes in a complete orthonormal operator basis subject to Gaussian noise. Our method works by first changing basis yielding a candidate density matrix μ which may have nonphysical (negative) eigenvalues, and then finding the nearest physical state under the 2-norm. Our algorithm takes at worst O(d(4)) for the basis change plus O(d(3)) for finding ρ where d is the dimension of the quantum state. In the special case where the measurement basis is strings of Pauli operators, the basis change takes only O(d(3)) as well. The workhorse of the algorithm is a new linear-time method for finding the closest probability distribution (in Euclidean distance) to a set of real numbers summing to one.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Theophilou, Iris; Helbig, Nicole; Lathiotakis, Nektarios N.

Functionals of the one-body reduced density matrix (1-RDM) are routinely minimized under Coleman’s ensemble N-representability conditions. Recently, the topic of pure-state N-representability conditions, also known as generalized Pauli constraints, received increased attention following the discovery of a systematic way to derive them for any number of electrons and any finite dimensionality of the Hilbert space. The target of this work is to assess the potential impact of the enforcement of the pure-state conditions on the results of reduced density-matrix functional theory calculations. In particular, we examine whether the standard minimization of typical 1-RDM functionals under the ensemble N-representability conditions violatesmore » the pure-state conditions for prototype 3-electron systems. We also enforce the pure-state conditions, in addition to the ensemble ones, for the same systems and functionals and compare the correlation energies and optimal occupation numbers with those obtained by the enforcement of the ensemble conditions alone.« less

A meta-GGA level screened range-separated hybrid functional by employing short range Hartree-Fock with a long range semilocal functional.

PubMed

Jana, Subrata; Samal, Prasanjit

2018-03-28

The range-separated hybrid density functionals are very successful in describing a wide range of molecular and solid-state properties accurately. In principle, such functionals are designed from spherically averaged or system averaged as well as reverse engineered exchange holes. In the present attempt, the screened range-separated hybrid functional scheme has been applied to the meta-GGA rung by using the density matrix expansion based semilocal exchange hole (or functional). The hybrid functional proposed here utilizes the spherically averaged density matrix expansion based exchange hole in the range separation scheme. For slowly varying density correction the range separation scheme is employed only through the local density approximation based exchange hole coupled with the corresponding fourth order gradient approximate Tao-Mo enhancement factor. The comprehensive testing and performance of the newly constructed functional indicates its applicability in describing several molecular properties. The most appealing feature of this present screened hybrid functional is that it will be practically very useful in describing solid-state properties at the meta-GGA level.

Spin orbit coupling for molecular ab initio density matrix renormalization group calculations: Application to g-tensors

DOE Office of Scientific and Technical Information (OSTI.GOV)

Roemelt, Michael, E-mail: michael.roemelt@theochem.rub.de

Spin Orbit Coupling (SOC) is introduced to molecular ab initio density matrix renormalization group (DMRG) calculations. In the presented scheme, one first approximates the electronic ground state and a number of excited states of the Born-Oppenheimer (BO) Hamiltonian with the aid of the DMRG algorithm. Owing to the spin-adaptation of the algorithm, the total spin S is a good quantum number for these states. After the non-relativistic DMRG calculation is finished, all magnetic sublevels of the calculated states are constructed explicitly, and the SOC operator is expanded in the resulting basis. To this end, spin orbit coupled energies and wavefunctionsmore » are obtained as eigenvalues and eigenfunctions of the full Hamiltonian matrix which is composed of the SOC operator matrix and the BO Hamiltonian matrix. This treatment corresponds to a quasi-degenerate perturbation theory approach and can be regarded as the molecular equivalent to atomic Russell-Saunders coupling. For the evaluation of SOC matrix elements, the full Breit-Pauli SOC Hamiltonian is approximated by the widely used spin-orbit mean field operator. This operator allows for an efficient use of the second quantized triplet replacement operators that are readily generated during the non-relativistic DMRG algorithm, together with the Wigner-Eckart theorem. With a set of spin-orbit coupled wavefunctions at hand, the molecular g-tensors are calculated following the scheme proposed by Gerloch and McMeeking. It interprets the effective molecular g-values as the slope of the energy difference between the lowest Kramers pair with respect to the strength of the applied magnetic field. Test calculations on a chemically relevant Mo complex demonstrate the capabilities of the presented method.« less

Real time evolution at finite temperatures with operator space matrix product states

NASA Astrophysics Data System (ADS)

Pižorn, Iztok; Eisler, Viktor; Andergassen, Sabine; Troyer, Matthias

2014-07-01

We propose a method to simulate the real time evolution of one-dimensional quantum many-body systems at finite temperature by expressing both the density matrices and the observables as matrix product states. This allows the calculation of expectation values and correlation functions as scalar products in operator space. The simulations of density matrices in inverse temperature and the local operators in the Heisenberg picture are independent and result in a grid of expectation values for all intermediate temperatures and times. Simulations can be performed using real arithmetics with only polynomial growth of computational resources in inverse temperature and time for integrable systems. The method is illustrated for the XXZ model and the single impurity Anderson model.

Ising tricriticality in the extended Hubbard model with bond dimerization

NASA Astrophysics Data System (ADS)

Fehske, Holger; Ejima, Satoshi; Lange, Florian; Essler, Fabian H. L.

We explore the quantum phase transition between Peierls and charge-density-wave insulating states in the one-dimensional, half-filled, extended Hubbard model with explicit bond dimerization. We show that the critical line of the continuous Ising transition terminates at a tricritical point, belonging to the universality class of the tricritical Ising model with central charge c=7/10. Above this point, the quantum phase transition becomes first order. Employing a numerical matrix-product-state based (infinite) density-matrix renormalization group method we determine the ground-state phase diagram, the spin and two-particle charge excitations gaps, and the entanglement properties of the model with high precision. Performing a bosonization analysis we can derive a field description of the transition region in terms of a triple sine-Gordon model. This allows us to derive field theory predictions for the power-law (exponential) decay of the density-density (spin-spin) and bond-order-wave correlation functions, which are found to be in excellent agreement with our numerical results. This work was supported by Deutsche Forschungsgemeinschaft (Germany), SFB 652, project B5, and by the EPSRC under Grant No. EP/N01930X/1 (FHLE).

CUGatesDensity—Quantum circuit analyser extended to density matrices

NASA Astrophysics Data System (ADS)

Loke, T.; Wang, J. B.

2013-12-01

CUGatesDensity is an extension of the original quantum circuit analyser CUGates (Loke and Wang, 2011) [7] to provide explicit support for the use of density matrices. The new package enables simulation of quantum circuits involving statistical ensemble of mixed quantum states. Such analysis is of vital importance in dealing with quantum decoherence, measurements, noise and error correction, and fault tolerant computation. Several examples involving mixed state quantum computation are presented to illustrate the use of this package. Catalogue identifier: AEPY_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEPY_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 5368 No. of bytes in distributed program, including test data, etc.: 143994 Distribution format: tar.gz Programming language: Mathematica. Computer: Any computer installed with a copy of Mathematica 6.0 or higher. Operating system: Any system with a copy of Mathematica 6.0 or higher installed. Classification: 4.15. Nature of problem: To simulate arbitrarily complex quantum circuits comprised of single/multiple qubit and qudit quantum gates with mixed state registers. Solution method: A density matrix representation for mixed states and a state vector representation for pure states are used. The construct is based on an irreducible form of matrix decomposition, which allows a highly efficient implementation of general controlled gates with multiple conditionals. Running time: The examples provided in the notebook CUGatesDensity.nb take approximately 30 s to run on a laptop PC.

Ground-state densities from the Rayleigh-Ritz variation principle and from density-functional theory.

PubMed

Kvaal, Simen; Helgaker, Trygve

2015-11-14

The relationship between the densities of ground-state wave functions (i.e., the minimizers of the Rayleigh-Ritz variation principle) and the ground-state densities in density-functional theory (i.e., the minimizers of the Hohenberg-Kohn variation principle) is studied within the framework of convex conjugation, in a generic setting covering molecular systems, solid-state systems, and more. Having introduced admissible density functionals as functionals that produce the exact ground-state energy for a given external potential by minimizing over densities in the Hohenberg-Kohn variation principle, necessary and sufficient conditions on such functionals are established to ensure that the Rayleigh-Ritz ground-state densities and the Hohenberg-Kohn ground-state densities are identical. We apply the results to molecular systems in the Born-Oppenheimer approximation. For any given potential v ∈ L(3/2)(ℝ(3)) + L(∞)(ℝ(3)), we establish a one-to-one correspondence between the mixed ground-state densities of the Rayleigh-Ritz variation principle and the mixed ground-state densities of the Hohenberg-Kohn variation principle when the Lieb density-matrix constrained-search universal density functional is taken as the admissible functional. A similar one-to-one correspondence is established between the pure ground-state densities of the Rayleigh-Ritz variation principle and the pure ground-state densities obtained using the Hohenberg-Kohn variation principle with the Levy-Lieb pure-state constrained-search functional. In other words, all physical ground-state densities (pure or mixed) are recovered with these functionals and no false densities (i.e., minimizing densities that are not physical) exist. The importance of topology (i.e., choice of Banach space of densities and potentials) is emphasized and illustrated. The relevance of these results for current-density-functional theory is examined.

Localization of soft modes at the depinning transition

NASA Astrophysics Data System (ADS)

Cao, Xiangyu; Bouzat, Sebastian; Kolton, Alejandro B.; Rosso, Alberto

2018-02-01

We characterize the soft modes of the dynamical matrix at the depinning transition, and compare the matrix with the properties of the Anderson model (and long-range generalizations). The density of states at the edge of the spectrum displays a universal linear tail, different from the Lifshitz tails. The eigenvectors are instead very similar in the two matrix ensembles. We focus on the ground state (soft mode), which represents the epicenter of avalanche instabilities. We expect it to be localized in all finite dimensions, and make a clear connection between its localization length and the Larkin length of the depinning model. In the fully connected model, we show that the weak-strong pinning transition coincides with a peculiar localization transition of the ground state.

A well-scaling natural orbital theory

DOE PAGES

Gebauer, Ralph; Cohen, Morrel H.; Car, Roberto

2016-11-01

Here, we introduce an energy functional for ground-state electronic structure calculations. Its variables are the natural spin-orbitals of singlet many-body wave functions and their joint occupation probabilities deriving from controlled approximations to the two-particle density matrix that yield algebraic scaling in general, and Hartree–Fock scaling in its seniority-zero version. Results from the latter version for small molecular systems are compared with those of highly accurate quantum-chemical computations. The energies lie above full configuration interaction calculations, close to doubly occupied configuration interaction calculations. Their accuracy is considerably greater than that obtained from current density-functional theory approximations and from current functionals ofmore » the oneparticle density matrix.« less

A well-scaling natural orbital theory

PubMed Central

Gebauer, Ralph; Cohen, Morrel H.; Car, Roberto

2016-01-01

We introduce an energy functional for ground-state electronic structure calculations. Its variables are the natural spin-orbitals of singlet many-body wave functions and their joint occupation probabilities deriving from controlled approximations to the two-particle density matrix that yield algebraic scaling in general, and Hartree–Fock scaling in its seniority-zero version. Results from the latter version for small molecular systems are compared with those of highly accurate quantum-chemical computations. The energies lie above full configuration interaction calculations, close to doubly occupied configuration interaction calculations. Their accuracy is considerably greater than that obtained from current density-functional theory approximations and from current functionals of the one-particle density matrix. PMID:27803328

Magnetic phase diagrams of amorphous (Ni100-xFex)-metalloid alloys: The key role of the electronic density of states at the Fermi level for the onset of magnetic order

NASA Astrophysics Data System (ADS)

Kiss, L. F.; Bakonyi, I.

2017-11-01

There have been extended studies on the appearance of ferromagnetism in transition-metal-metalloid (MD) glasses. In particular, the paramagnetic (PM) to ferromagnetic (FM) transition has been investigated on numerous (Ni100-xFex)-MD alloys upon the introduction of Fe where MD can represent a combination of various metalloid elements, while keeping the metal/metalloid ratio constant. It has been reported that adding a sufficient amount of Fe to a Pauli PM Ni-MD alloy matrix first induces a spin-glass (SG) state at low temperatures which goes over to a PM state at higher temperatures. Beyond a certain Fe content, xc, the SG state transforms to a FM state upon increasing the temperature. By plotting the characteristic transition temperatures as a function of the Fe content, a magnetic phase diagram can be constructed for each Ni-Fe-MD system which has a multicritical point (MCP) at xc. By using the reported magnetic phase diagrams of various Ni-Fe-MD alloy systems, it is shown that the critical Fe content, xc scales inversely with the density of states at the Fermi level, N(EF), of the parent Ni-MD matrix. This means that the higher the N(EF), the lower the critical Fe content to induce ferromagnetism in the Ni-MD matrix. This is then discussed in terms of the Stoner enhancement factor, S, which characterizes the tendency of the matrix to become ferromagnetic.

T-matrix modeling of linear depolarization by morphologically complex soot and soot-containing aerosols

NASA Astrophysics Data System (ADS)

Mishchenko, Michael I.; Liu, Li; Mackowski, Daniel W.

2013-07-01

We use state-of-the-art public-domain Fortran codes based on the T-matrix method to calculate orientation and ensemble averaged scattering matrix elements for a variety of morphologically complex black carbon (BC) and BC-containing aerosol particles, with a special emphasis on the linear depolarization ratio (LDR). We explain theoretically the quasi-Rayleigh LDR peak at side-scattering angles typical of low-density soot fractals and conclude that the measurement of this feature enables one to evaluate the compactness state of BC clusters and trace the evolution of low-density fluffy fractals into densely packed aggregates. We show that small backscattering LDRs measured with ground-based, airborne, and spaceborne lidars for fresh smoke generally agree with the values predicted theoretically for fluffy BC fractals and densely packed near-spheroidal BC aggregates. To reproduce higher lidar LDRs observed for aged smoke, one needs alternative particle models such as shape mixtures of BC spheroids or cylinders.

T-Matrix Modeling of Linear Depolarization by Morphologically Complex Soot and Soot-Containing Aerosols

NASA Technical Reports Server (NTRS)

Mishchenko, Michael I.; Liu, Li; Mackowski, Daniel W.

2013-01-01

We use state-of-the-art public-domain Fortran codes based on the T-matrix method to calculate orientation and ensemble averaged scattering matrix elements for a variety of morphologically complex black carbon (BC) and BC-containing aerosol particles, with a special emphasis on the linear depolarization ratio (LDR). We explain theoretically the quasi-Rayleigh LDR peak at side-scattering angles typical of low-density soot fractals and conclude that the measurement of this feature enables one to evaluate the compactness state of BC clusters and trace the evolution of low-density fluffy fractals into densely packed aggregates. We show that small backscattering LDRs measured with groundbased, airborne, and spaceborne lidars for fresh smoke generally agree with the values predicted theoretically for fluffy BC fractals and densely packed near-spheroidal BC aggregates. To reproduce higher lidar LDRs observed for aged smoke, one needs alternative particle models such as shape mixtures of BC spheroids or cylinders.

High-efficiency tomographic reconstruction of quantum states by quantum nondemolition measurements

DOE Office of Scientific and Technical Information (OSTI.GOV)

Huang, J. S.; Centre for Quantum Technologies and Department of Physics, National University of Singapore, 3 Science Drive 2, Singapore 117542; Wei, L. F.

We propose a high-efficiency scheme to tomographically reconstruct an unknown quantum state by using a series of quantum nondemolition (QND) measurements. The proposed QND measurements of the qubits are implemented by probing the stationary transmissions through a driven dispersively coupled resonator. It is shown that only one kind of QND measurement is sufficient to determine all the diagonal elements of the density matrix of the detected quantum state. The remaining nondiagonal elements can be similarly determined by transferring them to the diagonal locations after a series of unitary operations. Compared with the tomographic reconstructions based on the usual destructive projectivemore » measurements (wherein one such measurement can determine only one diagonal element of the density matrix), the present reconstructive approach exhibits significantly high efficiency. Specifically, our generic proposal is demonstrated by the experimental circuit quantum electrodynamics systems with a few Josephson charge qubits.« less

The density matrix method in photonic bandgap and antiferromagnetic materials

NASA Astrophysics Data System (ADS)

Barrie, Scott B.

In this thesis, a theory for dispersive polaritonic bandgap (DPBG) and photonic bandgap (PBG) materials is developed. An ensemble of multi-level nanoparticles, such as non-interacting two-, three- and four-level atoms doped in DPBG and PBG materials is considered. The optical properties of these materials such as spontaneous emission, line broadening, fluorescence and narrowing of the natural linewidth have been studied using the density matrix method. Numerical simulations for these properties have been performed for the DPBG materials SiC and InAs, and for a PBG material with a 20 percent gap-to-midgap ratio. When a three-level nanoparticle is doped into a DPBG material, it is predicted that one or two bound states exist when one or both resonance energies, respectively, lie in the bandgap. It is shown when a resonance energy lies below the bandgap, its spectral density peak weakens and broadens as the resonance energy increases to the lower band edge. For the first time it is predicted that when a nanoparticle's resonance energy lies above the bandgap, its spectral density peak weakens and broadens as the resonance energy increases. A relation is also found between spectral structure and gap-to-midgap ratios. The dressed states of a two-level atom doped into a DPBG material under the influence of an intense monochromatic laser field are examined. The splitting of the dressed state energies is calculated, and it is predicted that the splitting depends on the polariton density of states and the Rabi frequency of laser field. The fluoresence is also examined, and for the first time two distinct control processes are found for the transition from one peak to three peaks. It was previously known that the Rabi frequency controlled the Stark effect, but this thesis predicts that the local of the peak with respect to the optical bandgap can cause a transition from one to three peaks even with a weak Rabi frequency. The transient linewidth narrowing of PBG crystal emission peaks doped with four-level atoms is studied. It is found that linewidth narrowing is only dependent upon time delay when the resonance energy is not near a band edge. This is a new discovery. The density matrix method is employed to find the critical magnetic field at which spin flopping occurs in antiferromagnetic high temperature superconductors. It is found that this magnetic field depends upon the temperature, the anisotropy parameter and the doping concentration. Results are calculated for 1-2-3 HTSCs. Keywords. Quantum Optics, Density Matrix, Photonic Bandgap Materials, Dispersive Polaritonic Bandgap Materials, Antiferromagnets.

An efficient matrix product operator representation of the quantum chemical Hamiltonian

DOE Office of Scientific and Technical Information (OSTI.GOV)

Keller, Sebastian, E-mail: sebastian.keller@phys.chem.ethz.ch; Reiher, Markus, E-mail: markus.reiher@phys.chem.ethz.ch; Dolfi, Michele, E-mail: dolfim@phys.ethz.ch

We describe how to efficiently construct the quantum chemical Hamiltonian operator in matrix product form. We present its implementation as a density matrix renormalization group (DMRG) algorithm for quantum chemical applications. Existing implementations of DMRG for quantum chemistry are based on the traditional formulation of the method, which was developed from the point of view of Hilbert space decimation and attained higher performance compared to straightforward implementations of matrix product based DMRG. The latter variationally optimizes a class of ansatz states known as matrix product states, where operators are correspondingly represented as matrix product operators (MPOs). The MPO construction schememore » presented here eliminates the previous performance disadvantages while retaining the additional flexibility provided by a matrix product approach, for example, the specification of expectation values becomes an input parameter. In this way, MPOs for different symmetries — abelian and non-abelian — and different relativistic and non-relativistic models may be solved by an otherwise unmodified program.« less

Time dependent Schrödinger equation for black hole evaporation: No information loss

NASA Astrophysics Data System (ADS)

Corda, Christian

2015-02-01

In 1976 S. Hawking claimed that "Because part of the information about the state of the system is lost down the hole, the final situation is represented by a density matrix rather than a pure quantum state".1 In a series of papers, together with collaborators, we naturally interpreted BH quasi-normal modes (QNMs) in terms of quantum levels discussing a model of excited BH somewhat similar to the historical semi-classical Bohr model of the structure of a hydrogen atom. Here we explicitly write down, for the same model, a time dependent Schrödinger equation for the system composed by Hawking radiation and BH QNMs. The physical state and the correspondent wave function are written in terms of a unitary evolution matrix instead of a density matrix. Thus, the final state results to be a pure quantum state instead of a mixed one. Hence, Hawking's claim is falsified because BHs result to be well defined quantum mechanical systems, having ordered, discrete quantum spectra, which respect 't Hooft's assumption that Schrödinger equations can be used universally for all dynamics in the universe. As a consequence, information comes out in BH evaporation in terms of pure states in a unitary time dependent evolution. In Section 4 of this paper we show that the present approach permits also to solve the entanglement problem connected with the information paradox.

Lanczos algorithm with matrix product states for dynamical correlation functions

NASA Astrophysics Data System (ADS)

Dargel, P. E.; Wöllert, A.; Honecker, A.; McCulloch, I. P.; Schollwöck, U.; Pruschke, T.

2012-05-01

The density-matrix renormalization group (DMRG) algorithm can be adapted to the calculation of dynamical correlation functions in various ways which all represent compromises between computational efficiency and physical accuracy. In this paper we reconsider the oldest approach based on a suitable Lanczos-generated approximate basis and implement it using matrix product states (MPS) for the representation of the basis states. The direct use of matrix product states combined with an ex post reorthogonalization method allows us to avoid several shortcomings of the original approach, namely the multitargeting and the approximate representation of the Hamiltonian inherent in earlier Lanczos-method implementations in the DMRG framework, and to deal with the ghost problem of Lanczos methods, leading to a much better convergence of the spectral weights and poles. We present results for the dynamic spin structure factor of the spin-1/2 antiferromagnetic Heisenberg chain. A comparison to Bethe ansatz results in the thermodynamic limit reveals that the MPS-based Lanczos approach is much more accurate than earlier approaches at minor additional numerical cost.

Symmetry-conserving purification of quantum states within the density matrix renormalization group

DOE PAGES

Nocera, Alberto; Alvarez, Gonzalo

2016-01-28

The density matrix renormalization group (DMRG) algorithm was originally designed to efficiently compute the zero-temperature or ground-state properties of one-dimensional strongly correlated quantum systems. The development of the algorithm at finite temperature has been a topic of much interest, because of the usefulness of thermodynamics quantities in understanding the physics of condensed matter systems, and because of the increased complexity associated with efficiently computing temperature-dependent properties. The ancilla method is a DMRG technique that enables the computation of these thermodynamic quantities. In this paper, we review the ancilla method, and improve its performance by working on reduced Hilbert spaces andmore » using canonical approaches. Furthermore we explore its applicability beyond spins systems to t-J and Hubbard models.« less

Density matrix-based time-dependent configuration interaction approach to ultrafast spin-flip dynamics

NASA Astrophysics Data System (ADS)

Wang, Huihui; Bokarev, Sergey I.; Aziz, Saadullah G.; Kühn, Oliver

2017-08-01

Recent developments in attosecond spectroscopy yield access to the correlated motion of electrons on their intrinsic timescales. Spin-flip dynamics is usually considered in the context of valence electronic states, where spin-orbit coupling is weak and processes related to the electron spin are usually driven by nuclear motion. However, for core-excited states, where the core-hole has a nonzero angular momentum, spin-orbit coupling is strong enough to drive spin-flips on a much shorter timescale. Using density matrix-based time-dependent restricted active space configuration interaction including spin-orbit coupling, we address an unprecedentedly short spin-crossover for the example of L-edge (2p→3d) excited states of a prototypical Fe(II) complex. This process occurs on a timescale, which is faster than that of Auger decay (∼4 fs) treated here explicitly. Modest variations of carrier frequency and pulse duration can lead to substantial changes in the spin-state yield, suggesting its control by soft X-ray light.

Bone Mineral 31P and Matrix-Bound Water Densities Measured by Solid-State 1H and 31P MRI

PubMed Central

Seifert, Alan C.; Li, Cheng; Rajapakse, Chamith S.; Bashoor- Zadeh, Mahdieh; Bhagat, Yusuf A.; Wright, Alexander C.; Zemel, Babette S.; Zavaliangos, Antonios; Wehrli, Felix W.

2014-01-01

Bone is a composite material consisting of mineral and hydrated collagen fractions. MRI of bone is challenging due to extremely short transverse relaxation times, but solid-state imaging sequences exist that can acquire the short-lived signal from bone tissue. Previous work to quantify bone density via MRI used powerful experimental scanners. This work seeks to establish the feasibility of MRI-based measurement on clinical scanners of bone mineral and collagen-bound water densities, the latter as a surrogate of matrix density, and to examine the associations of these parameters with porosity and donors’ age. Mineral and matrix-bound water images of reference phantoms and cortical bone from 16 human donors, ages 27-97 years, were acquired by zero-echo-time 31P and 1H MRI on whole body 7T and 3T scanners, respectively. Images were corrected for relaxation and RF inhomogeneity to obtain density maps. Cortical porosity was measured by micro-CT, and apparent mineral density by pQCT. MRI-derived densities were compared to x-ray-based measurements by least-squares regression. Mean bone mineral 31P density was 6.74±1.22 mol/L (corresponding to 1129±204 mg/cc mineral), and mean bound water 1H density was 31.3±4.2 mol/L (corresponding to 28.3±3.7 %v/v). Both 31P and bound water (BW) densities were correlated negatively with porosity (31P: R2 = 0.32, p < 0.005; BW: R2 = 0.63, p < 0.0005) and age (31P: R2 = 0.39, p < 0.05; BW: R2 = 0.70, p < 0.0001), and positively with pQCT density (31P: R2 = 0.46, p < 0.05; BW: R2 = 0.50, p < 0.005). In contrast, the bone mineralization ratio (expressed here as the ratio of 31P density to bound water density), which is proportional to true bone mineralization, was found to be uncorrelated with porosity, age, or pQCT density. This work establishes the feasibility of image-based quantification of bone mineral and bound water densities using clinical hardware. PMID:24846186

Random density matrices versus random evolution of open system

NASA Astrophysics Data System (ADS)

Pineda, Carlos; Seligman, Thomas H.

2015-10-01

We present and compare two families of ensembles of random density matrices. The first, static ensemble, is obtained foliating an unbiased ensemble of density matrices. As criterion we use fixed purity as the simplest example of a useful convex function. The second, dynamic ensemble, is inspired in random matrix models for decoherence where one evolves a separable pure state with a random Hamiltonian until a given value of purity in the central system is achieved. Several families of Hamiltonians, adequate for different physical situations, are studied. We focus on a two qubit central system, and obtain exact expressions for the static case. The ensemble displays a peak around Werner-like states, modulated by nodes on the degeneracies of the density matrices. For moderate and strong interactions good agreement between the static and the dynamic ensembles is found. Even in a model where one qubit does not interact with the environment excellent agreement is found, but only if there is maximal entanglement with the interacting one. The discussion is started recalling similar considerations for scattering theory. At the end, we comment on the reach of the results for other convex functions of the density matrix, and exemplify the situation with the von Neumann entropy.

Dynamical simulation of electron transfer processes in self-assembled monolayers at metal surfaces using a density matrix approach.

PubMed

Prucker, V; Bockstedte, M; Thoss, M; Coto, P B

2018-03-28

A single-particle density matrix approach is introduced to simulate the dynamics of heterogeneous electron transfer (ET) processes at interfaces. The characterization of the systems is based on a model Hamiltonian parametrized by electronic structure calculations and a partitioning method. The method is applied to investigate ET in a series of nitrile-substituted (poly)(p-phenylene)thiolate self-assembled monolayers adsorbed at the Au(111) surface. The results show a significant dependence of the ET on the orbital symmetry of the donor state and on the molecular and electronic structure of the spacer.

Density matrix renormalization group for a highly degenerate quantum system: Sliding environment block approach

NASA Astrophysics Data System (ADS)

Schmitteckert, Peter

2018-04-01

We present an infinite lattice density matrix renormalization group sweeping procedure which can be used as a replacement for the standard infinite lattice blocking schemes. Although the scheme is generally applicable to any system, its main advantages are the correct representation of commensurability issues and the treatment of degenerate systems. As an example we apply the method to a spin chain featuring a highly degenerate ground-state space where the new sweeping scheme provides an increase in performance as well as accuracy by many orders of magnitude compared to a recently published work.

Growth and yield of all-aged Douglas-fir -- western hemlock forest stands: a matrix model with stand diversity effects.

Treesearch

Jingjing Liang; Joseph Buonglorno; Robert A. Monserud

2005-01-01

A density-dependent matrix model was developed for Douglas-fir (Pseudotsuga menziesii (Mirb.) Franco) -- western hemlock (Tsuga heterophylla (Raf.) Sarg.) forest stands in the Pacific Northwest of the United States. The model predicted the number and volume of trees for 4 species groups and 19 diameter classes. The parameters...

Quadratic canonical transformation theory and higher order density matrices.

PubMed

Neuscamman, Eric; Yanai, Takeshi; Chan, Garnet Kin-Lic

2009-03-28

Canonical transformation (CT) theory provides a rigorously size-extensive description of dynamic correlation in multireference systems, with an accuracy superior to and cost scaling lower than complete active space second order perturbation theory. Here we expand our previous theory by investigating (i) a commutator approximation that is applied at quadratic, as opposed to linear, order in the effective Hamiltonian, and (ii) incorporation of the three-body reduced density matrix in the operator and density matrix decompositions. The quadratic commutator approximation improves CT's accuracy when used with a single-determinant reference, repairing the previous formal disadvantage of the single-reference linear CT theory relative to singles and doubles coupled cluster theory. Calculations on the BH and HF binding curves confirm this improvement. In multireference systems, the three-body reduced density matrix increases the overall accuracy of the CT theory. Tests on the H(2)O and N(2) binding curves yield results highly competitive with expensive state-of-the-art multireference methods, such as the multireference Davidson-corrected configuration interaction (MRCI+Q), averaged coupled pair functional, and averaged quadratic coupled cluster theories.

Generalized Reduction Formula for Discrete Wigner Functions of Multiqubit Systems

NASA Astrophysics Data System (ADS)

Srinivasan, K.; Raghavan, G.

2018-03-01

Density matrices and Discrete Wigner Functions are equally valid representations of multiqubit quantum states. For density matrices, the partial trace operation is used to obtain the quantum state of subsystems, but an analogous prescription is not available for discrete Wigner Functions. Further, the discrete Wigner function corresponding to a density matrix is not unique but depends on the choice of the quantum net used for its reconstruction. In the present work, we derive a reduction formula for discrete Wigner functions of a general multiqubit state which works for arbitrary quantum nets. These results would be useful for the analysis and classification of entangled states and the study of decoherence purely in a discrete phase space setting and also in applications to quantum computing.

Excited states in polydiacetylene chains: A density matrix renormalization group study

NASA Astrophysics Data System (ADS)

Barcza, Gergely; Barford, William; Gebhard, Florian; Legeza, Örs

2013-06-01

We study theoretically polydiacetylene chains diluted in their monomer matrix. We employ the density matrix renormalization group method on finite chains to calculate the ground state and low-lying excitations of the corresponding Peierls-Hubbard-Ohno Hamiltonian which is characterized by the electron transfer amplitude t0 between nearest neighbors, by the electron-phonon coupling constant α, by the Hubbard interaction U, and by the long-range interaction V. We treat the lattice relaxation in the adiabatic limit, i.e., we calculate the polaronic lattice distortions for each excited state. Using chains with up to 102 lattice sites, we can safely perform the extrapolation to the thermodynamic limit for the ground-state energy and conformation, the single-particle gap, and the energies of the singlet exciton, the triplet ground state, and the optical excitation of the triplet ground state. The corresponding gaps are known with high precision from experiments. We determine a coherent parameter set (t0*=2.4eV,α*=3.4eV/Å,U*=6eV,V*=3eV) from a fit of the experimental gap energies to the theoretical values which we obtain for 81 parameter points in the four-dimensional search space (t0,α,U,V). We identify dark in-gap states in the singlet and triplet sectors as seen in experiments. Using a fairly stiff spring constant, the length of our unit cell is about 1% larger than its experimental value.

Weak Measurement and Quantum Smoothing of a Superconducting Qubit

NASA Astrophysics Data System (ADS)

Tan, Dian

In quantum mechanics, the measurement outcome of an observable in a quantum system is intrinsically random, yielding a probability distribution. The state of the quantum system can be described by a density matrix rho(t), which depends on the information accumulated until time t, and represents our knowledge about the system. The density matrix rho(t) gives probabilities for the outcomes of measurements at time t. Further probing of the quantum system allows us to refine our prediction in hindsight. In this thesis, we experimentally examine a quantum smoothing theory in a superconducting qubit by introducing an auxiliary matrix E(t) which is conditioned on information obtained from time t to a final time T. With the complete information before and after time t, the pair of matrices [rho(t), E(t)] can be used to make smoothed predictions for the measurement outcome at time t. We apply the quantum smoothing theory in the case of continuous weak measurement unveiling the retrodicted quantum trajectories and weak values. In the case of strong projective measurement, while the density matrix rho(t) with only diagonal elements in a given basis |n〉 may be treated as a classical mixture, we demonstrate a failure of this classical mixture description in determining the smoothed probabilities for the measurement outcome at time t with both diagonal rho(t) and diagonal E(t). We study the correlations between quantum states and weak measurement signals and examine aspects of the time symmetry of continuous quantum measurement. We also extend our study of quantum smoothing theory to the case of resonance fluorescence of a superconducting qubit with homodyne measurement and observe some interesting effects such as the modification of the excited state probabilities, weak values, and evolution of the predicted and retrodicted trajectories.

Symmetry properties of the configuration interaction space in relation to one- and two-particle operators: The splitting theorem

NASA Astrophysics Data System (ADS)

Živković, Tomislav P.

1984-09-01

The configuration interaction (CI) space Xn built upon n electrons moving over 2n orthonormalized orbitals χi is considered. It is shown that the space Xn splits into two complementary subspaces X+n and X-n having special properties: each state Ψ+∈X+n and Ψ-∈X-n is ``alternantlike'' in the sense that it has a uniform charge density distribution over all orbitals χi and vanishing bond-orders between all orbitals of the same parity. In addition, matrix elements Γ(ij;kl) of a two-particle density matrix vanish whenever four distinct orbitals are involved and there is an odd number of orbitals of the same parity. Further, Γ(ij;lj)=γ(il)/4 ( j≠i,l), whenever (i) and (l) are of different parity. This last relation shows the connection between a two-particle (Γ) and a one-particle (γ) density matrix. ``Elementary'' alternant and antialternant operators are identified. These operators connect either only the states in the same subspace, or only the states in different subspaces, and each one- and two-particle symmetric operator can be represented by their linear combination. Alternant Hamiltonians, which can be represented as linear combinations of elementary alternant operators, have alternantlike eigenstates. It is also shown that each symmetric Hamiltonian possessing alternantlike eigenstates can be represented as such a linear combination. In particular, the PPP Hamiltonian describing an alternant hydrocarbon system is such a case. Complementary subspaces X+n and X-n can be explicitly constructed using the so-called regular resonance structures (RRS's) which are normalized determinants containing mutually disjunct bond orbitals. Expressions for the derivation of matrix elements of one- and two-particle operators between different RRS's are also derived.

Symmetrized density matrix renormalization group algorithm for low-lying excited states of conjugated carbon systems: Application to 1,12-benzoperylene and polychrysene

NASA Astrophysics Data System (ADS)

Prodhan, Suryoday; Ramasesha, S.

2018-05-01

The symmetry adapted density matrix renormalization group (SDMRG) technique has been an efficient method for studying low-lying eigenstates in one- and quasi-one-dimensional electronic systems. However, the SDMRG method had bottlenecks involving the construction of linearly independent symmetry adapted basis states as the symmetry matrices in the DMRG basis were not sparse. We have developed a modified algorithm to overcome this bottleneck. The new method incorporates end-to-end interchange symmetry (C2) , electron-hole symmetry (J ) , and parity or spin-flip symmetry (P ) in these calculations. The one-to-one correspondence between direct-product basis states in the DMRG Hilbert space for these symmetry operations renders the symmetry matrices in the new basis with maximum sparseness, just one nonzero matrix element per row. Using methods similar to those employed in the exact diagonalization technique for Pariser-Parr-Pople (PPP) models, developed in the 1980s, it is possible to construct orthogonal SDMRG basis states while bypassing the slow step of the Gram-Schmidt orthonormalization procedure. The method together with the PPP model which incorporates long-range electronic correlations is employed to study the correlated excited-state spectra of 1,12-benzoperylene and a narrow mixed graphene nanoribbon with a chrysene molecule as the building unit, comprising both zigzag and cove-edge structures.

Efficient Algorithms for Estimating the Absorption Spectrum within Linear Response TDDFT

DOE Office of Scientific and Technical Information (OSTI.GOV)

Brabec, Jiri; Lin, Lin; Shao, Meiyue

We present two iterative algorithms for approximating the absorption spectrum of molecules within linear response of time-dependent density functional theory (TDDFT) framework. These methods do not attempt to compute eigenvalues or eigenvectors of the linear response matrix. They are designed to approximate the absorption spectrum as a function directly. They take advantage of the special structure of the linear response matrix. Neither method requires the linear response matrix to be constructed explicitly. They only require a procedure that performs the multiplication of the linear response matrix with a vector. These methods can also be easily modified to efficiently estimate themore » density of states (DOS) of the linear response matrix without computing the eigenvalues of this matrix. We show by computational experiments that the methods proposed in this paper can be much more efficient than methods that are based on the exact diagonalization of the linear response matrix. We show that they can also be more efficient than real-time TDDFT simulations. We compare the pros and cons of these methods in terms of their accuracy as well as their computational and storage cost.« less

Density matrix renormalization group study of Y-junction spin systems

NASA Astrophysics Data System (ADS)

Guo, Haihui

Junction systems are important to understand both from the fundamental and the practical point of view, as they are essential components in existing and future electronic and spintronic devices. With the continuous advance of technology, device size will eventual reach the atomic scale. Some of the most interesting and useful junction systems will be strongly correlated. We chose the Density Matrix Renormalization Group method to study two types of Y-junction systems, the Y and YDelta junctions, on strongly correlated spin chains. With new ideas coming from the quantum information field, we have made a very efficient. Y-junction DMRG algorithm, which improves the overall CUB cost from O(m6) to O(m4), where m is the number of states kept per block. We studied the ground state properties, the correlation length, and investigated the degeneracy problem on the Y and YDelta junctions. For the excited states, we researched the existence of magnon bound states for various conditions, and have shown that the bound state exists when the central coupling constant is small.

Fast reconstruction of high-qubit-number quantum states via low-rate measurements

NASA Astrophysics Data System (ADS)

Li, K.; Zhang, J.; Cong, S.

2017-07-01

Due to the exponential complexity of the resources required by quantum state tomography (QST), people are interested in approaches towards identifying quantum states which require less effort and time. In this paper, we provide a tailored and efficient method for reconstructing mixed quantum states up to 12 (or even more) qubits from an incomplete set of observables subject to noises. Our method is applicable to any pure or nearly pure state ρ and can be extended to many states of interest in quantum information processing, such as a multiparticle entangled W state, Greenberger-Horne-Zeilinger states, and cluster states that are matrix product operators of low dimensions. The method applies the quantum density matrix constraints to a quantum compressive sensing optimization problem and exploits a modified quantum alternating direction multiplier method (quantum-ADMM) to accelerate the convergence. Our algorithm takes 8 ,35 , and 226 seconds, respectively, to reconstruct superposition state density matrices of 10 ,11 ,and12 qubits with acceptable fidelity using less than 1 % of measurements of expectation. To our knowledge it is the fastest realization that people can achieve using a normal desktop. We further discuss applications of this method using experimental data of mixed states obtained in an ion trap experiment of up to 8 qubits.

Dynamics of entanglement in expanding quantum fields

NASA Astrophysics Data System (ADS)

Berges, Jürgen; Floerchinger, Stefan; Venugopalan, Raju

2018-04-01

We develop a functional real-time approach to computing the entanglement between spatial regions for Gaussian states in quantum field theory. The entanglement entropy is characterized in terms of local correlation functions on space-like Cauchy hypersurfaces. The framework is applied to explore an expanding light cone geometry in the particular case of the Schwinger model for quantum electrodynamics in 1+1 space-time dimensions. We observe that the entanglement entropy becomes extensive in rapidity at early times and that the corresponding local reduced density matrix is a thermal density matrix for excitations around a coherent field with a time dependent temperature. Since the Schwinger model successfully describes many features of multiparticle production in e + e - collisions, our results provide an attractive explanation in this framework for the apparent thermal nature of multiparticle production even in the absence of significant final state scattering.

Probabilistic low-rank factorization accelerates tensor network simulations of critical quantum many-body ground states.

PubMed

Kohn, Lucas; Tschirsich, Ferdinand; Keck, Maximilian; Plenio, Martin B; Tamascelli, Dario; Montangero, Simone

2018-01-01

We provide evidence that randomized low-rank factorization is a powerful tool for the determination of the ground-state properties of low-dimensional lattice Hamiltonians through tensor network techniques. In particular, we show that randomized matrix factorization outperforms truncated singular value decomposition based on state-of-the-art deterministic routines in time-evolving block decimation (TEBD)- and density matrix renormalization group (DMRG)-style simulations, even when the system under study gets close to a phase transition: We report linear speedups in the bond or local dimension of up to 24 times in quasi-two-dimensional cylindrical systems.

Probabilistic low-rank factorization accelerates tensor network simulations of critical quantum many-body ground states

NASA Astrophysics Data System (ADS)

Kohn, Lucas; Tschirsich, Ferdinand; Keck, Maximilian; Plenio, Martin B.; Tamascelli, Dario; Montangero, Simone

2018-01-01

We provide evidence that randomized low-rank factorization is a powerful tool for the determination of the ground-state properties of low-dimensional lattice Hamiltonians through tensor network techniques. In particular, we show that randomized matrix factorization outperforms truncated singular value decomposition based on state-of-the-art deterministic routines in time-evolving block decimation (TEBD)- and density matrix renormalization group (DMRG)-style simulations, even when the system under study gets close to a phase transition: We report linear speedups in the bond or local dimension of up to 24 times in quasi-two-dimensional cylindrical systems.

Numerical time evolution of ETH spin chains by means of matrix product density operators

NASA Astrophysics Data System (ADS)

White, Christopher; Zaletel, Michael; Mong, Roger; Refael, Gil

We introduce a method for approximating density operators of 1D systems that, when combined with a standard framework for time evolution (TEBD), makes possible simulation of the dynamics of strongly thermalizing systems to arbitrary times. We demonstrate that the method works on both near-equilibrium initial states (Gibbs states with spatially varying temperatures) and far-from-equilibrium initial states, including quenches across phase transitions and pure states. This work was supported by the National Science Foundation Graduate Research Fellowship under Grant No. DGE \\x901144469 and by the Caltech IQIM, an NSF Physics Frontiers Center with support of the Gordon and Betty Moore.

Engine materials characterization and damage monitoring by using x ray technologies

NASA Technical Reports Server (NTRS)

Baaklini, George Y.

1993-01-01

X ray attenuation measurement systems that are capable of characterizing density variations in monolithic ceramics and damage due to processing and/or mechanical testing in ceramic and intermetallic matrix composites are developed and applied. Noninvasive monitoring of damage accumulation and failure sequences in ceramic matrix composites is used during room-temperature tensile testing. This work resulted in the development of a point-scan digital radiography system and an in situ x ray material testing system. The former is used to characterize silicon carbide and silicon nitride specimens, and the latter is used to image the failure behavior of silicon-carbide-fiber-reinforced, reaction-bonded silicon nitride matrix composites. State-of-the-art x ray computed tomography is investigated to determine its capabilities and limitations in characterizing density variations of subscale engine components (e.g., a silicon carbide rotor, a silicon nitride blade, and a silicon-carbide-fiber-reinforced beta titanium matrix rod, rotor, and ring). Microfocus radiography, conventional radiography, scanning acoustic microscopy, and metallography are used to substantiate the x ray computed tomography findings. Point-scan digital radiography is a viable technique for characterizing density variations in monolithic ceramic specimens. But it is very limited and time consuming in characterizing ceramic matrix composites. Precise x ray attenuation measurements, reflecting minute density variations, are achieved by photon counting and by using microcollimators at the source and the detector. X ray computed tomography is found to be a unique x ray attenuation measurement technique capable of providing cross-sectional spatial density information in monolithic ceramics and metal matrix composites. X ray computed tomography is proven to accelerate generic composite component development. Radiographic evaluation before, during, and after loading shows the effect of preexisting volume flaws on the fracture behavior of composites. Results from one-, three-, five-, and eight-ply ceramic composite specimens show that x ray film radiography can monitor damage accumulation during tensile loading. Matrix cracking, fiber-matrix debonding, fiber bridging, and fiber pullout are imaged throughout the tensile loading of the specimens. In situ film radiography is found to be a practical technique for estimating interfacial shear strength between the silicon carbide fibers and the reaction-bonded silicon nitride matrix. It is concluded that pretest, in situ, and post-test x ray imaging can provide greater understanding of ceramic matrix composite mechanical behavior.

Ultrafast energy transfer with competing channels: Non-equilibrium Förster and Modified Redfield theories

NASA Astrophysics Data System (ADS)

Seibt, Joachim; Mančal, Tomáš

2017-05-01

We derive equations of motion for the reduced density matrix of a molecular system which undergoes energy transfer dynamics competing with fast internal conversion channels. Environmental degrees of freedom of such a system have no time to relax to quasi-equilibrium in the electronic excited state of the donor molecule, and thus the conditions of validity of Förster and Modified Redfield theories in their standard formulations do not apply. We derive non-equilibrium versions of the two well-known rate theories and apply them to the case of carotenoid-chlorophyll energy transfer. Although our reduced density matrix approach does not account for the formation of vibronic excitons, it still confirms the important role of the donor ground-state vibrational states in establishing the resonance energy transfer conditions. We show that it is essential to work with a theory valid in a strong system-bath interaction regime to obtain correct dependence of the rates on donor-acceptor energy gap.

Generic construction of efficient matrix product operators

NASA Astrophysics Data System (ADS)

Hubig, C.; McCulloch, I. P.; Schollwöck, U.

2017-01-01

Matrix product operators (MPOs) are at the heart of the second-generation density matrix renormalization group (DMRG) algorithm formulated in matrix product state language. We first summarize the widely known facts on MPO arithmetic and representations of single-site operators. Second, we introduce three compression methods (rescaled SVD, deparallelization, and delinearization) for MPOs and show that it is possible to construct efficient representations of arbitrary operators using MPO arithmetic and compression. As examples, we construct powers of a short-ranged spin-chain Hamiltonian, a complicated Hamiltonian of a two-dimensional system and, as proof of principle, the long-range four-body Hamiltonian from quantum chemistry.

Identification of metal s states in Sn-doped anatase by polarisation dependent hard X-ray photoelectron spectroscopy

NASA Astrophysics Data System (ADS)

Regoutz, A.; Oropeza, F. E.; Poll, C. G.; Payne, D. J.; Palgrave, R. G.; Panaccione, G.; Borgatti, F.; Agrestini, S.; Utsumi, Y.; Tsuei, K. D.; Liao, Y. F.; Watson, G. W.; Egdell, R. G.

2016-03-01

The contributions of Sn 5s and Ti 4s states to the valence band electronic structure of Sn-doped anatase have been identified by hard X-ray photoelectron spectroscopy. The metal s state intensity is strongly enhanced relative to that of O 2p states at high photon energies due to matrix element effects when electrons are detected parallel to the direction of the polarisation vector of the synchrotron beam, but becomes negligible in the perpendicular direction. The experimental spectra in both polarisations are in good agreement with cross section and asymmetry parameter weighted partial densities of states derived from density functional theory calculations.

Micromechanics effects in creep of metal-matrix composites

NASA Astrophysics Data System (ADS)

Davis, L. C.; Allison, J. E.

1995-12-01

The creep of metal-matrix composites is analyzed by finite element techniques. An axisymmetric unit-cell model with spherical reinforcing particles is used. Parameters appropriate to TiC particles in a precipitation-hardened (2219) Al matrix are chosen. The effects of matrix plasticity and residual stresses on the creep of the composite are calculated. We confirm (1) that the steady-state rate is independent of the particle elastic moduli and the matrix elastic and plastic properties, (2) that the ratio of composite to matrix steady-state rates depends only on the volume fraction and geometry of the reinforcing phase, and (3) that this ratio can be determined from a calculation of the stress-strain relation for the geometrically identical composite (same phase volume and geometry) with rigid particles in the appropriate power-law hardening matrix. The values of steady-state creep are compared to experimental ones (Krajewski et al.). Continuum mechanics predictions give a larger reduction of the composite creep relative to the unreinforced material than measured, suggesting that the effective creep rate of the matrix is larger than in unreinforced precipitation-hardened Al due to changes in microstructure, dislocation density, or creep mechanism. Changes in matrix creep properties are also suggested by the comparison of calculated and measured creep strain rates in the primary creep regime, where significantly different time dependencies are found. It is found that creep calculations performed for a timeindependent matrix creep law can be transformed to obtain the creep for a time-dependent creep law.

Watching excitons move: the time-dependent transition density matrix

NASA Astrophysics Data System (ADS)

Ullrich, Carsten

2012-02-01

Time-dependent density-functional theory allows one to calculate excitation energies and the associated transition densities in principle exactly. The transition density matrix (TDM) provides additional information on electron-hole localization and coherence of specific excitations of the many-body system. We have extended the TDM concept into the real-time domain in order to visualize the excited-state dynamics in conjugated molecules. The time-dependent TDM is defined as an implicit density functional, and can be approximately obtained from the time-dependent Kohn-Sham orbitals. The quality of this approximation is assessed in simple model systems. A computational scheme for real molecular systems is presented: the time-dependent Kohn-Sham equations are solved with the OCTOPUS code and the time-dependent Kohn-Sham TDM is calculated using a spatial partitioning scheme. The method is applied to show in real time how locally created electron-hole pairs spread out over neighboring conjugated molecular chains. The coupling mechanism, electron-hole coherence, and the possibility of charge separation are discussed.

Fourier-Legendre expansion of the one-electron density matrix of ground-state two-electron atoms.

PubMed

Ragot, Sébastien; Ruiz, María Belén

2008-09-28

The density matrix rho(r,r(')) of a spherically symmetric system can be expanded as a Fourier-Legendre series of Legendre polynomials P(l)(cos theta=rr(')rr(')). Application is here made to harmonically trapped electron pairs (i.e., Moshinsky's and Hooke's atoms), for which exact wavefunctions are known, and to the helium atom, using a near-exact wavefunction. In the present approach, generic closed form expressions are derived for the series coefficients of rho(r,r(')). The series expansions are shown to converge rapidly in each case, with respect to both the electron number and the kinetic energy. In practice, a two-term expansion accounts for most of the correlation effects, so that the correlated density matrices of the atoms at issue are essentially a linear functions of P(l)(cos theta)=cos theta. For example, in the case of Hooke's atom, a two-term expansion takes in 99.9% of the electrons and 99.6% of the kinetic energy. The correlated density matrices obtained are finally compared to their determinantal counterparts, using a simplified representation of the density matrix rho(r,r(')), suggested by the Legendre expansion. Interestingly, two-particle correlation is shown to impact the angular delocalization of each electron, in the one-particle space spanned by the r and r(') variables.

Entropy Production and Non-Equilibrium Steady States

NASA Astrophysics Data System (ADS)

Suzuki, Masuo

2013-01-01

The long-term issue of entropy production in transport phenomena is solved by separating the symmetry of the non-equilibrium density matrix ρ(t) in the von Neumann equation, as ρ(t) = ρs(t) + ρa(t) with the symmetric part ρs(t) and antisymmetric part ρa(t). The irreversible entropy production (dS/dt)irr is given in M. Suzuki, Physica A 390(2011)1904 by (dS/dt)irr = Tr( {H}(dρ s{(t)/dt))}/T for the Hamiltonian {H} of the relevant system. The general formulation of the extended von Neumann equation with energy supply and heat extraction is reviewed from the author's paper (M. S.,Physica A391(2012)1074). irreversibility; entropy production; transport phenomena; electric conduction; thermal conduction; linear response; Kubo formula; steady state; non-equilibrium density matrix; energy supply; symmetry-separated von Neumann equation; unboundedness.

Ground states of linear rotor chains via the density matrix renormalization group

NASA Astrophysics Data System (ADS)

Iouchtchenko, Dmitri; Roy, Pierre-Nicholas

2018-04-01

In recent years, experimental techniques have enabled the creation of ultracold optical lattices of molecules and endofullerene peapod nanomolecular assemblies. It was previously suggested that the rotor model resulting from the placement of dipolar linear rotors in one-dimensional lattices at low temperature has a transition between ordered and disordered phases. We use the density matrix renormalization group (DMRG) to compute ground states of chains of up to 100 rotors and provide further evidence of the phase transition in the form of a diverging entanglement entropy. We also propose two methods and present some first steps toward rotational spectra of such molecular assemblies using DMRG. The present work showcases the power of DMRG in this new context of interacting molecular rotors and opens the door to the study of fundamental questions regarding criticality in systems with continuous degrees of freedom.

Quantitative Tomography for Continuous Variable Quantum Systems

NASA Astrophysics Data System (ADS)

Landon-Cardinal, Olivier; Govia, Luke C. G.; Clerk, Aashish A.

2018-03-01

We present a continuous variable tomography scheme that reconstructs the Husimi Q function (Wigner function) by Lagrange interpolation, using measurements of the Q function (Wigner function) at the Padua points, conjectured to be optimal sampling points for two dimensional reconstruction. Our approach drastically reduces the number of measurements required compared to using equidistant points on a regular grid, although reanalysis of such experiments is possible. The reconstruction algorithm produces a reconstructed function with exponentially decreasing error and quasilinear runtime in the number of Padua points. Moreover, using the interpolating polynomial of the Q function, we present a technique to directly estimate the density matrix elements of the continuous variable state, with only a linear propagation of input measurement error. Furthermore, we derive a state-independent analytical bound on this error, such that our estimate of the density matrix is accompanied by a measure of its uncertainty.

Critical behavior of the extended Hubbard model with bond dimerization

NASA Astrophysics Data System (ADS)

Ejima, Satoshi; Lange, Florian; Essler, Fabian H. L.; Fehske, Holger

2018-05-01

Exploiting the matrix-product-state based density-matrix renormalization group (DMRG) technique we study the one-dimensional extended (U-V) Hubbard model with explicit bond dimerization in the half-filled band sector. In particular we investigate the nature of the quantum phase transition, taking place with growing ratio V / U between the symmetry-protected-topological and charge-density-wave insulating states. The (weak-coupling) critical line of continuous Ising transitions with central charge c = 1 / 2 terminates at a tricritical point belonging to the universality class of the dilute Ising model with c = 7 / 10 . We demonstrate that our DMRG data perfectly match with (tricritical) Ising exponents, e.g., for the order parameter β = 1 / 8 (1/24) and correlation length ν = 1 (5/9). Beyond the tricritical Ising point, in the strong-coupling regime, the quantum phase transition becomes first order.

Almost sure convergence in quantum spin glasses

DOE Office of Scientific and Technical Information (OSTI.GOV)

Buzinski, David, E-mail: dab197@case.edu; Meckes, Elizabeth, E-mail: elizabeth.meckes@case.edu

2015-12-15

Recently, Keating, Linden, and Wells [Markov Processes Relat. Fields 21(3), 537-555 (2015)] showed that the density of states measure of a nearest-neighbor quantum spin glass model is approximately Gaussian when the number of particles is large. The density of states measure is the ensemble average of the empirical spectral measure of a random matrix; in this paper, we use concentration of measure and entropy techniques together with the result of Keating, Linden, and Wells to show that in fact the empirical spectral measure of such a random matrix is almost surely approximately Gaussian itself with no ensemble averaging. We alsomore » extend this result to a spherical quantum spin glass model and to the more general coupling geometries investigated by Erdős and Schröder [Math. Phys., Anal. Geom. 17(3-4), 441–464 (2014)].« less

N-representability-driven reconstruction of the two-electron reduced-density matrix for a real-time time-dependent electronic structure method

NASA Astrophysics Data System (ADS)

Jeffcoat, David B.; DePrince, A. Eugene

2014-12-01

Propagating the equations of motion (EOM) for the one-electron reduced-density matrix (1-RDM) requires knowledge of the corresponding two-electron RDM (2-RDM). We show that the indeterminacy of this expression can be removed through a constrained optimization that resembles the variational optimization of the ground-state 2-RDM subject to a set of known N-representability conditions. Electronic excitation energies can then be obtained by propagating the EOM for the 1-RDM and following the dipole moment after the system interacts with an oscillating external electric field. For simple systems with well-separated excited states whose symmetry differs from that of the ground state, excitation energies obtained from this method are comparable to those obtained from full configuration interaction computations. Although the optimized 2-RDM satisfies necessary N-representability conditions, the procedure cannot guarantee a unique mapping from the 1-RDM to the 2-RDM. This deficiency is evident in the mean-field-quality description of transitions to states of the same symmetry as the ground state, as well as in the inability of the method to describe Rabi oscillations.

Crystallization of dense neutron matter

NASA Technical Reports Server (NTRS)

Canuto, V.; Chitre, S. M.

1974-01-01

The equation of state for cold neutron matter at high density is studied in the t-matrix formulation, and it is shown that energetically it is convenient to have neutrons in a crystalline configuration rather than in a liquid state for values of the density exceeding 1600 Tg/cu cm. The study of the mechanical properties indicates that the system is stable against shearing stresses. A solid core in the deep interior of heavy neutron stars appears to offer the most plausible explanation of speed-ups observed in the Vela pulsar.

Entanglement convertibility by sweeping through the quantum phases of the alternating bonds XXZ chain

PubMed Central

Tzeng, Yu-Chin; Dai, Li; Chung, Ming-Chiang; Amico, Luigi; Kwek, Leong-Chuan

2016-01-01

We study the entanglement structure and the topological edge states of the ground state of the spin-1/2 XXZ model with bond alternation. We employ parity-density matrix renormalization group with periodic boundary conditions. The finite-size scaling of Rényi entropies S2 and S∞ are used to construct the phase diagram of the system. The phase diagram displays three possible phases: Haldane type (an example of symmetry protected topological ordered phases), Classical Dimer and Néel phases, the latter bounded by two continuous quantum phase transitions. The entanglement and non-locality in the ground state are studied and quantified by the entanglement convertibility. We found that, at small spatial scales, the ground state is not convertible within the topological Haldane dimer phase. The phenomenology we observe can be described in terms of correlations between edge states. We found that the entanglement spectrum also exhibits a distinctive response in the topological phase: the effective rank of the reduced density matrix displays a specifically large “susceptibility” in the topological phase. These findings support the idea that although the topological order in the ground state cannot be detected by local inspection, the ground state response at local scale can tell the topological phases apart from the non-topological phases. PMID:27216970

Entanglement convertibility by sweeping through the quantum phases of the alternating bonds XXZ chain.

PubMed

Tzeng, Yu-Chin; Dai, Li; Chung, Ming-Chiang; Amico, Luigi; Kwek, Leong-Chuan

2016-05-24

We study the entanglement structure and the topological edge states of the ground state of the spin-1/2 XXZ model with bond alternation. We employ parity-density matrix renormalization group with periodic boundary conditions. The finite-size scaling of Rényi entropies S2 and S∞ are used to construct the phase diagram of the system. The phase diagram displays three possible phases: Haldane type (an example of symmetry protected topological ordered phases), Classical Dimer and Néel phases, the latter bounded by two continuous quantum phase transitions. The entanglement and non-locality in the ground state are studied and quantified by the entanglement convertibility. We found that, at small spatial scales, the ground state is not convertible within the topological Haldane dimer phase. The phenomenology we observe can be described in terms of correlations between edge states. We found that the entanglement spectrum also exhibits a distinctive response in the topological phase: the effective rank of the reduced density matrix displays a specifically large "susceptibility" in the topological phase. These findings support the idea that although the topological order in the ground state cannot be detected by local inspection, the ground state response at local scale can tell the topological phases apart from the non-topological phases.

Differential cross sections and polarization observables from CLAS K* photoproduction and the search for new N* states

NASA Astrophysics Data System (ADS)

Anisovich, A. V.; Hicks, K.; Klempt, E.; Nikonov, V. A.; Sarantsev, A.; Tang, W.; Adikaram, D.; Akbar, Z.; Amaryan, M. J.; Anefalos Pereira, S.; Badui, R. A.; Ball, J.; Battaglieri, M.; Batourine, V.; Bedlinskiy, I.; Biselli, A. S.; Briscoe, W. J.; Burkert, V. D.; Carman, D. S.; Celentano, A.; Chandavar, S.; Chetry, T.; Ciullo, G.; Clark, L.; Cole, P. L.; Compton, N.; Contalbrigo, M.; Crede, V.; D'Angelo, A.; Dashyan, N.; De Vita, R.; De Sanctis, E.; Deur, A.; Djalali, C.; Dugger, M.; Dupre, R.; Egiyan, H.; El Alaoui, A.; El Fassi, L.; Eugenio, P.; Fanchini, E.; Fedotov, G.; Filippi, A.; Fleming, J. A.; Gevorgyan, N.; Ghandilyan, Y.; Giovanetti, K. L.; Girod, F. X.; Gleason, C.; Gothe, R. W.; Griffioen, K. A.; Guo, L.; Hanretty, C.; Harrison, N.; Hattawy, M.; Holtrop, M.; Hughes, S. M.; Ilieva, Y.; Ireland, D. G.; Ishkhanov, B. S.; Isupov, E. L.; Jenkins, D.; Jiang, H.; Jo, H. S.; Joosten, S.; Keller, D.; Khachatryan, G.; Khandaker, M.; Kim, W.; Klein, F. J.; Kubarovsky, V.; Lanza, L.; Lenisa, P.; Livingston, K.; MacGregor, I. J. D.; Markov, N.; McKinnon, B.; Meyer, C. A.; Mirazita, M.; Mokeev, V.; Montgomery, R. A.; Movsisyan, A.; Munevar, E.; Munoz Camacho, C.; Murdoch, G.; Nadel-Turonski, P.; Net, L. A.; Ni, A.; Niccolai, S.; Niculescu, I.; Osipenko, M.; Ostrovidov, A. I.; Paolone, M.; Paremuzyan, R.; Park, K.; Pasyuk, E.; Peng, P.; Phelps, W.; Pisano, S.; Pogorelko, O.; Price, J. W.; Prok, Y.; Puckett, A. J. R.; Raue, B. A.; Ripani, M.; Ritchie, B. G.; Rosner, G.; Roy, P.; Sabatié, F.; Schumacher, R. A.; Sharabian, Y. G.; Skorodumina, Iu.; Smith, G. D.; Sokhan, D.; Sparveris, N.; Stankovic, I.; Stepanyan, S.; Strauch, S.; Sytnik, V.; Tian, Ye.; Ungaro, M.; Voskanyan, H.; Voutier, E.; Walford, N. K.; Watts, D. P.; Wood, M. H.; Zachariou, N.; Zhang, J.; Zonta, I.; CLAS Collaboration

2017-08-01

The reaction γp →K*+ Λ was measured using the CLAS detector for photon energies between the threshold and 3.9 GeV at the Thomas Jefferson National Accelerator Facility. For the first time, spin-density matrix elements have been extracted for this reaction. Differential cross sections, spin density matrix elements, and the Λ recoil polarization are compared with theoretical predictions using the BnGa partial wave analysis. The main result is the evidence for significant contributions from N (1895) 1 /2- and N (2100) 1 /2+ to the reaction. Branching ratios for decays into K* Λ for these resonances and further resonances are reported.

Horizon Entropy from Quantum Gravity Condensates.

PubMed

Oriti, Daniele; Pranzetti, Daniele; Sindoni, Lorenzo

2016-05-27

We construct condensate states encoding the continuum spherically symmetric quantum geometry of a horizon in full quantum gravity, i.e., without any classical symmetry reduction, in the group field theory formalism. Tracing over the bulk degrees of freedom, we show how the resulting reduced density matrix manifestly exhibits a holographic behavior. We derive a complete orthonormal basis of eigenstates for the reduced density matrix of the horizon and use it to compute the horizon entanglement entropy. By imposing consistency with the horizon boundary conditions and semiclassical thermodynamical properties, we recover the Bekenstein-Hawking entropy formula for any value of the Immirzi parameter. Our analysis supports the equivalence between the von Neumann (entanglement) entropy interpretation and the Boltzmann (statistical) one.

Structure of the first order reduced density matrix in three electron systems: A generalized Pauli constraints assisted study.

PubMed

Theophilou, Iris; Lathiotakis, Nektarios N; Helbig, Nicole

2018-03-21

We investigate the structure of the one-body reduced density matrix of three electron systems, i.e., doublet and quadruplet spin configurations, corresponding to the smallest interacting system with an open-shell ground state. To this end, we use configuration interaction (CI) expansions of the exact wave function in Slater determinants built from natural orbitals in a finite dimensional Hilbert space. With the exception of maximally polarized systems, the natural orbitals of spin eigenstates are generally spin dependent, i.e., the spatial parts of the up and down natural orbitals form two different sets. A measure to quantify this spin dependence is introduced and it is shown that it varies by several orders of magnitude depending on the system. We also study the ordering issue of the spin-dependent occupation numbers which has practical implications in reduced density matrix functional theory minimization schemes, when generalized Pauli constraints (GPCs) are imposed and in the form of the CI expansion in terms of the natural orbitals. Finally, we discuss the aforementioned CI expansion when there are GPCs that are almost "pinned."

Anisotropy-driven transition from the Moore-Read state to quantum Hall stripes

NASA Astrophysics Data System (ADS)

Zhu, Zheng; Sodemann, Inti; Sheng, D. N.; Fu, Liang

2017-05-01

We investigate the nature of the quantum Hall liquid in a half-filled second Landau level (n =1 ) as a function of band mass anisotropy using numerical exact diagonalization and density matrix renormalization group methods. We find increasing the mass anisotropy induces a quantum phase transition from the Moore-Read state to a charge density wave state. By analyzing the energy spectrum, guiding center structure factors, and by adding weak pinning potentials, we show that this charge density wave is a unidirectional quantum Hall stripe, which has a periodicity of a few magnetic lengths and survives in the thermodynamic limit. We find smooth profiles for the guiding center occupation function that reveal the strong coupling nature of the array of chiral Luttinger liquids residing at the stripe edges.

Random matrix theory for transition strengths: Applications and open questions

NASA Astrophysics Data System (ADS)

Kota, V. K. B.

2017-12-01

Embedded random matrix ensembles are generic models for describing statistical properties of finite isolated interacting quantum many-particle systems. A finite quantum system, induced by a transition operator, makes transitions from its states to the states of the same system or to those of another system. Examples are electromagnetic transitions (then the initial and final systems are same), nuclear beta and double beta decay (then the initial and final systems are different) and so on. Using embedded ensembles (EE), there are efforts to derive a good statistical theory for transition strengths. With m fermions (or bosons) in N mean-field single particle levels and interacting via two-body forces, we have with GOE embedding, the so called EGOE(1+2). Now, the transition strength density (transition strength multiplied by the density of states at the initial and final energies) is a convolution of the density generated by the mean-field one-body part with a bivariate spreading function due to the two-body interaction. Using the embedding U(N) algebra, it is established, for a variety of transition operators, that the spreading function, for sufficiently strong interactions, is close to a bivariate Gaussian. Also, as the interaction strength increases, the spreading function exhibits a transition from bivariate Breit-Wigner to bivariate Gaussian form. In appropriate limits, this EE theory reduces to the polynomial theory of Draayer, French and Wong on one hand and to the theory due to Flambaum and Izrailev for one-body transition operators on the other. Using spin-cutoff factors for projecting angular momentum, the theory is applied to nuclear matrix elements for neutrinoless double beta decay (NDBD). In this paper we will describe: (i) various developments in the EE theory for transition strengths; (ii) results for nuclear matrix elements for 130Te and 136Xe NDBD; (iii) important open questions in the current form of the EE theory.

Nonharmonicity in vibrated granular solids

NASA Astrophysics Data System (ADS)

Schreck, Carl

2012-02-01

We have shown that granular packings composed of frictionless particles with repulsive contact interactions are strongly nonharmonic. When infinitesimally perturbed along linear response eigenmodes of the static packing, energy leaks from the original mode of vibration to a continuum of frequencies due solely to contact breaking even when the system is under significant compression. Further, vibrated packings possess well-defined equilibrium positions that are different than those of the unperturbed packing. The vibrational density of states obtained using the displacement matrix and velocity autocorrelation function methods exhibit an increase in the number of low-frequency modes over that obtained from linear response of the static packing. The form of the density of states in vibrated granular packings is reminiscent of the low-frequency behavior of the vibrational density of states in fluid systems. We also investigate the effects of inter-particle friction, dissipation, particle shape, and degree of positional order on the density of states and thermal transport properties in driven granular packings.

Density matrix reconstruction of a large angular momentum

NASA Astrophysics Data System (ADS)

Klose, Gerd

2001-10-01

A complete description of the quantum state of a physical system is the fundamental knowledge necessary to statistically predict the outcome of measurements. In turning this statement around, Wolfgang Pauli raised already in 1933 the question, whether an unknown quantum state could be uniquely determined by appropriate measurements-a problem that has gained new relevance in recent years. In order to harness the prospects of quantum computing, secure communication, teleportation, and the like, the development of techniques to accurately control and measure quantum states has now become a matter of practical as well as fundamental interest. However, there is no general answer to Pauli's very basic question, and quantum state reconstruction algorithms have been developed and experimentally demonstrated only for a few systems so far. This thesis presents a novel experimental method to measure the unknown and generally mixed quantum state for an angular momentum of arbitrary magnitude. The (2F + 1) x (2F + 1) density matrix describing the quantum state is hereby completely determined from a set of Stern-Gerlach measurements with (4F + 1) different orientations of the quantization axis. This protocol is implemented for laser cooled Cesium atoms in the 6S1/2(F = 4) hyperfine ground state manifold, and is applied to a number of test states prepared by optical pumping and Larmor precession. A comparison of the input and the measured states shows successful reconstructions with fidelities of about 0.95.

Quantifying Complexity in Quantum Phase Transitions via Mutual Information Complex Networks

NASA Astrophysics Data System (ADS)

Valdez, Marc Andrew; Jaschke, Daniel; Vargas, David L.; Carr, Lincoln D.

2017-12-01

We quantify the emergent complexity of quantum states near quantum critical points on regular 1D lattices, via complex network measures based on quantum mutual information as the adjacency matrix, in direct analogy to quantifying the complexity of electroencephalogram or functional magnetic resonance imaging measurements of the brain. Using matrix product state methods, we show that network density, clustering, disparity, and Pearson's correlation obtain the critical point for both quantum Ising and Bose-Hubbard models to a high degree of accuracy in finite-size scaling for three classes of quantum phase transitions, Z2, mean field superfluid to Mott insulator, and a Berzinskii-Kosterlitz-Thouless crossover.

Ground-state properties of anyons in a one-dimensional lattice

NASA Astrophysics Data System (ADS)

Tang, Guixin; Eggert, Sebastian; Pelster, Axel

2015-12-01

Using the Anyon-Hubbard Hamiltonian, we analyze the ground-state properties of anyons in a one-dimensional lattice. To this end we map the hopping dynamics of correlated anyons to an occupation-dependent hopping Bose-Hubbard model using the fractional Jordan-Wigner transformation. In particular, we calculate the quasi-momentum distribution of anyons, which interpolates between Bose-Einstein and Fermi-Dirac statistics. Analytically, we apply a modified Gutzwiller mean-field approach, which goes beyond a classical one by including the influence of the fractional phase of anyons within the many-body wavefunction. Numerically, we use the density-matrix renormalization group by relying on the ansatz of matrix product states. As a result it turns out that the anyonic quasi-momentum distribution reveals both a peak-shift and an asymmetry which mainly originates from the nonlocal string property. In addition, we determine the corresponding quasi-momentum distribution of the Jordan-Wigner transformed bosons, where, in contrast to the hard-core case, we also observe an asymmetry for the soft-core case, which strongly depends on the particle number density.

Time dependent Schrödinger equation for black hole evaporation: No information loss

DOE Office of Scientific and Technical Information (OSTI.GOV)

Corda, Christian, E-mail: cordac.galilei@gmail.com

2015-02-15

In 1976 S. Hawking claimed that “Because part of the information about the state of the system is lost down the hole, the final situation is represented by a density matrix rather than a pure quantum state”. This was the starting point of the popular “black hole (BH) information paradox”. In a series of papers, together with collaborators, we naturally interpreted BH quasi-normal modes (QNMs) in terms of quantum levels discussing a model of excited BH somewhat similar to the historical semi-classical Bohr model of the structure of a hydrogen atom. Here we explicitly write down, for the same model,more » a time dependent Schrödinger equation for the system composed by Hawking radiation and BH QNMs. The physical state and the correspondent wave function are written in terms of a unitary evolution matrix instead of a density matrix. Thus, the final state results to be a pure quantum state instead of a mixed one. Hence, Hawking’s claim is falsified because BHs result to be well defined quantum mechanical systems, having ordered, discrete quantum spectra, which respect ’t Hooft’s assumption that Schrödinger equations can be used universally for all dynamics in the universe. As a consequence, information comes out in BH evaporation in terms of pure states in a unitary time dependent evolution. In Section 4 of this paper we show that the present approach permits also to solve the entanglement problem connected with the information paradox.« less

Full characterization of a three-photon Greenberger-Horne-Zeilinger state using quantum state tomography.

PubMed

Resch, K J; Walther, P; Zeilinger, A

2005-02-25

We have performed the first experimental tomographic reconstruction of a three-photon polarization state. Quantum state tomography is a powerful tool for fully describing the density matrix of a quantum system. We measured 64 three-photon polarization correlations and used a "maximum-likelihood" reconstruction method to reconstruct the Greenberger-Horne-Zeilinger state. The entanglement class has been characterized using an entanglement witness operator and the maximum predicted values for the Mermin inequality were extracted.

Universal Features of Left-Right Entanglement Entropy.

PubMed

Das, Diptarka; Datta, Shouvik

2015-09-25

We show the presence of universal features in the entanglement entropy of regularized boundary states for (1+1)D conformal field theories on a circle when the reduced density matrix is obtained by tracing over right- or left-moving modes. We derive a general formula for the left-right entanglement entropy in terms of the central charge and the modular S matrix of the theory. When the state is chosen to be an Ishibashi state, this measure of entanglement is shown to precisely reproduce the spatial entanglement entropy of a (2+1)D topological quantum field theory. We explicitly evaluate the left-right entanglement entropies for the Ising model, the tricritical Ising model and the su[over ^](2)_{k} Wess-Zumino-Witten model as examples.

Coherence Evolution and Transfer Supplemented by Sender's Initial-State Restoring

NASA Astrophysics Data System (ADS)

Fel'dman, E. B.; Zenchuk, A. I.

2017-12-01

The evolution of quantum coherences comes with a set of conservation laws provided that the Hamiltonian governing this evolution conserves the spin-excitation number. At that, coherences do not intertwist during the evolution. Using the transmission line and the receiver in the initial ground state we can transfer the coherences to the receiver without interaction between them, although the matrix elements contributing to each particular coherence intertwist in the receiver's state. Therefore we propose a tool based on the unitary transformation at the receiver side to untwist these elements and thus restore (at least partially) the structure of the sender's initial density matrix. A communication line with two-qubit sender and receiver is considered as an example of implementation of this technique.

Excitation energies of dissociating H2: A problematic case for the adiabatic approximation of time-dependent density functional theory

NASA Astrophysics Data System (ADS)

Gritsenko, O. V.; van Gisbergen, S. J. A.; Görling, A.; Baerends, E. J.

2000-11-01

Time-dependent density functional theory (TDDFT) is applied for calculation of the excitation energies of the dissociating H2 molecule. The standard TDDFT method of adiabatic local density approximation (ALDA) totally fails to reproduce the potential curve for the lowest excited singlet 1Σu+ state of H2. Analysis of the eigenvalue problem for the excitation energies as well as direct derivation of the exchange-correlation (xc) kernel fxc(r,r',ω) shows that ALDA fails due to breakdown of its simple spatially local approximation for the kernel. The analysis indicates a complex structure of the function fxc(r,r',ω), which is revealed in a different behavior of the various matrix elements K1c,1cxc (between the highest occupied Kohn-Sham molecular orbital ψ1 and virtual MOs ψc) as a function of the bond distance R(H-H). The effect of nonlocality of fxc(r,r') is modeled by using different expressions for the corresponding matrix elements of different orbitals. Asymptotically corrected ALDA (ALDA-AC) expressions for the matrix elements K12,12xc(στ) are proposed, while for other matrix elements the standard ALDA expressions are retained. This approach provides substantial improvement over the standard ALDA. In particular, the ALDA-AC curve for the lowest singlet excitation qualitatively reproduces the shape of the exact curve. It displays a minimum and approaches a relatively large positive energy at large R(H-H). ALDA-AC also produces a substantial improvement for the calculated lowest triplet excitation, which is known to suffer from the triplet instability problem of the restricted KS ground state. Failure of the ALDA for the excitation energies is related to the failure of the local density as well as generalized gradient approximations to reproduce correctly the polarizability of dissociating H2. The expression for the response function χ is derived to show the origin of the field-counteracting term in the xc potential, which is lacking in the local density and generalized gradient approximations and which is required to obtain a correct polarizability.

Continuous fiber ceramic matrix composites for heat engine components

NASA Technical Reports Server (NTRS)

Tripp, David E.

1988-01-01

High strength at elevated temperatures, low density, resistance to wear, and abundance of nonstrategic raw materials make structural ceramics attractive for advanced heat engine applications. Unfortunately, ceramics have a low fracture toughness and fail catastrophically because of overload, impact, and contact stresses. Ceramic matrix composites provide the means to achieve improved fracture toughness while retaining desirable characteristics, such as high strength and low density. Materials scientists and engineers are trying to develop the ideal fibers and matrices to achieve the optimum ceramic matrix composite properties. A need exists for the development of failure models for the design of ceramic matrix composite heat engine components. Phenomenological failure models are currently the most frequently used in industry, but they are deterministic and do not adequately describe ceramic matrix composite behavior. Semi-empirical models were proposed, which relate the failure of notched composite laminates to the stress a characteristic distance away from the notch. Shear lag models describe composite failure modes at the micromechanics level. The enhanced matrix cracking stress occurs at the same applied stress level predicted by the two models of steady state cracking. Finally, statistical models take into consideration the distribution in composite failure strength. The intent is to develop these models into computer algorithms for the failure analysis of ceramic matrix composites under monotonically increasing loads. The algorithms will be included in a postprocessor to general purpose finite element programs.

Ising antiferromagnet on a finite triangular lattice with free boundary conditions

NASA Astrophysics Data System (ADS)

Kim, Seung-Yeon

2015-11-01

The exact integer values for the density of states of the Ising model on an equilateral triangular lattice with free boundary conditions are evaluated up to L = 24 spins on a side for the first time by using the microcanonical transfer matrix. The total number of states is 2 N s = 2300 ≈ 2.037 × 1090 for L = 24, where N s = L( L+1)/2 is the number of spins. Classifying all 2300 spin states according to their energy values is an enormous work. From the density of states, the exact partition function zeros in the complex temperature plane of the triangular-lattice Ising model are evaluated. Using the density of states and the partition function zeros, we investigate the properties of the triangularlattice Ising antiferromagnet. The scaling behavior of the ground-state entropy and the form of the correlation length at T = 0 are studied for the triangular-lattice Ising antiferromagnet with free boundary conditions. Also, the scaling behavior of the Fisher edge singularity is investigated.

Fragile entanglement statistics

NASA Astrophysics Data System (ADS)

Brody, Dorje C.; Hughston, Lane P.; Meier, David M.

2015-10-01

If X and Y are independent, Y and Z are independent, and so are X and Z, one might be tempted to conclude that X, Y, and Z are independent. But it has long been known in classical probability theory that, intuitive as it may seem, this is not true in general. In quantum mechanics one can ask whether analogous statistics can emerge for configurations of particles in certain types of entangled states. The explicit construction of such states, along with the specification of suitable sets of observables that have the purported statistical properties, is not entirely straightforward. We show that an example of such a configuration arises in the case of an N-particle GHZ state, and we are able to identify a family of observables with the property that the associated measurement outcomes are independent for any choice of 2,3,\\ldots ,N-1 of the particles, even though the measurement outcomes for all N particles are not independent. Although such states are highly entangled, the entanglement turns out to be ‘fragile’, i.e. the associated density matrix has the property that if one traces out the freedom associated with even a single particle, the resulting reduced density matrix is separable.

Interacting hadron resonance gas model in the K -matrix formalism

NASA Astrophysics Data System (ADS)

Dash, Ashutosh; Samanta, Subhasis; Mohanty, Bedangadas

2018-05-01

An extension of hadron resonance gas (HRG) model is constructed to include interactions using relativistic virial expansion of partition function. The noninteracting part of the expansion contains all the stable baryons and mesons and the interacting part contains all the higher mass resonances which decay into two stable hadrons. The virial coefficients are related to the phase shifts which are calculated using K -matrix formalism in the present work. We have calculated various thermodynamics quantities like pressure, energy density, and entropy density of the system. A comparison of thermodynamic quantities with noninteracting HRG model, calculated using the same number of hadrons, shows that the results of the above formalism are larger. A good agreement between equation of state calculated in K -matrix formalism and lattice QCD simulations is observed. Specifically, the lattice QCD calculated interaction measure is well described in our formalism. We have also calculated second-order fluctuations and correlations of conserved charges in K -matrix formalism. We observe a good agreement of second-order fluctuations and baryon-strangeness correlation with lattice data below the crossover temperature.

Differential cross sections and polarization observables from CLAS K *photoproduction and the search for new N* states

DOE Office of Scientific and Technical Information (OSTI.GOV)

Anisovich, A. V.

The reactionmore » $$\\gamma p \\to K^{*+} \\Lambda$$ was measured using the CLAS detector for photon energies between the threshold and 3.9 GeV at the Thomas Jefferson National Accelerator Facility. For the first time, spin-density matrix elements have been extracted for this reaction. Differential cross sections, spin density matrix elements, and the $$\\Lambda$$ recoil polarization are compared with theoretical predictions using the BnGa partial wave analysis. The main result is the evidence for significant contributions from $N(1895)1/2^-$ and $N(2100)1/2^+$ to the reaction. Branching ratios for decays into $$K^*\\Lambda$$ for these resonances and further resonances are reported.« less

Study of laser cooling in deep optical lattice: two-level quantum model

NASA Astrophysics Data System (ADS)

Prudnikov, O. N.; Il'enkov, R. Ya.; Taichenachev, A. V.; Yudin, V. I.; Rasel, E. M.

2018-01-01

We study a possibility of laser cooling of 24Mg atoms in deep optical lattice formed by intense off-resonant laser field in a presence of cooling field resonant to narrow (3s3s) 1 S 0 → (3s3p)3 P 1 (λ = 457 nm) optical transition. For description of laser cooling with taking into account quantum recoil effects we consider two quantum models. The first one is based on direct numerical solution of quantum kinetic equation for atom density matrix and the second one is simplified model based on decomposition of atom density matrix over vibration states in the lattice wells. We search cooling field intensity and detuning for minimum cooling energy and fast laser cooling.

Differential cross sections and polarization observables from CLAS K *photoproduction and the search for new N* states

DOE PAGES

Anisovich, A. V.

2017-05-16

The reactionmore » $$\\gamma p \\to K^{*+} \\Lambda$$ was measured using the CLAS detector for photon energies between the threshold and 3.9 GeV at the Thomas Jefferson National Accelerator Facility. For the first time, spin-density matrix elements have been extracted for this reaction. Differential cross sections, spin density matrix elements, and the $$\\Lambda$$ recoil polarization are compared with theoretical predictions using the BnGa partial wave analysis. The main result is the evidence for significant contributions from $N(1895)1/2^-$ and $N(2100)1/2^+$ to the reaction. Branching ratios for decays into $$K^*\\Lambda$$ for these resonances and further resonances are reported.« less

Typical entanglement

NASA Astrophysics Data System (ADS)

Deelan Cunden, Fabio; Facchi, Paolo; Florio, Giuseppe; Pascazio, Saverio

2013-05-01

Let a pure state | ψ> be chosen randomly in an NM-dimensional Hilbert space, and consider the reduced density matrix ρ A of an N-dimensional subsystem. The bipartite entanglement properties of | ψ> are encoded in the spectrum of ρ A . By means of a saddle point method and using a "Coulomb gas" model for the eigenvalues, we obtain the typical spectrum of reduced density matrices. We consider the cases of an unbiased ensemble of pure states and of a fixed value of the purity. We finally obtain the eigenvalue distribution by using a statistical mechanics approach based on the introduction of a partition function.

Matrix cracking in laminated composites under monotonic and cyclic loadings

NASA Technical Reports Server (NTRS)

Allen, David H.; Lee, Jong-Won

1991-01-01

An analytical model based on the internal state variable (ISV) concept and the strain energy method is proposed for characterizing the monotonic and cyclic response of laminated composites containing matrix cracks. A modified constitution is formulated for angle-ply laminates under general in-plane mechanical loading and constant temperature change. A monotonic matrix cracking criterion is developed for predicting the crack density in cross-ply laminates as a function of the applied laminate axial stress. An initial formulation for a cyclic matrix cracking criterion for cross-ply laminates is also discussed. For the monotonic loading case, a number of experimental data and well-known models are compared with the present study for validating the practical applicability of the ISV approach.

Spin-Projected Matrix Product States: Versatile Tool for Strongly Correlated Systems.

PubMed

Li, Zhendong; Chan, Garnet Kin-Lic

2017-06-13

We present a new wave function ansatz that combines the strengths of spin projection with the language of matrix product states (MPS) and matrix product operators (MPO) as used in the density matrix renormalization group (DMRG). Specifically, spin-projected matrix product states (SP-MPS) are constructed as [Formula: see text], where [Formula: see text] is the spin projector for total spin S and |Ψ MPS (N,M) ⟩ is an MPS wave function with a given particle number N and spin projection M. This new ansatz possesses several attractive features: (1) It provides a much simpler route to achieve spin adaptation (i.e., to create eigenfunctions of Ŝ 2 ) compared to explicitly incorporating the non-Abelian SU(2) symmetry into the MPS. In particular, since the underlying state |Ψ MPS (N,M) ⟩ in the SP-MPS uses only Abelian symmetries, one does not need the singlet embedding scheme for nonsinglet states, as normally employed in spin-adapted DMRG, to achieve a single consistent variationally optimized state. (2) Due to the use of |Ψ MPS (N,M) ⟩ as its underlying state, the SP-MPS can be closely connected to broken-symmetry mean-field states. This allows one to straightforwardly generate the large number of broken-symmetry guesses needed to explore complex electronic landscapes in magnetic systems. Further, this connection can be exploited in the future development of quantum embedding theories for open-shell systems. (3) The sum of MPOs representation for the Hamiltonian and spin projector [Formula: see text] naturally leads to an embarrassingly parallel algorithm for computing expectation values and optimizing SP-MPS. (4) Optimizing SP-MPS belongs to the variation-after-projection (VAP) class of spin-projected theories. Unlike usual spin-projected theories based on determinants, the SP-MPS ansatz can be made essentially exact simply by increasing the bond dimensions in |Ψ MPS (N,M) ⟩. Computing excited states is also simple by imposing orthogonality constraints, which are simple to implement with MPS. To illustrate the versatility of SP-MPS, we formulate algorithms for the optimization of ground and excited states, develop perturbation theory based on SP-MPS, and describe how to evaluate spin-independent and spin-dependent properties such as the reduced density matrices. We demonstrate the numerical performance of SP-MPS with applications to several models typical of strong correlation, including the Hubbard model, and [2Fe-2S] and [4Fe-4S] model complexes.

Matching-pursuit/split-operator-Fourier-transform computations of thermal correlation functions.

PubMed

Chen, Xin; Wu, Yinghua; Batista, Victor S

2005-02-08

A rigorous and practical methodology for evaluating thermal-equilibrium density matrices, finite-temperature time-dependent expectation values, and time-correlation functions is described. The method involves an extension of the matching-pursuit/split-operator-Fourier-transform method to the solution of the Bloch equation via imaginary-time propagation of the density matrix and the evaluation of Heisenberg time-evolution operators through real-time propagation in dynamically adaptive coherent-state representations.

QCD-inspired spectra from Blue's functions

NASA Astrophysics Data System (ADS)

Nowak, Maciej A.; Papp, Gábor; Zahed, Ismail

1996-02-01

We use the law of addition in random matrix theory to analyze the spectral distributions of a variety of chiral random matrix models as inspired from QCD whether through symmetries or models. In terms of the Blue's functions recently discussed by Zee, we show that most of the spectral distributions in the macroscopic limit and the quenched approximation, follow algebraically from the discontinuity of a pertinent solution to a cubic (Cardano) or a quartic (Ferrari) equation. We use the end-point equation of the energy spectra in chiral random matrix models to argue for novel phase structures, in which the Dirac density of states plays the role of an order parameter.

Kibble Zurek mechanism of topological defect formation in quantum field theory with matrix product states

NASA Astrophysics Data System (ADS)

Gillman, Edward; Rajantie, Arttu

2018-05-01

The Kibble Zurek mechanism in a relativistic ϕ4 scalar field theory in D =(1 +1 ) is studied using uniform matrix product states. The equal time two point function in momentum space G2(k ) is approximated as the system is driven through a quantum phase transition at a variety of different quench rates τQ. We focus on looking for signatures of topological defect formation in the system and demonstrate the consistency of the picture that the two point function G2(k ) displays two characteristic scales, the defect density n and the kink width dK. Consequently, G2(k ) provides a clear signature for the formation of defects and a well defined measure of the defect density in the system. These results provide a benchmark for the use of tensor networks as powerful nonperturbative nonequilibrium methods for relativistic quantum field theory, providing a promising technique for the future study of high energy physics and cosmology.

Solutions of the two-dimensional Hubbard model: Benchmarks and results from a wide range of numerical algorithms

DOE PAGES

LeBlanc, J. P. F.; Antipov, Andrey E.; Becca, Federico; ...

2015-12-14

Numerical results for ground-state and excited-state properties (energies, double occupancies, and Matsubara-axis self-energies) of the single-orbital Hubbard model on a two-dimensional square lattice are presented, in order to provide an assessment of our ability to compute accurate results in the thermodynamic limit. Many methods are employed, including auxiliary-field quantum Monte Carlo, bare and bold-line diagrammatic Monte Carlo, method of dual fermions, density matrix embedding theory, density matrix renormalization group, dynamical cluster approximation, diffusion Monte Carlo within a fixed-node approximation, unrestricted coupled cluster theory, and multireference projected Hartree-Fock methods. Comparison of results obtained by different methods allows for the identification ofmore » uncertainties and systematic errors. The importance of extrapolation to converged thermodynamic-limit values is emphasized. Furthermore, cases where agreement between different methods is obtained establish benchmark results that may be useful in the validation of new approaches and the improvement of existing methods.« less

Study of decoherence in a system of superconducting flux-qubits interacting with an ensemble of electrons

DOE Office of Scientific and Technical Information (OSTI.GOV)

Reboiro, M., E-mail: reboiro@fisica.unlp.edu.ar; Civitarese, O., E-mail: osvaldo.civitarese@fisica.unlp.edu.ar; Ramírez, R.

2017-03-15

The degree of coherence in a hybrid system composed of superconducting flux-qubits and an electron ensemble is analysed. Both, the interactions among the electrons and among the superconducting flux-qubits are taken into account. The time evolution of the hybrid system is solved exactly, and discussed in terms of the reduced density matrix of each subsystem. It is seen that the inclusion of a line width, for the electrons and for the superconducting flux-qubits, influences the pattern of spin-squeezing and the coherence of the superconducting flux qubits. - Highlights: • The degree of coherence in a hybrid system, composed of superconductingmore » flux qubits and an electron ensemble, is analysed. • The time evolution of the hybrid system is solved exactly and discussed in terms of the reduced density matrix of each subsystem. • It is shown that the initial state of the system evolves to a stationary squeezed state.« less

Geometric multiaxial representation of N -qubit mixed symmetric separable states

NASA Astrophysics Data System (ADS)

SP, Suma; Sirsi, Swarnamala; Hegde, Subramanya; Bharath, Karthik

2017-08-01

The study of N -qubit mixed symmetric separable states is a longstanding challenging problem as no unique separability criterion exists. In this regard, we take up the N -qubit mixed symmetric separable states for a detailed study as these states are of experimental importance and offer an elegant mathematical analysis since the dimension of the Hilbert space is reduced from 2N to N +1 . Since there exists a one-to-one correspondence between the spin-j system and an N -qubit symmetric state, we employ Fano statistical tensor parameters for the parametrization of the spin-density matrix. Further, we use a geometric multiaxial representation (MAR) of the density matrix to characterize the mixed symmetric separable states. Since the separability problem is NP-hard, we choose to study it in the continuum limit where mixed symmetric separable states are characterized by the P -distribution function λ (θ ,ϕ ) . We show that the N -qubit mixed symmetric separable states can be visualized as a uniaxial system if the distribution function is independent of θ and ϕ . We further choose a distribution function to be the most general positive function on a sphere and observe that the statistical tensor parameters characterizing the N -qubit symmetric system are the expansion coefficients of the distribution function. As an example for the discrete case, we investigate the MAR of a uniformly weighted two-qubit mixed symmetric separable state. We also observe that there exists a correspondence between the separability and classicality of states.

Flavin Charge Transfer Transitions Assist DNA Photolyase Electron Transfer

NASA Astrophysics Data System (ADS)

Skourtis, Spiros S.; Prytkova, Tatiana; Beratan, David N.

2007-12-01

This contribution describes molecular dynamics, semi-empirical and ab-initio studies of the primary photo-induced electron transfer reaction in DNA photolyase. DNA photolyases are FADH--containing proteins that repair UV-damaged DNA by photo-induced electron transfer. A DNA photolyase recognizes and binds to cyclobutatne pyrimidine dimer lesions of DNA. The protein repairs a bound lesion by transferring an electron to the lesion from FADH-, upon photo-excitation of FADH- with 350-450 nm light. We compute the lowest singlet excited states of FADH- in DNA photolyase using INDO/S configuration interaction, time-dependent density-functional, and time-dependent Hartree-Fock methods. The calculations identify the lowest singlet excited state of FADH- that is populated after photo-excitation and that acts as the electron donor. For this donor state we compute conformationally-averaged tunneling matrix elements to empty electron-acceptor states of a thymine dimer bound to photolyase. The conformational averaging involves different FADH--thymine dimer confromations obtained from molecular dynamics simulations of the solvated protein with a thymine dimer docked in its active site. The tunneling matrix element computations use INDO/S-level Green's function, energy splitting, and Generalized Mulliken-Hush methods. These calculations indicate that photo-excitation of FADH- causes a π→π* charge-transfer transition that shifts electron density to the side of the flavin isoalloxazine ring that is adjacent to the docked thymine dimer. This shift in electron density enhances the FADH--to-dimer electronic coupling, thus inducing rapid electron transfer.

A Comparative Study of Collagen Matrix Density Effect on Endothelial Sprout Formation Using Experimental and Computational Approaches.

PubMed

Shamloo, Amir; Mohammadaliha, Negar; Heilshorn, Sarah C; Bauer, Amy L

2016-04-01

A thorough understanding of determining factors in angiogenesis is a necessary step to control the development of new blood vessels. Extracellular matrix density is known to have a significant influence on cellular behaviors and consequently can regulate vessel formation. The utilization of experimental platforms in combination with numerical models can be a powerful method to explore the mechanisms of new capillary sprout formation. In this study, using an integrative method, the interplay between the matrix density and angiogenesis was investigated. Owing the fact that the extracellular matrix density is a global parameter that can affect other parameters such as pore size, stiffness, cell-matrix adhesion and cross-linking, deeper understanding of the most important biomechanical or biochemical properties of the ECM causing changes in sprout morphogenesis is crucial. Here, we implemented both computational and experimental methods to analyze the mechanisms responsible for the influence of ECM density on the sprout formation that is difficult to be investigated comprehensively using each of these single methods. For this purpose, we first utilized an innovative approach to quantify the correspondence of the simulated collagen fibril density to the collagen density in the experimental part. Comparing the results of the experimental study and computational model led to some considerable achievements. First, we verified the results of the computational model using the experimental results. Then, we reported parameters such as the ratio of proliferating cells to migrating cells that was difficult to obtain from experimental study. Finally, this integrative system led to gain an understanding of the possible mechanisms responsible for the effect of ECM density on angiogenesis. The results showed that stable and long sprouts were observed at an intermediate collagen matrix density of 1.2 and 1.9 mg/ml due to a balance between the number of migrating and proliferating cells. As a result of weaker connections between the cells and matrix, a lower collagen matrix density (0.7 mg/ml) led to unstable and broken sprouts. However, higher matrix density (2.7 mg/ml) suppressed sprout formation due to the high level of matrix entanglement, which inhibited cell migration. This study also showed that extracellular matrix density can influence sprout branching. Our experimental results support this finding.

How electronic dynamics with Pauli exclusion produces Fermi-Dirac statistics.

PubMed

Nguyen, Triet S; Nanguneri, Ravindra; Parkhill, John

2015-04-07

It is important that any dynamics method approaches the correct population distribution at long times. In this paper, we derive a one-body reduced density matrix dynamics for electrons in energetic contact with a bath. We obtain a remarkable equation of motion which shows that in order to reach equilibrium properly, rates of electron transitions depend on the density matrix. Even though the bath drives the electrons towards a Boltzmann distribution, hole blocking factors in our equation of motion cause the electronic populations to relax to a Fermi-Dirac distribution. These factors are an old concept, but we show how they can be derived with a combination of time-dependent perturbation theory and the extended normal ordering of Mukherjee and Kutzelnigg for a general electronic state. The resulting non-equilibrium kinetic equations generalize the usual Redfield theory to many-electron systems, while ensuring that the orbital occupations remain between zero and one. In numerical applications of our equations, we show that relaxation rates of molecules are not constant because of the blocking effect. Other applications to model atomic chains are also presented which highlight the importance of treating both dephasing and relaxation. Finally, we show how the bath localizes the electron density matrix.

Kinetic and spectral descriptions of autoionization phenomena associated with atomic processes in plasmas

NASA Astrophysics Data System (ADS)

Jacobs, Verne L.

2017-06-01

This investigation has been devoted to the theoretical description and computer modeling of atomic processes giving rise to radiative emission in energetic electron and ion beam interactions and in laboratory plasmas. We are also interested in the effects of directed electron and ion collisions and of anisotropic electric and magnetic fields. In the kinetic-theory description, we treat excitation, de-excitation, ionization, and recombination in electron and ion encounters with partially ionized atomic systems, including the indirect contributions from processes involving autoionizing resonances. These fundamental collisional and electromagnetic interactions also provide particle and photon transport mechanisms. From the spectral perspective, the analysis of atomic radiative emission can reveal detailed information on the physical properties in the plasma environment, such as non-equilibrium electron and charge-state distributions as well as electric and magnetic field distributions. In this investigation, a reduced-density-matrix formulation is developed for the microscopic description of atomic electromagnetic interactions in the presence of environmental (collisional and radiative) relaxation and decoherence processes. Our central objective is a fundamental microscopic description of atomic electromagnetic processes, in which both bound-state and autoionization-resonance phenomena can be treated in a unified and self-consistent manner. The time-domain (equation-of-motion) and frequency-domain (resolvent-operator) formulations of the reduced-density-matrix approach are developed in a unified and self-consistent manner. This is necessary for our ultimate goal of a systematic and self-consistent treatment of non-equilibrium (possibly coherent) atomic-state kinetics and high-resolution (possibly overlapping) spectral-line shapes. We thereby propose the introduction of a generalized collisional-radiative atomic-state kinetics model based on a reduced-density-matrix formulation. It will become apparent that the full atomic data needs for the precise modeling of extreme non-equilibrium plasma environments extend beyond the conventional radiative-transition-probability and collisional-cross-section data sets.

Time-Dependent Density Functional Theory for Open Systems and Its Applications.

PubMed

Chen, Shuguang; Kwok, YanHo; Chen, GuanHua

2018-02-20

Photovoltaic devices, electrochemical cells, catalysis processes, light emitting diodes, scanning tunneling microscopes, molecular electronics, and related devices have one thing in common: open quantum systems where energy and matter are not conserved. Traditionally quantum chemistry is confined to isolated and closed systems, while quantum dissipation theory studies open quantum systems. The key quantity in quantum dissipation theory is the reduced system density matrix. As the reduced system density matrix is an O(M! × M!) matrix, where M is the number of the particles of the system of interest, quantum dissipation theory can only be employed to simulate systems of a few particles or degrees of freedom. It is thus important to combine quantum chemistry and quantum dissipation theory so that realistic open quantum systems can be simulated from first-principles. We have developed a first-principles method to simulate the dynamics of open electronic systems, the time-dependent density functional theory for open systems (TDDFT-OS). Instead of the reduced system density matrix, the key quantity is the reduced single-electron density matrix, which is an N × N matrix where N is the number of the atomic bases of the system of interest. As the dimension of the key quantity is drastically reduced, the TDDFT-OS can thus be used to simulate the dynamics of realistic open electronic systems and efficient numerical algorithms have been developed. As an application, we apply the method to study how quantum interference develops in a molecular transistor in time domain. We include electron-phonon interaction in our simulation and show that quantum interference in the given system is robust against nuclear vibration not only in the steady state but also in the transient dynamics. As another application, by combining TDDFT-OS with Ehrenfest dynamics, we study current-induced dissociation of water molecules under scanning tunneling microscopy and follow its time dependent dynamics. Given the rapid development in ultrafast experiments with atomic resolution in recent years, time dependent simulation of open electronic systems will be useful to gain insight and understanding of such experiments. This Account will mainly focus on the practical aspects of the TDDFT-OS method, describing the numerical implementation and demonstrating the method with applications.

A reformulation of the coupled perturbed self-consistent field equations entirely within a local atomic orbital density matrix-based scheme

NASA Astrophysics Data System (ADS)

Ochsenfeld, Christian; Head-Gordon, Martin

1997-05-01

To exploit the exponential decay found in numerical studies for the density matrix and its derivative with respect to nuclear displacements, we reformulate the coupled perturbed self-consistent field (CPSCF) equations and a quadratically convergent SCF (QCSCF) method for Hartree-Fock and density functional theory within a local density matrix-based scheme. Our D-CPSCF (density matrix-based CPSCF) and D-QCSCF schemes open the way for exploiting sparsity and to achieve asymptotically linear scaling of computational complexity with molecular size ( M), in case of D-CPSCF for all O( M) derivative densities. Furthermore, these methods are even for small molecules strongly competitive to conventional algorithms.

Thermalization and revivals after a quantum quench in conformal field theory.

PubMed

Cardy, John

2014-06-06

We consider a quantum quench in a finite system of length L described by a 1+1-dimensional conformal field theory (CFT), of central charge c, from a state with finite energy density corresponding to an inverse temperature β≪L. For times t such that ℓ/2

A sparse matrix-vector multiplication based algorithm for accurate density matrix computations on systems of millions of atoms

NASA Astrophysics Data System (ADS)

Ghale, Purnima; Johnson, Harley T.

2018-06-01

We present an efficient sparse matrix-vector (SpMV) based method to compute the density matrix P from a given Hamiltonian in electronic structure computations. Our method is a hybrid approach based on Chebyshev-Jackson approximation theory and matrix purification methods like the second order spectral projection purification (SP2). Recent methods to compute the density matrix scale as O(N) in the number of floating point operations but are accompanied by large memory and communication overhead, and they are based on iterative use of the sparse matrix-matrix multiplication kernel (SpGEMM), which is known to be computationally irregular. In addition to irregularity in the sparse Hamiltonian H, the nonzero structure of intermediate estimates of P depends on products of H and evolves over the course of computation. On the other hand, an expansion of the density matrix P in terms of Chebyshev polynomials is straightforward and SpMV based; however, the resulting density matrix may not satisfy the required constraints exactly. In this paper, we analyze the strengths and weaknesses of the Chebyshev-Jackson polynomials and the second order spectral projection purification (SP2) method, and propose to combine them so that the accurate density matrix can be computed using the SpMV computational kernel only, and without having to store the density matrix P. Our method accomplishes these objectives by using the Chebyshev polynomial estimate as the initial guess for SP2, which is followed by using sparse matrix-vector multiplications (SpMVs) to replicate the behavior of the SP2 algorithm for purification. We demonstrate the method on a tight-binding model system of an oxide material containing more than 3 million atoms. In addition, we also present the predicted behavior of our method when applied to near-metallic Hamiltonians with a wide energy spectrum.

Electronic properties of disordered Weyl semimetals at charge neutrality

NASA Astrophysics Data System (ADS)

Holder, Tobias; Huang, Chia-Wei; Ostrovsky, Pavel M.

2017-11-01

Weyl semimetals have been intensely studied as a three-dimensional realization of a Dirac-like excitation spectrum where the conduction bands and valence bands touch at isolated Weyl points in momentum space. Like in graphene, this property entails various peculiar electronic properties. However, recent theoretical studies have suggested that resonant scattering from rare regions can give rise to a nonzero density of states even at charge neutrality. Here, we give a detailed account of this effect and demonstrate how the semimetallic nature is suppressed at the lowest scales. To this end, we develop a self-consistent T -matrix approach to investigate the density of states beyond the limit of weak disorder. Our results show a nonvanishing density of states at the Weyl point, which exhibits a nonanalytic dependence on the impurity density. This unusually strong effect of rare regions leads to a revised estimate for the conductivity close to the Weyl point and emphasizes possible deviations from semimetallic behavior in dirty Weyl semimetals at charge neutrality even with very low impurity concentration.

Semiclassics for matrix Hamiltonians: The Gutzwiller trace formula with applications to graphene-type systems

NASA Astrophysics Data System (ADS)

Vogl, M.; Pankratov, O.; Shallcross, S.

2017-07-01

We present a tractable and physically transparent semiclassical theory of matrix-valued Hamiltonians, i.e., those that describe quantum systems with internal degrees of freedoms, based on a generalization of the Gutzwiller trace formula for a n ×n dimensional Hamiltonian H (p ̂,q ̂) . The classical dynamics is governed by n Hamilton-Jacobi (HJ) equations that act in a phase space endowed with a classical Berry curvature encoding anholonomy in the parallel transport of the eigenvectors of H (p ,q ) ; these vectors describe the internal structure of the semiclassical particles. At the O (ℏ1) level and for nondegenerate HJ systems, this curvature results in an additional semiclassical phase composed of (i) a Berry phase and (ii) a dynamical phase resulting from the classical particles "moving through the Berry curvature". We show that the dynamical part of this semiclassical phase will, generally, be zero only for the case in which the Berry phase is topological (i.e., depends only on the winding number). We illustrate the method by calculating the Landau spectrum for monolayer graphene, the four-band model of AB bilayer graphene, and for a more complicated matrix Hamiltonian describing the silicene band structure. Finally, we apply our method to an inhomogeneous system consisting of a strain engineered one-dimensional moiré in bilayer graphene, finding localized states near the Dirac point that arise from electron trapping in a semiclassical moiré potential. The semiclassical density of states of these localized states we show to be in perfect agreement with an exact quantum mechanical calculation of the density of states.

Thermal Fatigue Limitations of Continuous Fiber Metal Matrix Composites

NASA Technical Reports Server (NTRS)

Halford, Gary R.; Arya, Vinod K.

1997-01-01

The potential structural benefits of unidirectional, continuous-fiber, metal matrix composites (MMC's) are legendary. When compared to their monolithic matrices, MMC's possess superior properties such as higher stiffness and tensile strength, and lower coefficient of thermal expansion in the direction of the reinforcing fibers. As an added bonus, the MMC density will be lower if the fibers are less dense than the matrix matErial they replace. The potential has been demonstrated unequivocally both analytically and experimentally, especially at ambient temperatures. Successes prompted heavily-funded National efforts within the United States (USAF and NASA) and elsewhere to extend the promise of MMC's into the temperature regime wherein creep, stress relaxation, oxidation, and thermal fatigue damage mechanisms lurk. This is the very regime for which alternative high-temperature materials are becoming mandatory, since further enhancement of state- of-the-art monolithic alloys is rapidly approaching a point of diminishing returns.

Symmetry-broken states in a system of interacting bosons on a two-leg ladder with a uniform Abelian gauge field

NASA Astrophysics Data System (ADS)

Greschner, S.; Piraud, M.; Heidrich-Meisner, F.; McCulloch, I. P.; Schollwöck, U.; Vekua, T.

2016-12-01

We study the quantum phases of bosons with repulsive contact interactions on a two-leg ladder in the presence of a uniform Abelian gauge field. The model realizes many interesting states, including Meissner phases, vortex fluids, vortex lattices, charge density waves, and the biased-ladder phase. Our work focuses on the subset of these states that breaks a discrete symmetry. We use density matrix renormalization group simulations to demonstrate the existence of three vortex-lattice states at different vortex densities and we characterize the phase transitions from these phases into neighboring states. Furthermore, we provide an intuitive explanation of the chiral-current reversal effect that is tied to some of these vortex lattices. We also study a charge-density-wave state that exists at 1/4 particle filling at large interaction strengths and flux values close to half a flux quantum. By changing the system parameters, this state can transition into a completely gapped vortex-lattice Mott-insulating state. We elucidate the stability of these phases against nearest-neighbor interactions on the rungs of the ladder relevant for experimental realizations with a synthetic lattice dimension. A charge-density-wave state at 1/3 particle filling can be stabilized for flux values close to half a flux quantum and for very strong on-site interactions in the presence of strong repulsion on the rungs. Finally, we analytically describe the emergence of these phases in the low-density regime, and, in particular, we obtain the boundaries of the biased-ladder phase, i.e., the phase that features a density imbalance between the legs. We make contact with recent quantum-gas experiments that realized related models and discuss signatures of these quantum states in experimentally accessible observables.

Multireference configuration interaction theory using cumulant reconstruction with internal contraction of density matrix renormalization group wave function.

PubMed

Saitow, Masaaki; Kurashige, Yuki; Yanai, Takeshi

2013-07-28

We report development of the multireference configuration interaction (MRCI) method that can use active space scalable to much larger size references than has previously been possible. The recent development of the density matrix renormalization group (DMRG) method in multireference quantum chemistry offers the ability to describe static correlation in a large active space. The present MRCI method provides a critical correction to the DMRG reference by including high-level dynamic correlation through the CI treatment. When the DMRG and MRCI theories are combined (DMRG-MRCI), the full internal contraction of the reference in the MRCI ansatz, including contraction of semi-internal states, plays a central role. However, it is thought to involve formidable complexity because of the presence of the five-particle rank reduced-density matrix (RDM) in the Hamiltonian matrix elements. To address this complexity, we express the Hamiltonian matrix using commutators, which allows the five-particle rank RDM to be canceled out without any approximation. Then we introduce an approximation to the four-particle rank RDM by using a cumulant reconstruction from lower-particle rank RDMs. A computer-aided approach is employed to derive the exceedingly complex equations of the MRCI in tensor-contracted form and to implement them into an efficient parallel computer code. This approach extends to the size-consistency-corrected variants of MRCI, such as the MRCI+Q, MR-ACPF, and MR-AQCC methods. We demonstrate the capability of the DMRG-MRCI method in several benchmark applications, including the evaluation of single-triplet gap of free-base porphyrin using 24 active orbitals.

Detection of Matrix Crack Density of CFRP using an Electrical Potential Change Method with Multiple Probes

NASA Astrophysics Data System (ADS)

Todoroki, Akira; Omagari, Kazuomi

Carbon Fiber Reinforced Plastic (CFRP) laminates are adopted for fuel tank structures of next generation space rockets or automobiles. Matrix cracks may cause fuel leak or trigger fatigue damage. A monitoring system of the matrix crack density is required. The authors have developed an electrical resistance change method for the monitoring of delamination cracks in CFRP laminates. Reinforcement fibers are used as a self-sensing system. In the present study, the electric potential method is adopted for matrix crack density monitoring. Finite element analysis (FEA) was performed to investigate the possibility of monitoring matrix crack density using multiple electrodes mounted on a single surface of a specimen. The FEA reveals the matrix crack density increases electrical resistance for a target segment between electrodes. Experimental confirmation was also performed using cross-ply laminates. Eight electrodes were mounted on a single surface of a specimen using silver paste after polishing of the specimen surface with sandpaper. The two outermost electrodes applied electrical current, and the inner electrodes measured electric voltage changes. The slope of electrical resistance during reloading is revealed to be an appropriate index for the detection of matrix crack density.

Communication: Spin densities within a unitary group based spin-adapted open-shell coupled-cluster theory: Analytic evaluation of isotropic hyperfine-coupling constants for the combinatoric open-shell coupled-cluster scheme

DOE Office of Scientific and Technical Information (OSTI.GOV)

Datta, Dipayan, E-mail: datta.dipayan@gmail.com; Gauss, Jürgen, E-mail: gauss@uni-mainz.de

We report analytical calculations of isotropic hyperfine-coupling constants in radicals using a spin-adapted open-shell coupled-cluster theory, namely, the unitary group based combinatoric open-shell coupled-cluster (COSCC) approach within the singles and doubles approximation. A scheme for the evaluation of the one-particle spin-density matrix required in these calculations is outlined within the spin-free formulation of the COSCC approach. In this scheme, the one-particle spin-density matrix for an open-shell state with spin S and M{sub S} = + S is expressed in terms of the one- and two-particle spin-free (charge) density matrices obtained from the Lagrangian formulation that is used for calculating themore » analytic first derivatives of the energy. Benchmark calculations are presented for NO, NCO, CH{sub 2}CN, and two conjugated π-radicals, viz., allyl and 1-pyrrolyl in order to demonstrate the performance of the proposed scheme.« less

Measurement of the entanglement of two superconducting qubits via state tomography.

PubMed

Steffen, Matthias; Ansmann, M; Bialczak, Radoslaw C; Katz, N; Lucero, Erik; McDermott, R; Neeley, Matthew; Weig, E M; Cleland, A N; Martinis, John M

2006-09-08

Demonstration of quantum entanglement, a key resource in quantum computation arising from a nonclassical correlation of states, requires complete measurement of all states in varying bases. By using simultaneous measurement and state tomography, we demonstrated entanglement between two solid-state qubits. Single qubit operations and capacitive coupling between two super-conducting phase qubits were used to generate a Bell-type state. Full two-qubit tomography yielded a density matrix showing an entangled state with fidelity up to 87%. Our results demonstrate a high degree of unitary control of the system, indicating that larger implementations are within reach.

Extending density functional embedding theory for covalently bonded systems.

PubMed

Yu, Kuang; Carter, Emily A

2017-12-19

Quantum embedding theory aims to provide an efficient solution to obtain accurate electronic energies for systems too large for full-scale, high-level quantum calculations. It adopts a hierarchical approach that divides the total system into a small embedded region and a larger environment, using different levels of theory to describe each part. Previously, we developed a density-based quantum embedding theory called density functional embedding theory (DFET), which achieved considerable success in metals and semiconductors. In this work, we extend DFET into a density-matrix-based nonlocal form, enabling DFET to study the stronger quantum couplings between covalently bonded subsystems. We name this theory density-matrix functional embedding theory (DMFET), and we demonstrate its performance in several test examples that resemble various real applications in both chemistry and biochemistry. DMFET gives excellent results in all cases tested thus far, including predicting isomerization energies, proton transfer energies, and highest occupied molecular orbital-lowest unoccupied molecular orbital gaps for local chromophores. Here, we show that DMFET systematically improves the quality of the results compared with the widely used state-of-the-art methods, such as the simple capped cluster model or the widely used ONIOM method.

Local entanglement entropy of fermions as a marker of quantum phase transition in the one-dimensional Hubbard model

NASA Astrophysics Data System (ADS)

Cha, Min-Chul; Chung, Myung-Hoon

2018-05-01

We study quantum phase transition of interacting fermions by measuring the local entanglement entropy in the one-dimensional Hubbard model. The reduced density matrices for blocks of a few sites are constructed from the ground state wave function in infinite systems by adopting the matrix product state representation where time-evolving block decimations are performed to obtain the lowest energy states. The local entanglement entropy, constructed from the reduced density matrices, as a function of the chemical potential shows clear signatures of the Mott transition. The value of the central charge, numerically determined from the universal properties of the local entanglement entropy, confirms that the transition is caused by the suppression of the charge degrees of freedom.

Majorana edge States in atomic wires coupled by pair hopping.

PubMed

Kraus, Christina V; Dalmonte, Marcello; Baranov, Mikhail A; Läuchli, Andreas M; Zoller, P

2013-10-25

We present evidence for Majorana edge states in a number conserving theory describing a system of spinless fermions on two wires that are coupled by pair hopping. Our analysis is based on a combination of a qualitative low energy approach and numerical techniques using the density matrix renormalization group. In addition, we discuss an experimental realization of pair-hopping interactions in cold atom gases confined in optical lattices.

Free energy and phase transition of the matrix model on a plane wave

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hadizadeh, Shirin; Ramadanovic, Bojan; Semenoff, Gordon W.

2005-03-15

It has recently been observed that the weakly coupled plane-wave matrix model has a density of states which grows exponentially at high energy. This implies that the model has a phase transition. The transition appears to be of first order. However, its exact nature is sensitive to interactions. In this paper, we analyze the effect of interactions by computing the relevant parts of the effective potential for the Polyakov loop operator in the finite temperature plane-wave matrix model to three-loop order. We show that the phase transition is indeed of first order. We also compute the correction to the Hagedornmore » temperature to order two loops.« less

Random pure states: Quantifying bipartite entanglement beyond the linear statistics.

PubMed

Vivo, Pierpaolo; Pato, Mauricio P; Oshanin, Gleb

2016-05-01

We analyze the properties of entangled random pure states of a quantum system partitioned into two smaller subsystems of dimensions N and M. Framing the problem in terms of random matrices with a fixed-trace constraint, we establish, for arbitrary N≤M, a general relation between the n-point densities and the cross moments of the eigenvalues of the reduced density matrix, i.e., the so-called Schmidt eigenvalues, and the analogous functionals of the eigenvalues of the Wishart-Laguerre ensemble of the random matrix theory. This allows us to derive explicit expressions for two-level densities, and also an exact expression for the variance of von Neumann entropy at finite N,M. Then, we focus on the moments E{K^{a}} of the Schmidt number K, the reciprocal of the purity. This is a random variable supported on [1,N], which quantifies the number of degrees of freedom effectively contributing to the entanglement. We derive a wealth of analytical results for E{K^{a}} for N=2 and 3 and arbitrary M, and also for square N=M systems by spotting for the latter a connection with the probability P(x_{min}^{GUE}≥sqrt[2N]ξ) that the smallest eigenvalue x_{min}^{GUE} of an N×N matrix belonging to the Gaussian unitary ensemble is larger than sqrt[2N]ξ. As a by-product, we present an exact asymptotic expansion for P(x_{min}^{GUE}≥sqrt[2N]ξ) for finite N as ξ→∞. Our results are corroborated by numerical simulations whenever possible, with excellent agreement.

Gradient-based stochastic estimation of the density matrix

NASA Astrophysics Data System (ADS)

Wang, Zhentao; Chern, Gia-Wei; Batista, Cristian D.; Barros, Kipton

2018-03-01

Fast estimation of the single-particle density matrix is key to many applications in quantum chemistry and condensed matter physics. The best numerical methods leverage the fact that the density matrix elements f(H)ij decay rapidly with distance rij between orbitals. This decay is usually exponential. However, for the special case of metals at zero temperature, algebraic decay of the density matrix appears and poses a significant numerical challenge. We introduce a gradient-based probing method to estimate all local density matrix elements at a computational cost that scales linearly with system size. For zero-temperature metals, the stochastic error scales like S-(d+2)/2d, where d is the dimension and S is a prefactor to the computational cost. The convergence becomes exponential if the system is at finite temperature or is insulating.

Decoherence and Noise in Spin-based Solid State Quantum Computers. Approximation-Free Numerical Simulations

DTIC Science & Technology

2007-07-21

the spin coherent states P-representation", Conference on Quantum Computations and Many- Body Systems, February 2006, Key West, FL 9. B. N. Harmon...solid-state spin-based qubit systems was the focus of our project. Since decoherence is a complex many- body non-equilibrium process, and its...representation of the density matrix, see Sec. 3 below). This work prompted J. Taylor from the experimental group of C. Marcus and M. Lukin (funded by

Charge-transfer contributions to the excitonic coupling matrix element in BODIPY-based energy transfer cassettes

NASA Astrophysics Data System (ADS)

Spiegel, J. Dominik; Lyskov, Igor; Kleinschmidt, Martin; Marian, Christel M.

2017-01-01

BODIPY-based dyads serve as model systems for the investigation of excitation energy transfer (EET). Through-space EET is brought about by direct and exchange interactions between the transition densities of donor and acceptor localized states. The presence of a molecular linker gives rise to additional charge transfer (CT) contributions. Here, we present a novel approach for the calculation of the excitonic coupling matrix element (ECME) including CT contributions which is based on supermolecular one-electron transition density matrices (STD). The validity of the approach is assessed for a model system of two π -stacked ethylene molecules at varying intermolecular separation. Wave functions and electronic excitation energies of five EET cassettes comprising anthracene as exciton donor and BODIPY as exciton acceptor are obtained by the redesigned combined density functional theory and multireference configuration interaction (DFT/MRCI-R) method. CT contributions to the ECME are shown to be important in the covalently linked EET cassettes.

Surface Snow Density of East Antarctica Derived from In-Situ Observations

NASA Astrophysics Data System (ADS)

Tian, Y.; Zhang, S.; Du, W.; Chen, J.; Xie, H.; Tong, X.; Li, R.

2018-04-01

Models based on physical principles or semi-empirical parameterizations have used to compute the firn density, which is essential for the study of surface processes in the Antarctic ice sheet. However, parameterization of surface snow density is often challenged by the description of detailed local characterization. In this study we propose to generate a surface density map for East Antarctica from all the filed observations that are available. Considering that the observations are non-uniformly distributed around East Antarctica, obtained by different methods, and temporally inhomogeneous, the field observations are used to establish an initial density map with a grid size of 30 × 30 km2 in which the observations are averaged at a temporal scale of five years. We then construct an observation matrix with its columns as the map grids and rows as the temporal scale. If a site has an unknown density value for a period, we will set it to 0 in the matrix. In order to construct the main spatial and temple information of surface snow density matrix we adopt Empirical Orthogonal Function (EOF) method to decompose the observation matrix and only take first several lower-order modes, because these modes already contain most information of the observation matrix. However, there are a lot of zeros in the matrix and we solve it by using matrix completion algorithm, and then we derive the time series of surface snow density at each observation site. Finally, we can obtain the surface snow density by multiplying the modes interpolated by kriging with the corresponding amplitude of the modes. Comparative analysis have done between our surface snow density map and model results. The above details will be introduced in the paper.

Topological entanglement Rényi entropy and reduced density matrix structure.

PubMed

Flammia, Steven T; Hamma, Alioscia; Hughes, Taylor L; Wen, Xiao-Gang

2009-12-31

We generalize the topological entanglement entropy to a family of topological Rényi entropies parametrized by a parameter alpha, in an attempt to find new invariants for distinguishing topologically ordered phases. We show that, surprisingly, all topological Rényi entropies are the same, independent of alpha for all nonchiral topological phases. This independence shows that topologically ordered ground-state wave functions have reduced density matrices with a certain simple structure, and no additional universal information can be extracted from the entanglement spectrum.

Topological Entanglement Rényi Entropy and Reduced Density Matrix Structure

NASA Astrophysics Data System (ADS)

Flammia, Steven T.; Hamma, Alioscia; Hughes, Taylor L.; Wen, Xiao-Gang

2009-12-01

We generalize the topological entanglement entropy to a family of topological Rényi entropies parametrized by a parameter α, in an attempt to find new invariants for distinguishing topologically ordered phases. We show that, surprisingly, all topological Rényi entropies are the same, independent of α for all nonchiral topological phases. This independence shows that topologically ordered ground-state wave functions have reduced density matrices with a certain simple structure, and no additional universal information can be extracted from the entanglement spectrum.

Geometric phase of mixed states for three-level open systems

NASA Astrophysics Data System (ADS)

Jiang, Yanyan; Ji, Y. H.; Xu, Hualan; Hu, Li-Yun; Wang, Z. S.; Chen, Z. Q.; Guo, L. P.

2010-12-01

Geometric phase of mixed state for three-level open system is defined by establishing in connecting density matrix with nonunit vector ray in a three-dimensional complex Hilbert space. Because the geometric phase depends only on the smooth curve on this space, it is formulated entirely in terms of geometric structures. Under the limiting of pure state, our approach is in agreement with the Berry phase, Pantcharatnam phase, and Aharonov and Anandan phase. We find that, furthermore, the Berry phase of mixed state correlated to population inversions of three-level open system.

Effects of increased collagen-matrix density on the mechanical properties and in vivo absorbability of hydroxyapatite-collagen composites as artificial bone materials.

PubMed

Yunoki, Shunji; Sugiura, Hiroaki; Ikoma, Toshiyuki; Kondo, Eiji; Yasuda, Kazunori; Tanaka, Junzo

2011-02-01

The aim of this study was to evaluate the effects of increased collagen-matrix density on the mechanical properties and in vivo absorbability of porous hydroxyapatite (HAp)-collagen composites as artificial bone materials. Seven types of porous HAp-collagen composites were prepared from HAp nanocrystals and dense collagen fibrils. Their densities and HAp/collagen weight ratios ranged from 122 to 331 mg cm⁻³ and from 20/80 to 80/20, respectively. The flexural modulus and strength increased with an increase in density, reaching 2.46 ± 0.48 and 0.651 ± 0.103 MPa, respectively. The porous composites with a higher collagen-matrix density exhibited much higher mechanical properties at the same densities, suggesting that increasing the collagen-matrix density is an effective way of improving the mechanical properties. It was also suggested that other structural factors in addition to collagen-matrix density are required to achieve bone-like mechanical properties. The in vivo absorbability of the composites was investigated in bone defects of rabbit femurs, demonstrating that the absorption rate decreased with increases in the composite density. An exhaustive increase in density is probably limited by decreases in absorbability as artificial bones.

Variational calculation of second-order reduced density matrices by strong N-representability conditions and an accurate semidefinite programming solver.

PubMed

Nakata, Maho; Braams, Bastiaan J; Fujisawa, Katsuki; Fukuda, Mituhiro; Percus, Jerome K; Yamashita, Makoto; Zhao, Zhengji

2008-04-28

The reduced density matrix (RDM) method, which is a variational calculation based on the second-order reduced density matrix, is applied to the ground state energies and the dipole moments for 57 different states of atoms, molecules, and to the ground state energies and the elements of 2-RDM for the Hubbard model. We explore the well-known N-representability conditions (P, Q, and G) together with the more recent and much stronger T1 and T2(') conditions. T2(') condition was recently rederived and it implies T2 condition. Using these N-representability conditions, we can usually calculate correlation energies in percentage ranging from 100% to 101%, whose accuracy is similar to CCSD(T) and even better for high spin states or anion systems where CCSD(T) fails. Highly accurate calculations are carried out by handling equality constraints and/or developing multiple precision arithmetic in the semidefinite programming (SDP) solver. Results show that handling equality constraints correctly improves the accuracy from 0.1 to 0.6 mhartree. Additionally, improvements by replacing T2 condition with T2(') condition are typically of 0.1-0.5 mhartree. The newly developed multiple precision arithmetic version of SDP solver calculates extraordinary accurate energies for the one dimensional Hubbard model and Be atom. It gives at least 16 significant digits for energies, where double precision calculations gives only two to eight digits. It also provides physically meaningful results for the Hubbard model in the high correlation limit.

Density functional theory study of defects in unalloyed δ-Pu

DOE PAGES

Hernandez, S. C.; Freibert, F. J.; Wills, J. M.

2017-03-19

Using density functional theory, we explore in this paper various classical point and complex defects within the face-centered cubic unalloyed δ-plutonium matrix that are potentially induced from self-irradiation. For plutonium only defects, the most energetically stable defect is a distorted split-interstitial. Gallium, the δ-phase stabilizer, is thermodynamically stable as a substitutional defect, but becomes unstable when participating in a complex defect configuration. Finally, complex uranium defects may thermodynamically exist as uranium substitutional with neighboring plutonium interstitial and stabilization of uranium within the lattice is shown via partial density of states and charge density difference plots to be 5f hybridization betweenmore » uranium and plutonium.« less

Density functional theory study of defects in unalloyed δ-Pu

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hernandez, S. C.; Freibert, F. J.; Wills, J. M.

Using density functional theory, we explore in this paper various classical point and complex defects within the face-centered cubic unalloyed δ-plutonium matrix that are potentially induced from self-irradiation. For plutonium only defects, the most energetically stable defect is a distorted split-interstitial. Gallium, the δ-phase stabilizer, is thermodynamically stable as a substitutional defect, but becomes unstable when participating in a complex defect configuration. Finally, complex uranium defects may thermodynamically exist as uranium substitutional with neighboring plutonium interstitial and stabilization of uranium within the lattice is shown via partial density of states and charge density difference plots to be 5f hybridization betweenmore » uranium and plutonium.« less

Natural occupation numbers: when do they vanish?

PubMed

Giesbertz, K J H; van Leeuwen, R

2013-09-14

The non-vanishing of the natural orbital (NO) occupation numbers of the one-particle density matrix of many-body systems has important consequences for the existence of a density matrix-potential mapping for nonlocal potentials in reduced density matrix functional theory and for the validity of the extended Koopmans' theorem. On the basis of Weyl's theorem we give a connection between the differentiability properties of the ground state wavefunction and the rate at which the natural occupations approach zero when ordered as a descending series. We show, in particular, that the presence of a Coulomb cusp in the wavefunction leads, in general, to a power law decay of the natural occupations, whereas infinitely differentiable wavefunctions typically have natural occupations that decay exponentially. We analyze for a number of explicit examples of two-particle systems that in case the wavefunction is non-analytic at its spatial diagonal (for instance, due to the presence of a Coulomb cusp) the natural orbital occupations are non-vanishing. We further derive a more general criterium for the non-vanishing of NO occupations for two-particle wavefunctions with a certain separability structure. On the basis of this criterium we show that for a two-particle system of harmonically confined electrons with a Coulombic interaction (the so-called Hookium) the natural orbital occupations never vanish.

A real-space stochastic density matrix approach for density functional electronic structure.

PubMed

Beck, Thomas L

2015-12-21

The recent development of real-space grid methods has led to more efficient, accurate, and adaptable approaches for large-scale electrostatics and density functional electronic structure modeling. With the incorporation of multiscale techniques, linear-scaling real-space solvers are possible for density functional problems if localized orbitals are used to represent the Kohn-Sham energy functional. These methods still suffer from high computational and storage overheads, however, due to extensive matrix operations related to the underlying wave function grid representation. In this paper, an alternative stochastic method is outlined that aims to solve directly for the one-electron density matrix in real space. In order to illustrate aspects of the method, model calculations are performed for simple one-dimensional problems that display some features of the more general problem, such as spatial nodes in the density matrix. This orbital-free approach may prove helpful considering a future involving increasingly parallel computing architectures. Its primary advantage is the near-locality of the random walks, allowing for simultaneous updates of the density matrix in different regions of space partitioned across the processors. In addition, it allows for testing and enforcement of the particle number and idempotency constraints through stabilization of a Feynman-Kac functional integral as opposed to the extensive matrix operations in traditional approaches.

Strongly correlated fermions after a quantum quench.

PubMed

Manmana, S R; Wessel, S; Noack, R M; Muramatsu, A

2007-05-25

Using the adaptive time-dependent density-matrix renormalization group method, we study the time evolution of strongly correlated spinless fermions on a one-dimensional lattice after a sudden change of the interaction strength. For certain parameter values, two different initial states (e.g., metallic and insulating) lead to observables which become indistinguishable after relaxation. We find that the resulting quasistationary state is nonthermal. This result holds for both integrable and nonintegrable variants of the system.

BRST technique for the cosmological density matrix

NASA Astrophysics Data System (ADS)

Barvinsky, A. O.

2013-10-01

The microcanonical density matrix in closed cosmology has a natural definition as a projector on the space of solutions of Wheeler-DeWitt equations, which is motivated by the absence of global non-vanishing charges and energy in spatially closed gravitational systems. Using the BRST/BFV formalism in relativistic phase space of gauge and ghost variables we derive the path integral representation for this projector and the relevant statistical sum. This derivation circumvents the difficulties associated with the open algebra of noncommutative quantum Dirac constraints and the construction/regularization of the physical inner product in the subspace of BRS singlets. This inner product is achieved via the Batalin-Marnelius gauge fixing in the space of BRS-invariant states, which in its turn is shown to be a result of truncation of the BRST/BFV formalism to the "matter" sector of relativistic phase space.

Semiclassical propagation: Hilbert space vs. Wigner representation

NASA Astrophysics Data System (ADS)

Gottwald, Fabian; Ivanov, Sergei D.

2018-03-01

A unified viewpoint on the van Vleck and Herman-Kluk propagators in Hilbert space and their recently developed counterparts in Wigner representation is presented. Based on this viewpoint, the Wigner Herman-Kluk propagator is conceptually the most general one. Nonetheless, the respective semiclassical expressions for expectation values in terms of the density matrix and the Wigner function are mathematically proven here to coincide. The only remaining difference is a mere technical flexibility of the Wigner version in choosing the Gaussians' width for the underlying coherent states beyond minimal uncertainty. This flexibility is investigated numerically on prototypical potentials and it turns out to provide neither qualitative nor quantitative improvements. Given the aforementioned generality, utilizing the Wigner representation for semiclassical propagation thus leads to the same performance as employing the respective most-developed (Hilbert-space) methods for the density matrix.

Relative Contribution of Matrix Structure, Patch Resources and Management to the Local Densities of Two Large Blue Butterfly Species

PubMed Central

Skórka, Piotr; Nowicki, Piotr; Bonk, Maciej; Król, Wiesław; Szpiłyk, Damian; Woyciechowski, Michal

2016-01-01

The type of matrix, the landscape surrounding habitat patches, may determine the distribution and function of local populations. However, the matrix is often heterogeneous, and its various components may differentially contribute to metapopulation processes at different spatial scales, a phenomenon that has rarely been investigated. The aim of this study was to estimate the relative importance of matrix composition and spatial scale, habitat quality, and management intensity on the occurrence and density of local populations of two endangered large blue butterflies: Phengaris teleius and P. nausithous. Presence and abundance data were assessed over two years, 2011–12, in 100 local patches within two heterogeneous regions (near Kraków and Tarnów, southern Poland). The matrix composition was analyzed at eight spatial scales. We observed high occupancy rates in both species, regions and years. With the exception of area and isolation, almost all of the matrix components contributed to Phengaris sp. densities. The different matrix components acted at different spatial scales (grassland cover within 4 and 3 km, field cover within 0.4 and 0.3 km and water cover within 4 km radii for P. teleius and P. nausithous, respectively) and provided the highest independent contribution to the butterfly densities. Additionally, the effects of a 0.4 km radius of forest cover and a food plant cover on P. teleius, and a 1 km radius of settlement cover and management intensity on P. nausithous densities were observed. Contrary to former studies we conclude that the matrix heterogeneity and spatial scale rather than general matrix type are of relevance for densities of butterflies. Conservation strategies for these umbrella species should concentrate on maintaining habitat quality and managing matrix composition at the most appropriate spatial scales. PMID:28005942

Relative Contribution of Matrix Structure, Patch Resources and Management to the Local Densities of Two Large Blue Butterfly Species.

PubMed

Kajzer-Bonk, Joanna; Skórka, Piotr; Nowicki, Piotr; Bonk, Maciej; Król, Wiesław; Szpiłyk, Damian; Woyciechowski, Michal

2016-01-01

The type of matrix, the landscape surrounding habitat patches, may determine the distribution and function of local populations. However, the matrix is often heterogeneous, and its various components may differentially contribute to metapopulation processes at different spatial scales, a phenomenon that has rarely been investigated. The aim of this study was to estimate the relative importance of matrix composition and spatial scale, habitat quality, and management intensity on the occurrence and density of local populations of two endangered large blue butterflies: Phengaris teleius and P. nausithous. Presence and abundance data were assessed over two years, 2011-12, in 100 local patches within two heterogeneous regions (near Kraków and Tarnów, southern Poland). The matrix composition was analyzed at eight spatial scales. We observed high occupancy rates in both species, regions and years. With the exception of area and isolation, almost all of the matrix components contributed to Phengaris sp. densities. The different matrix components acted at different spatial scales (grassland cover within 4 and 3 km, field cover within 0.4 and 0.3 km and water cover within 4 km radii for P. teleius and P. nausithous, respectively) and provided the highest independent contribution to the butterfly densities. Additionally, the effects of a 0.4 km radius of forest cover and a food plant cover on P. teleius, and a 1 km radius of settlement cover and management intensity on P. nausithous densities were observed. Contrary to former studies we conclude that the matrix heterogeneity and spatial scale rather than general matrix type are of relevance for densities of butterflies. Conservation strategies for these umbrella species should concentrate on maintaining habitat quality and managing matrix composition at the most appropriate spatial scales.

On the Role of Processing Parameters in Producing Recycled Aluminum AA6061 Based Metal Matrix Composite (MMC-AlR) Prepared Using Hot Press Forging (HPF) Process

PubMed Central

Ahmad, Azlan; Lajis, Mohd Amri

2017-01-01

Solid-state recycling, which involves the direct recycling of scrap metal into bulk material using severe plastic deformation, has emerged as a potential alternative to the conventional remelting and recycling techniques. Hot press forging has been identified as a sustainable direct recycling technique that has fewer steps and maintains excellent material performance. An experimental investigation was conducted to explore the hardness and density of a recycled aluminum-based metal matrix composite by varying operating temperature and holding time. A mixture of recycled aluminum, AA6061, and aluminum oxide were simultaneously heated to 430, 480, and 530 °C and forged for 60, 90, and 120 min. We found a positive increase in microhardness and density for all composites. The hardness increased approximately 33.85%, while density improved by about 15.25% whenever the temperature or the holding time were increased. Based on qualitative analysis, the composite endures substantial plastic deformation due to the presence of hardness properties due to the aluminum oxide embedded in the aluminum matrix. These increases were significantly affected by the operating temperature; the holding time also had a subordinate role in enhancing the metal matrix composite properties. Furthermore, in an effort to curb the shortage of primary resources, this study reviewed the promising performance of secondary resources produced by using recycled aluminum and aluminum oxide as the base matrix and reinforcement constituent, respectively. This study is an outline for machining practitioners and the manufacturing industry to help increase industry sustainability with the aim of preserving the Earth for our community in the future. PMID:28925963

On the Role of Processing Parameters in Producing Recycled Aluminum AA6061 Based Metal Matrix Composite (MMC-AlR) Prepared Using Hot Press Forging (HPF) Process.

PubMed

Ahmad, Azlan; Lajis, Mohd Amri; Yusuf, Nur Kamilah

2017-09-19

Solid-state recycling, which involves the direct recycling of scrap metal into bulk material using severe plastic deformation, has emerged as a potential alternative to the conventional remelting and recycling techniques. Hot press forging has been identified as a sustainable direct recycling technique that has fewer steps and maintains excellent material performance. An experimental investigation was conducted to explore the hardness and density of a recycled aluminum-based metal matrix composite by varying operating temperature and holding time. A mixture of recycled aluminum, AA6061, and aluminum oxide were simultaneously heated to 430, 480, and 530 °C and forged for 60, 90, and 120 min. We found a positive increase in microhardness and density for all composites. The hardness increased approximately 33.85%, while density improved by about 15.25% whenever the temperature or the holding time were increased. Based on qualitative analysis, the composite endures substantial plastic deformation due to the presence of hardness properties due to the aluminum oxide embedded in the aluminum matrix. These increases were significantly affected by the operating temperature; the holding time also had a subordinate role in enhancing the metal matrix composite properties. Furthermore, in an effort to curb the shortage of primary resources, this study reviewed the promising performance of secondary resources produced by using recycled aluminum and aluminum oxide as the base matrix and reinforcement constituent, respectively. This study is an outline for machining practitioners and the manufacturing industry to help increase industry sustainability with the aim of preserving the Earth for our community in the future.

Water in the presence of inert Lennard-Jones obstacles

NASA Astrophysics Data System (ADS)

Kurtjak, Mario; Urbic, Tomaz

2014-04-01

Water confined by the presence of a 'sea' of inert obstacles was examined. In the article, freely mobile two-dimensional Mercedes-Benz (MB) water put to a disordered, but fixed, matrix of Lennard-Jones disks was studied by the Monte Carlo computer simulations. For the MB water molecules in the matrix of Lennard-Jones disks, we explored the structures, hydrogen-bond-network formation and thermodynamics as a function of temperature and size and density of matrix particles. We found that the structure of model water is perturbed by the presence of the obstacles. Density of confined water, which was in equilibrium with the bulk water, was smaller than the density of the bulk water and the temperature dependence of the density of absorbed water did not show the density anomaly in the studied temperature range. The behaviour observed as a consequence of confinement is similar to that of increasing temperature, which can for a matrix lead to a process similar to capillary evaporation. At the same occupancy of space, smaller matrix molecules cause higher destruction effect on the absorbed water molecules than the bigger ones. We have also tested the hypothesis that at low matrix densities the obstacles induce an increased ordering and 'hydrogen bonding' of the MB model molecules, relative to pure fluid, while at high densities the obstacles reduce MB water structuring, as they prevent the fluid to form good 'hydrogen-bonding' networks. However, for the size of matrix molecules similar to that of water, we did not observe this effect.

Asymptotic analysis of the density of states in random matrix models associated with a slowly decaying weight

NASA Astrophysics Data System (ADS)

Kuijlaars, A. B. J.

2001-08-01

The asymptotic behavior of polynomials that are orthogonal with respect to a slowly decaying weight is very different from the asymptotic behavior of polynomials that are orthogonal with respect to a Freud-type weight. While the latter has been extensively studied, much less is known about the former. Following an earlier investigation into the zero behavior, we study here the asymptotics of the density of states in a unitary ensemble of random matrices with a slowly decaying weight. This measure is also naturally connected with the orthogonal polynomials. It is shown that, after suitable rescaling, the weak limit is the same as the weak limit of the rescaled zeros.

Quantum Jeffreys prior for displaced squeezed thermal states

NASA Astrophysics Data System (ADS)

Kwek, L. C.; Oh, C. H.; Wang, Xiang-Bin

1999-09-01

It is known that, by extending the equivalence of the Fisher information matrix to its quantum version, the Bures metric, the quantum Jeffreys prior can be determined from the volume element of the Bures metric. We compute the Bures metric for the displaced squeezed thermal state and analyse the quantum Jeffreys prior and its marginal probability distributions. To normalize the marginal probability density function, it is necessary to provide a range of values of the squeezing parameter or the inverse temperature. We find that if the range of the squeezing parameter is kept narrow, there are significant differences in the marginal probability density functions in terms of the squeezing parameters for the displaced and undisplaced situations. However, these differences disappear as the range increases. Furthermore, marginal probability density functions against temperature are very different in the two cases.

Communication: Wigner functions in action-angle variables, Bohr-Sommerfeld quantization, the Heisenberg correspondence principle, and a symmetrical quasi-classical approach to the full electronic density matrix

DOE PAGES

Miller, William H.; Cotton, Stephen J.

2016-08-28

It is pointed out that the classical phase space distribution in action-angle (a-a) variables obtained from a Wigner function depends on how the calculation is carried out: if one computes the standard Wigner function in Cartesian variables (p, x), and then replaces p and x by their expressions in terms of a-a variables, one obtains a different result than if the Wigner function is computed directly in terms of the a-a variables. Furthermore, the latter procedure gives a result more consistent with classical and semiclassical theory - e.g., by incorporating the Bohr-Sommerfeld quantization condition (quantum states defined by integer valuesmore » of the action variable) as well as the Heisenberg correspondence principle for matrix elements of an operator between such states - and has also been shown to be more accurate when applied to electronically non-adiabatic applications as implemented within the recently developed symmetrical quasi-classical (SQC) Meyer-Miller (MM) approach. Moreover, use of the Wigner function (obtained directly) in a-a variables shows how our standard SQC/MM approach can be used to obtain off-diagonal elements of the electronic density matrix by processing in a different way the same set of trajectories already used (in the SQC/MM methodology) to obtain the diagonal elements.« less

Communication: Wigner functions in action-angle variables, Bohr-Sommerfeld quantization, the Heisenberg correspondence principle, and a symmetrical quasi-classical approach to the full electronic density matrix.

PubMed

Miller, William H; Cotton, Stephen J

2016-08-28

It is pointed out that the classical phase space distribution in action-angle (a-a) variables obtained from a Wigner function depends on how the calculation is carried out: if one computes the standard Wigner function in Cartesian variables (p, x), and then replaces p and x by their expressions in terms of a-a variables, one obtains a different result than if the Wigner function is computed directly in terms of the a-a variables. Furthermore, the latter procedure gives a result more consistent with classical and semiclassical theory-e.g., by incorporating the Bohr-Sommerfeld quantization condition (quantum states defined by integer values of the action variable) as well as the Heisenberg correspondence principle for matrix elements of an operator between such states-and has also been shown to be more accurate when applied to electronically non-adiabatic applications as implemented within the recently developed symmetrical quasi-classical (SQC) Meyer-Miller (MM) approach. Moreover, use of the Wigner function (obtained directly) in a-a variables shows how our standard SQC/MM approach can be used to obtain off-diagonal elements of the electronic density matrix by processing in a different way the same set of trajectories already used (in the SQC/MM methodology) to obtain the diagonal elements.

Kohn-Sham potentials from electron densities using a matrix representation within finite atomic orbital basis sets

NASA Astrophysics Data System (ADS)

Zhang, Xing; Carter, Emily A.

2018-01-01

We revisit the static response function-based Kohn-Sham (KS) inversion procedure for determining the KS effective potential that corresponds to a given target electron density within finite atomic orbital basis sets. Instead of expanding the potential in an auxiliary basis set, we directly update the potential in its matrix representation. Through numerical examples, we show that the reconstructed density rapidly converges to the target density. Preliminary results are presented to illustrate the possibility of obtaining a local potential in real space from the optimized potential in its matrix representation. We have further applied this matrix-based KS inversion approach to density functional embedding theory. A proof-of-concept study of a solvated proton transfer reaction demonstrates the method's promise.

On Schrödinger's bridge problem

NASA Astrophysics Data System (ADS)

Friedland, S.

2017-11-01

In the first part of this paper we generalize Georgiou-Pavon's result that a positive square matrix can be scaled uniquely to a column stochastic matrix which maps a given positive probability vector to another given positive probability vector. In the second part we prove that a positive quantum channel can be scaled to another positive quantum channel which maps a given positive definite density matrix to another given positive definite density matrix using Brouwer's fixed point theorem. This result proves the Georgiou-Pavon conjecture for two positive definite density matrices, made in their recent paper. We show that the fixed points are unique for certain pairs of positive definite density matrices. Bibliography: 15 titles.

I-V characterization of a quantum well infrared photodetector with stepped and graded barriers

NASA Astrophysics Data System (ADS)

Nutku, F.; Erol, A.; Gunes, M.; Buklu, L. B.; Ergun, Y.; Arikan, M. C.

2012-09-01

I-V characterization of an n-type quantum well infrared photodetector which consists of stepped and graded barriers has been done under dark at temperatures between 20-300 K. Different current transport mechanisms and transition between them have been observed at temperature around 47 K. Activation energies of the electrons at various bias voltages have been obtained from the temperature dependent I-V measurements. Activation energy at zero bias has been calculated by extrapolating the bias dependence of the activation energies. Ground state energies and barrier heights of the four different quantum wells have been calculated by using an iterative technique, which depends on experimentally obtained activation energy. Ground state energies also have been calculated with transfer matrix technique and compared with iteration results. Incorporating the effect of high electron density induced electron exchange interaction on ground state energies; more consistent results with theoretical transfer matrix calculations have been obtained.

Halogen atom effect on the photophysical properties of substituted aza-BODIPY derivatives.

PubMed

De Simone, B C; Mazzone, G; Pirillo, J; Russo, N; Sicilia, E

2017-01-18

The influence of halogen atom substitution (Br and I), in different amounts and positions in an aza-BODIPY skeleton, on the photophysical properties of some aza-BODIPY derivatives has been investigated by using density functional theory and its time-dependent extension. The heavy atom effect on excitation energies, singlet-triplet energy gaps and spin-orbit matrix elements has been considered. The maximum absorption within the therapeutic window has been confirmed for all the aza-BODIPY derivatives. The feasible intersystem spin crossing pathways for the population of the lowest triplet state, that will depend on the values of the spin-orbit matrix elements, the energy gap as well as the orbital composition of the involved states have been found to most likely involve the S 1 and T 1 or T 2 states. The outcomes of computations support the potential therapeutic use of these compounds as photosensitizers in photodynamic therapy.

Frustration-induced internal stresses are responsible for quasilocalized modes in structural glasses

NASA Astrophysics Data System (ADS)

Lerner, Edan; Bouchbinder, Eran

2018-03-01

It has been recently shown [E. Lerner, G. Düring, and E. Bouchbinder, Phys. Rev. Lett. 117, 035501 (2016), 10.1103/PhysRevLett.117.035501] that the nonphononic vibrational modes of structural glasses at low frequencies ω are quasilocalized and follow a universal density of states D (ω ) ˜ω4 . Here we show that the gapless nature of the observed density of states depends on the existence of internal stresses that generically emerge in glasses due to frustration, thus elucidating a basic element underlying this universal behavior. Similarly to jammed particulate packings, low-frequency modes in structural glasses emerge from a balance between a local elasticity term and an internal stress term in the dynamical matrix, where the difference between them is orders of magnitude smaller than their typical magnitude. By artificially reducing the magnitude of internal stresses in a computer glass former in three dimensions, we show that a gap is formed in the density of states below which no vibrational modes exist, thus demonstrating the crucial importance of internal stresses. Finally, we show that while better annealing the glass upon cooling from the liquid state significantly reduces its internal stresses, the self-organizational processes during cooling render the gapless D (ω ) ˜ω4 density of state unaffected.

Harnessing molecular excited states with Lanczos chains.

PubMed

Baroni, Stefano; Gebauer, Ralph; Bariş Malcioğlu, O; Saad, Yousef; Umari, Paolo; Xian, Jiawei

2010-02-24

The recursion method of Haydock, Heine and Kelly is a powerful tool for calculating diagonal matrix elements of the resolvent of quantum-mechanical Hamiltonian operators by elegantly expressing them in terms of continued fractions. In this paper we extend the recursion method to off-diagonal matrix elements of general (possibly non-Hermitian) operators and apply it to the simulation of molecular optical absorption and photoemission spectra within time-dependent density-functional and many-body perturbation theories, respectively. This method is demonstrated with a couple of applications to the optical absorption and photoemission spectra of the caffeine molecule.

Harnessing molecular excited states with Lanczos chains

NASA Astrophysics Data System (ADS)

Baroni, Stefano; Gebauer, Ralph; Bariş Malcioğlu, O.; Saad, Yousef; Umari, Paolo; Xian, Jiawei

2010-02-01

The recursion method of Haydock, Heine and Kelly is a powerful tool for calculating diagonal matrix elements of the resolvent of quantum-mechanical Hamiltonian operators by elegantly expressing them in terms of continued fractions. In this paper we extend the recursion method to off-diagonal matrix elements of general (possibly non-Hermitian) operators and apply it to the simulation of molecular optical absorption and photoemission spectra within time-dependent density-functional and many-body perturbation theories, respectively. This method is demonstrated with a couple of applications to the optical absorption and photoemission spectra of the caffeine molecule.

Continued-fraction representation of the Kraus map for non-Markovian reservoir damping

NASA Astrophysics Data System (ADS)

van Wonderen, A. J.; Suttorp, L. G.

2018-04-01

Quantum dissipation is studied for a discrete system that linearly interacts with a reservoir of harmonic oscillators at thermal equilibrium. Initial correlations between system and reservoir are assumed to be absent. The dissipative dynamics as determined by the unitary evolution of system and reservoir is described by a Kraus map consisting of an infinite number of matrices. For all Laplace-transformed Kraus matrices exact solutions are constructed in terms of continued fractions that depend on the pair correlation functions of the reservoir. By performing factorizations in the Kraus map a perturbation theory is set up that conserves in arbitrary perturbative order both positivity and probability of the density matrix. The latter is determined by an integral equation for a bitemporal matrix and a finite hierarchy for Kraus matrices. In the lowest perturbative order this hierarchy reduces to one equation for one Kraus matrix. Its solution is given by a continued fraction of a much simpler structure as compared to the non-perturbative case. In the lowest perturbative order our non-Markovian evolution equations are applied to the damped Jaynes–Cummings model. From the solution for the atomic density matrix it is found that the atom may remain in the state of maximum entropy for a significant time span that depends on the initial energy of the radiation field.

Real-time observation of valence electron motion.

PubMed

Goulielmakis, Eleftherios; Loh, Zhi-Heng; Wirth, Adrian; Santra, Robin; Rohringer, Nina; Yakovlev, Vladislav S; Zherebtsov, Sergey; Pfeifer, Thomas; Azzeer, Abdallah M; Kling, Matthias F; Leone, Stephen R; Krausz, Ferenc

2010-08-05

The superposition of quantum states drives motion on the atomic and subatomic scales, with the energy spacing of the states dictating the speed of the motion. In the case of electrons residing in the outer (valence) shells of atoms and molecules which are separated by electronvolt energies, this means that valence electron motion occurs on a subfemtosecond to few-femtosecond timescale (1 fs = 10(-15) s). In the absence of complete measurements, the motion can be characterized in terms of a complex quantity, the density matrix. Here we report an attosecond pump-probe measurement of the density matrix of valence electrons in atomic krypton ions. We generate the ions with a controlled few-cycle laser field and then probe them through the spectrally resolved absorption of an attosecond extreme-ultraviolet pulse, which allows us to observe in real time the subfemtosecond motion of valence electrons over a multifemtosecond time span. We are able to completely characterize the quantum mechanical electron motion and determine its degree of coherence in the specimen of the ensemble. Although the present study uses a simple, prototypical open system, attosecond transient absorption spectroscopy should be applicable to molecules and solid-state materials to reveal the elementary electron motions that control physical, chemical and biological properties and processes.

The influence of hyaluronic acid hydrogel crosslinking density and macromolecular diffusivity on human MSC chondrogenesis and hypertrophy.

PubMed

Bian, Liming; Hou, Chieh; Tous, Elena; Rai, Reena; Mauck, Robert L; Burdick, Jason A

2013-01-01

Hyaluronic acid (HA) hydrogels formed via photocrosslinking provide stable 3D hydrogel environments that support the chondrogenesis of mesenchymal stem cells (MSCs). Crosslinking density has a significant impact on the physical properties of hydrogels, including their mechanical stiffness and macromolecular diffusivity. Variations in the HA hydrogel crosslinking density can be obtained by either changes in the HA macromer concentration (1, 3, or 5% w/v at 15 min exposure) or the extent of reaction through light exposure time (5% w/v at 5, 10, or 15 min). In this work, increased crosslinking by either method resulted in an overall decrease in cartilage matrix content and more restricted matrix distribution. Increased crosslinking also promoted hypertrophic differentiation of the chondrogenically induced MSCs, resulting in more matrix calcification in vitro. For example, type X collagen expression in the high crosslinking density 5% 15 min group was ~156 and 285% higher when compared to the low crosslinking density 1% 15 min and 5% 5 min groups on day 42, respectively. Supplementation with inhibitors of the small GTPase pathway involved in cytoskeletal tension or myosin II had no effect on hypertrophic differentiation and matrix calcification, indicating that the differential response is unlikely to be related to force-sensing mechanotransduction mechanisms. When implanted subcutaneously in nude mice, higher crosslinking density again resulted in reduced cartilage matrix content, restricted matrix distribution, and increased matrix calcification. This study demonstrates that hydrogel properties mediated through alterations in crosslinking density must be considered in the context of the hypertrophic differentiation of chondrogenically induced MSCs. Copyright © 2012 Elsevier Ltd. All rights reserved.

Entropy-driven phase transitions of entanglement

NASA Astrophysics Data System (ADS)

Facchi, Paolo; Florio, Giuseppe; Parisi, Giorgio; Pascazio, Saverio; Yuasa, Kazuya

2013-05-01

We study the behavior of bipartite entanglement at fixed von Neumann entropy. We look at the distribution of the entanglement spectrum, that is, the eigenvalues of the reduced density matrix of a quantum system in a pure state. We report the presence of two continuous phase transitions, characterized by different entanglement spectra, which are deformations of classical eigenvalue distributions.

X-ray peak broadening analysis of AA 6061{sub 100-x} - x wt.% Al{sub 2}O{sub 3} nanocomposite prepared by mechanical alloying

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sivasankaran, S., E-mail: sivasankarangs1979@gmail.com; Sivaprasad, K., E-mail: ksp@nitt.edu; Narayanasamy, R., E-mail: narayan@nitt.edu

2011-07-15

Nanocrystalline AA 6061 alloy reinforced with alumina (0, 4, 8, and 12 wt.%) in amorphized state composite powder was synthesized by mechanical alloying and consolidated by conventional powder metallurgy route. The as-milled and as-sintered (573 K and 673 K) nanocomposites were characterized by X-ray diffraction (XRD) and transmission electron microscopy (TEM). The peaks corresponding to fine alumina was not observed by XRD patterns due to amorphization. Using high-resolution transmission electron microscope, it is confirmed that the presence of amorphized alumina observed in Al lattice fringes. The crystallite size, lattice strain, deformation stress, and strain energy density of AA 6061 matrixmore » were determined precisely from the first five most intensive reflection of XRD using simple Williamson-Hall models; uniform deformation model, uniform stress deformation model, and uniform energy density deformation model. Among the developed models, uniform energy density deformation model was observed to be the best fit and realistic model for mechanically alloyed powders. This model evidenced the more anisotropic nature of the ball milled powders. The XRD peaks of as-milled powder samples demonstrated a considerable broadening with percentage of reinforcement due to grain refinement and lattice distortions during same milling time (40 h). The as-sintered (673 K) unreinforced AA 6061 matrix crystallite size from well fitted uniform energy density deformation model was 98 nm. The as-milled and as-sintered (673 K) nanocrystallite matrix sizes for 12 wt.% Al{sub 2}O{sub 3} well fitted by uniform energy density deformation model were 38 nm and 77 nm respectively, which indicate that the fine Al{sub 2}O{sub 3} pinned the matrix grain boundary and prevented the grain growth during sintering. Finally, the lattice parameter of Al matrix in as-milled and as-sintered conditions was also investigated in this paper. Research highlights: {yields} Integral breadth methods using various Williamson-Hall models were investigated for line profile analysis. {yields} Uniform energy density deformation model is observed to the best realistic model. {yields} The present analysis is used for understanding the stress and the strain present in the nanocomposites.« less

Spectral functions with the density matrix renormalization group: Krylov-space approach for correction vectors

DOE Office of Scientific and Technical Information (OSTI.GOV)

None, None

Frequency-dependent correlations, such as the spectral function and the dynamical structure factor, help illustrate condensed matter experiments. Within the density matrix renormalization group (DMRG) framework, an accurate method for calculating spectral functions directly in frequency is the correction-vector method. The correction vector can be computed by solving a linear equation or by minimizing a functional. Our paper proposes an alternative to calculate the correction vector: to use the Krylov-space approach. This paper also studies the accuracy and performance of the Krylov-space approach, when applied to the Heisenberg, the t-J, and the Hubbard models. The cases we studied indicate that themore » Krylov-space approach can be more accurate and efficient than the conjugate gradient, and that the error of the former integrates best when a Krylov-space decomposition is also used for ground state DMRG.« less

Density-matrix simulation of small surface codes under current and projected experimental noise

NASA Astrophysics Data System (ADS)

O'Brien, T. E.; Tarasinski, B.; DiCarlo, L.

2017-09-01

We present a density-matrix simulation of the quantum memory and computing performance of the distance-3 logical qubit Surface-17, following a recently proposed quantum circuit and using experimental error parameters for transmon qubits in a planar circuit QED architecture. We use this simulation to optimize components of the QEC scheme (e.g., trading off stabilizer measurement infidelity for reduced cycle time) and to investigate the benefits of feedback harnessing the fundamental asymmetry of relaxation-dominated error in the constituent transmons. A lower-order approximate calculation extends these predictions to the distance-5 Surface-49. These results clearly indicate error rates below the fault-tolerance threshold of the surface code, and the potential for Surface-17 to perform beyond the break-even point of quantum memory. However, Surface-49 is required to surpass the break-even point of computation at state-of-the-art qubit relaxation times and readout speeds.

Crowding of Interacting Fluid Particles in Porous Media through Molecular Dynamics: Breakdown of Universality for Soft Interactions.

PubMed

Schnyder, Simon K; Horbach, Jürgen

2018-02-16

Molecular dynamics simulations of interacting soft disks confined in a heterogeneous quenched matrix of soft obstacles show dynamics which is fundamentally different from that of hard disks. The interactions between the disks can enhance transport when their density is increased, as disks cooperatively help each other over the finite energy barriers in the matrix. The system exhibits a transition from a diffusive to a localized state, but the transition is strongly rounded. Effective exponents in the mean-squared displacement can be observed over three decades in time but depend on the density of the disks and do not correspond to asymptotic behavior in the vicinity of a critical point, thus, showing that it is incorrect to relate them to the critical exponents in the Lorentz model scenario. The soft interactions are, therefore, responsible for a breakdown of the universality of the dynamics.

Spectral functions with the density matrix renormalization group: Krylov-space approach for correction vectors

DOE PAGES

None, None

2016-11-21

Frequency-dependent correlations, such as the spectral function and the dynamical structure factor, help illustrate condensed matter experiments. Within the density matrix renormalization group (DMRG) framework, an accurate method for calculating spectral functions directly in frequency is the correction-vector method. The correction vector can be computed by solving a linear equation or by minimizing a functional. Our paper proposes an alternative to calculate the correction vector: to use the Krylov-space approach. This paper also studies the accuracy and performance of the Krylov-space approach, when applied to the Heisenberg, the t-J, and the Hubbard models. The cases we studied indicate that themore » Krylov-space approach can be more accurate and efficient than the conjugate gradient, and that the error of the former integrates best when a Krylov-space decomposition is also used for ground state DMRG.« less

Density matrix modeling of quantum cascade lasers without an artificially localized basis: A generalized scattering approach

NASA Astrophysics Data System (ADS)

Pan, Andrew; Burnett, Benjamin A.; Chui, Chi On; Williams, Benjamin S.

2017-08-01

We derive a density matrix (DM) theory for quantum cascade lasers (QCLs) that describes the influence of scattering on coherences through a generalized scattering superoperator. The theory enables quantitative modeling of QCLs, including localization and tunneling effects, using the well-defined energy eigenstates rather than the ad hoc localized basis states required by most previous DM models. Our microscopic approach to scattering also eliminates the need for phenomenological transition or dephasing rates. We discuss the physical interpretation and numerical implementation of the theory, presenting sets of both energy-resolved and thermally averaged equations, which can be used for detailed or compact device modeling. We illustrate the theory's applications by simulating a high performance resonant-phonon terahertz (THz) QCL design, which cannot be easily or accurately modeled using conventional DM methods. We show that the theory's inclusion of coherences is crucial for describing localization and tunneling effects consistent with experiment.

Physical aging and its influence on the reliability of network epoxies and epoxy-matrix composites

NASA Technical Reports Server (NTRS)

Heinemann, K.

1983-01-01

The matrix-dominated physical and mechanical properties of a carbon fiber reinforced epoxy composite and a neat epoxy resin were found to be affected by sub-Tg annealing in nitrogen and dark atmosphere. Postcured specimens of Thornel 300 carbon-fiber/Fiberite 934 epoxy as well as Fiberite 934 epoxy resin were quenched from above Tg and given annealing at 140 C, 110 C, or 80 C, for time up to one-hundred thousand minutes. No weight loss was observed during annealing at these temperatures. Significant variations were found in density, modulus, hardness, damping, moisture absorption ability, thermal expansivity. Moisture-epoxy interactious were also studied. The kinetics of aging as well as the molecular aggregation during this densification process were monitored by differential scanning calorimetry, dynamic mechanical analysis, density gradient column, microhardness tester, Instron, and solid-state nuclear magnetic resonance spectroscopy.

Crowding of Interacting Fluid Particles in Porous Media through Molecular Dynamics: Breakdown of Universality for Soft Interactions

NASA Astrophysics Data System (ADS)

Schnyder, Simon K.; Horbach, Jürgen

2018-02-01

Molecular dynamics simulations of interacting soft disks confined in a heterogeneous quenched matrix of soft obstacles show dynamics which is fundamentally different from that of hard disks. The interactions between the disks can enhance transport when their density is increased, as disks cooperatively help each other over the finite energy barriers in the matrix. The system exhibits a transition from a diffusive to a localized state, but the transition is strongly rounded. Effective exponents in the mean-squared displacement can be observed over three decades in time but depend on the density of the disks and do not correspond to asymptotic behavior in the vicinity of a critical point, thus, showing that it is incorrect to relate them to the critical exponents in the Lorentz model scenario. The soft interactions are, therefore, responsible for a breakdown of the universality of the dynamics.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Herbrych, Jacek W.; Feiguin, Adrian E.; Dagotto, Elbio R.

Here, we present a time-dependent density-matrix renormalization group investigation of the quantum distillation process within the Fermi-Hubbard model on a quasi-one-dimensional ladder geometry. The term distillation refers to the dynamical, spatial separation of singlons and doublons in the sudden expansion of interacting particles in an optical lattice, i.e., the release of a cloud of atoms from a trapping potential. Remarkably, quantum distillation can lead to a contraction of the doublon cloud, resulting in an increased density of the doublons in the core region compared to the initial state. As a main result, we show that this phenomenon is not limitedmore » to chains that were previously studied. Interestingly, there are additional dynamical processes on the two-leg ladder such as density oscillations and self-trapping of defects that lead to a less efficient distillation process. An investigation of the time evolution starting from product states provides an explanation for this behavior. Initial product states are also considered since in optical lattice experiments, such states are often used as the initial setup. We propose configurations that lead to a fast and efficient quantum distillation.« less

Subgap in the Surface Bound States Spectrum of Superfluid (3) 3 He-B with Rough Surface

NASA Astrophysics Data System (ADS)

Nagato, Y.; Higashitani, S.; Nagai, K.

2018-03-01

The subgap structure in the surface bound states spectrum of superfluid ^3He-B with rough surface is discussed. The subgap is formed by the level repulsion between the surface bound state and the continuum states in the course of multiple scattering by the surface roughness. We show that the level repulsion is originated from the nature of the wave function of the surface bound state that is now recognized as Majorana fermion. We study the superfluid ^3He-B with a rough surface and in a magnetic field perpendicular to the surface using the quasi-classical Green function together with a random S-matrix model. We calculate the self-consistent order parameters, the spin polarization density and the surface density of states. It is shown that the subgap is found also in a magnetic field perpendicular to the surface. The magnetic field dependence of the transverse acoustic impedance is also discussed.

One-electron reduced density matrices of strongly correlated harmonium atoms.

PubMed

Cioslowski, Jerzy

2015-03-21

Explicit asymptotic expressions are derived for the reduced one-electron density matrices (the 1-matrices) of strongly correlated two- and three-electron harmonium atoms in the ground and first excited states. These expressions, which are valid at the limit of small confinement strength ω, yield electron densities and kinetic energies in agreement with the published values. In addition, they reveal the ω(5/6) asymptotic scaling of the exchange components of the electron-electron repulsion energies that differs from the ω(2/3) scaling of their Coulomb and correlation counterparts. The natural orbitals of the totally symmetric ground state of the two-electron harmonium atom are found to possess collective occupancies that follow a mixed power/Gaussian dependence on the angular momentum in variance with the simple power-law prediction of Hill's asymptotics. Providing rigorous constraints on energies as functionals of 1-matrices, these results are expected to facilitate development of approximate implementations of the density matrix functional theory and ensure their proper description of strongly correlated systems.

Matrix Methods for Estimating the Coherence Functions from Estimates of the Cross-Spectral Density Matrix

DOE PAGES

Smallwood, D. O.

1996-01-01

It is shown that the usual method for estimating the coherence functions (ordinary, partial, and multiple) for a general multiple-input! multiple-output problem can be expressed as a modified form of Cholesky decomposition of the cross-spectral density matrix of the input and output records. The results can be equivalently obtained using singular value decomposition (SVD) of the cross-spectral density matrix. Using SVD suggests a new form of fractional coherence. The formulation as a SVD problem also suggests a way to order the inputs when a natural physical order of the inputs is absent.

Entanglement transitions induced by large deviations

NASA Astrophysics Data System (ADS)

Bhosale, Udaysinh T.

2017-12-01

The probability of large deviations of the smallest Schmidt eigenvalue for random pure states of bipartite systems, denoted as A and B , is computed analytically using a Coulomb gas method. It is shown that this probability, for large N , goes as exp[-β N2Φ (ζ ) ] , where the parameter β is the Dyson index of the ensemble, ζ is the large deviation parameter, while the rate function Φ (ζ ) is calculated exactly. Corresponding equilibrium Coulomb charge density is derived for its large deviations. Effects of the large deviations of the extreme (largest and smallest) Schmidt eigenvalues on the bipartite entanglement are studied using the von Neumann entropy. Effect of these deviations is also studied on the entanglement between subsystems 1 and 2, obtained by further partitioning the subsystem A , using the properties of the density matrix's partial transpose ρ12Γ. The density of states of ρ12Γ is found to be close to the Wigner's semicircle law with these large deviations. The entanglement properties are captured very well by a simple random matrix model for the partial transpose. The model predicts the entanglement transition across a critical large deviation parameter ζ . Log negativity is used to quantify the entanglement between subsystems 1 and 2. Analytical formulas for it are derived using the simple model. Numerical simulations are in excellent agreement with the analytical results.

Entanglement transitions induced by large deviations.

PubMed

Bhosale, Udaysinh T

2017-12-01

The probability of large deviations of the smallest Schmidt eigenvalue for random pure states of bipartite systems, denoted as A and B, is computed analytically using a Coulomb gas method. It is shown that this probability, for large N, goes as exp[-βN^{2}Φ(ζ)], where the parameter β is the Dyson index of the ensemble, ζ is the large deviation parameter, while the rate function Φ(ζ) is calculated exactly. Corresponding equilibrium Coulomb charge density is derived for its large deviations. Effects of the large deviations of the extreme (largest and smallest) Schmidt eigenvalues on the bipartite entanglement are studied using the von Neumann entropy. Effect of these deviations is also studied on the entanglement between subsystems 1 and 2, obtained by further partitioning the subsystem A, using the properties of the density matrix's partial transpose ρ_{12}^{Γ}. The density of states of ρ_{12}^{Γ} is found to be close to the Wigner's semicircle law with these large deviations. The entanglement properties are captured very well by a simple random matrix model for the partial transpose. The model predicts the entanglement transition across a critical large deviation parameter ζ. Log negativity is used to quantify the entanglement between subsystems 1 and 2. Analytical formulas for it are derived using the simple model. Numerical simulations are in excellent agreement with the analytical results.

Homodyne versus photon-counting quantum trajectories for dissipative Kerr resonators with two-photon driving

NASA Astrophysics Data System (ADS)

Bartolo, Nicola; Minganti, Fabrizio; Lolli, Jared; Ciuti, Cristiano

2017-07-01

We investigate two different kinds of quantum trajectories for a nonlinear photon resonator subject to two-photon pumping, a configuration recently studied for the generation of photonic Schrödinger cat states. In the absence of feedback control and in the strong-driving limit, the steady-state density matrix is a statistical mixture of two states with equal weight. While along a single photon-counting trajectory the systems intermittently switches between an odd and an even cat state, we show that upon homodyne detection the situation is different. Indeed, homodyne quantum trajectories reveal switches between coherent states of opposite phase.

Correlations and Werner states in finite spin linear arrays

NASA Astrophysics Data System (ADS)

Wells, P. R.; Chaves, C. M.; d'Albuquerque e Castro, J.; Koiller, Belita

2013-10-01

Pairwise quantum correlations in the ground state of an N-spins antiferromagnetic Heisenberg chain are investigated. By varying the exchange coupling between two neighboring sites, it is possible to reversibly drive spins from entangled to disentangled states. For even N, the two-spin density matrix is written in the form of a Werner state, allowing identification of its single parameter with the usual spin-spin correlation function. The N = 4 chain is identified as a promising system for practical demonstrations of non-classical correlations and the realization of Werner states in familiar condensed matter systems. Fabrication and measurement ingredients are within current capabilities.

Benchmarking a quantum teleportation protocol in superconducting circuits using tomography and an entanglement witness.

PubMed

Baur, M; Fedorov, A; Steffen, L; Filipp, S; da Silva, M P; Wallraff, A

2012-01-27

Teleportation of a quantum state may be used for distributing entanglement between distant qubits in quantum communication and for quantum computation. Here we demonstrate the implementation of a teleportation protocol, up to the single-shot measurement step, with superconducting qubits coupled to a microwave resonator. Using full quantum state tomography and evaluating an entanglement witness, we show that the protocol generates a genuine tripartite entangled state of all three qubits. Calculating the projection of the measured density matrix onto the basis states of two qubits allows us to reconstruct the teleported state. Repeating this procedure for a complete set of input states we find an average output state fidelity of 86%.

Perturbation theory corrections to the two-particle reduced density matrix variational method.

PubMed

Juhasz, Tamas; Mazziotti, David A

2004-07-15

In the variational 2-particle-reduced-density-matrix (2-RDM) method, the ground-state energy is minimized with respect to the 2-particle reduced density matrix, constrained by N-representability conditions. Consider the N-electron Hamiltonian H(lambda) as a function of the parameter lambda where we recover the Fock Hamiltonian at lambda=0 and we recover the fully correlated Hamiltonian at lambda=1. We explore using the accuracy of perturbation theory at small lambda to correct the 2-RDM variational energies at lambda=1 where the Hamiltonian represents correlated atoms and molecules. A key assumption in the correction is that the 2-RDM method will capture a fairly constant percentage of the correlation energy for lambda in (0,1] because the nonperturbative 2-RDM approach depends more significantly upon the nature rather than the strength of the two-body Hamiltonian interaction. For a variety of molecules we observe that this correction improves the 2-RDM energies in the equilibrium bonding region, while the 2-RDM energies at stretched or nearly dissociated geometries, already highly accurate, are not significantly changed. At equilibrium geometries the corrected 2-RDM energies are similar in accuracy to those from coupled-cluster singles and doubles (CCSD), but at nonequilibrium geometries the 2-RDM energies are often dramatically more accurate as shown in the bond stretching and dissociation data for water and nitrogen. (c) 2004 American Institute of Physics.

Leptogenesis with heavy neutrino flavours: from density matrix to Boltzmann equations

NASA Astrophysics Data System (ADS)

Blanchet, Steve; Di Bari, Pasquale; Jones, David A.; Marzola, Luca

2013-01-01

Leptogenesis with heavy neutrino flavours is discussed within a density matrix formalism. We write the density matrix equation, describing the generation of the matter-antimatter asymmetry, for an arbitrary choice of the right-handed (RH) neutrino masses. For hierarchical RH neutrino masses lying in the fully flavoured regimes, this reduces to multiple-stage Boltzmann equations. In this case we recover and extend results previously derived within a quantum state collapse description. We confirm the generic existence of phantom terms. However, taking into account the effect of gauge interactions, we show that they are washed out at the production with a wash-out rate that is halved compared to that one acting on the total asymmetry. In the N1-dominated scenario they cancel without contributing to the final baryon asymmetry. In other scenarios they do not in general and they have to be taken into account. We also confirm that there is a (orthogonal) component in the asymmetry produced by the heavier RH neutrinos which completely escapes the washout from the lighter RH neutrinos and show that phantom terms additionally contribute to it. The other (parallel) component is washed out with the usual exponential factor, even for weak washout. Finally, as an illustration, we study the two RH neutrino model in the light of the above findings, showing that phantom terms can contribute to the final asymmetry also in this case.

Referee Networks and Their Spectral Properties

NASA Astrophysics Data System (ADS)

Slanina, F.; Zhang, Y.-Ch.

2005-09-01

The bipartite graph connecting products and reviewers of that product is studied empirically in the case of amazon.com. We find that the network has power-law degree distribution on the side of reviewers, while on the side of products the distribution is better fitted by stretched exponential. The spectrum of normalised adjacency matrix shows power-law tail in the density of states. Establishing the community structures by finding localised eigenstates is not straightforward as the localised and delocalised states are mixed throughout the whole support of the spectrum.

Emergence of a new pair-coherent phase in many-body quenches of repulsive bosons

NASA Astrophysics Data System (ADS)

Fischer, Uwe R.; Lee, Kang-Soo; Xiong, Bo

2011-07-01

We investigate the dynamical mode population statistics and associated first- and second-order coherence of an interacting bosonic two-mode model when the pair-exchange coupling is quenched from negative to positive values. It is shown that for moderately rapid second-order transitions, a new pair-coherent phase emerges on the positive coupling side in an excited state, which is not fragmented as the ground-state single-particle density matrix would prescribe it to be.

Theory of an optomechanical quantum heat engine

DTIC Science & Technology

2014-08-12

control number. PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ADDRESS. University of Arizona 888 N . Euclid Ave. Tucson, AZ 85719 -4824 ABSTRACT Theory of an...modes, with a cutoff number state | N 〉 with N n̄a(b), so that the total dimension of the density matrix ρsys is ( N + 1)4. As a result the simulations...become very time consuming even for relatively modest values of N . However, due to the diagonality of thermal states in an energy basis the total

Invariant criteria for bound states, degree of ionization, and plasma phase transition

NASA Technical Reports Server (NTRS)

Girardeau, M. D.

1990-01-01

Basis invariant characterizations of bound states and bound fraction of a partially ionized hydrogen plasma are given in terms of properties of the spectrum of eigenvalues and eigenfunctions of the equilibrium quantum statistical one-proton-one-electron reduced density matrix. It is suggested that these can be used to place theories of a proposed plasma-ionization phase transition on a firm foundation. This general approach may be relevant to cosmological questions such as the quark deconfinement-confinement transition.

Modulation of hematopoietic progenitor cell fate in vitro by varying collagen oligomer matrix stiffness in the presence or absence of osteoblasts.

PubMed

Chitteti, Brahmananda Reddy; Kacena, Melissa A; Voytik-Harbin, Sherry L; Srour, Edward F

2015-10-01

To recreate the in vivo hematopoietic cell microenvironment or niche and to study the impact of extracellular matrix (ECM) biophysical properties on hematopoietic progenitor cell (HPC) proliferation and function, mouse bone-marrow derived HPC (Lin-Sca1+cKit+/(LSK) were cultured within three-dimensional (3D) type I collagen oligomer matrices. To generate a more physiologic milieu, 3D cultures were established in both the presence and absence of calvariae-derived osteoblasts (OB). Collagen oligomers were polymerized at varying concentration to give rise to matrices of different fibril densities and therefore matrix stiffness (shear storage modulus, 50-800 Pa). Decreased proliferation and increased clonogenicity of LSK cells was associated with increase of matrix stiffness regardless of whether OB were present or absent from the 3D culture system. Also, regardless of whether OB were or were not added to the 3D co-culture system, LSK within 800 Pa collagen oligomer matrices maintained the highest percentage of Lin-Sca1+ cells as well as higher percentage of cells in quiescent state (G0/G1) compared to 50 Pa or 200Pa matrices. Collectively, these data illustrate that biophysical features of collagen oligomer matrices, specifically fibril density-induced modulation of matrix stiffness, provide important guidance cues in terms of LSK expansion and differentiation and therefore maintenance of progenitor cell function. Copyright © 2015. Published by Elsevier B.V.

Tracking Multiple Video Targets with an Improved GM-PHD Tracker

PubMed Central

Zhou, Xiaolong; Yu, Hui; Liu, Honghai; Li, Youfu

2015-01-01

Tracking multiple moving targets from a video plays an important role in many vision-based robotic applications. In this paper, we propose an improved Gaussian mixture probability hypothesis density (GM-PHD) tracker with weight penalization to effectively and accurately track multiple moving targets from a video. First, an entropy-based birth intensity estimation method is incorporated to eliminate the false positives caused by noisy video data. Then, a weight-penalized method with multi-feature fusion is proposed to accurately track the targets in close movement. For targets without occlusion, a weight matrix that contains all updated weights between the predicted target states and the measurements is constructed, and a simple, but effective method based on total weight and predicted target state is proposed to search the ambiguous weights in the weight matrix. The ambiguous weights are then penalized according to the fused target features that include spatial-colour appearance, histogram of oriented gradient and target area and further re-normalized to form a new weight matrix. With this new weight matrix, the tracker can correctly track the targets in close movement without occlusion. For targets with occlusion, a robust game-theoretical method is used. Finally, the experiments conducted on various video scenarios validate the effectiveness of the proposed penalization method and show the superior performance of our tracker over the state of the art. PMID:26633422

Tripartite-to-Bipartite Entanglement Transformation by Stochastic Local Operations and Classical Communication and the Structure of Matrix Spaces

NASA Astrophysics Data System (ADS)

Li, Yinan; Qiao, Youming; Wang, Xin; Duan, Runyao

2018-03-01

We study the problem of transforming a tripartite pure state to a bipartite one using stochastic local operations and classical communication (SLOCC). It is known that the tripartite-to-bipartite SLOCC convertibility is characterized by the maximal Schmidt rank of the given tripartite state, i.e. the largest Schmidt rank over those bipartite states lying in the support of the reduced density operator. In this paper, we further study this problem and exhibit novel results in both multi-copy and asymptotic settings, utilizing powerful results from the structure of matrix spaces. In the multi-copy regime, we observe that the maximal Schmidt rank is strictly super-multiplicative, i.e. the maximal Schmidt rank of the tensor product of two tripartite pure states can be strictly larger than the product of their maximal Schmidt ranks. We then provide a full characterization of those tripartite states whose maximal Schmidt rank is strictly super-multiplicative when taking tensor product with itself. Notice that such tripartite states admit strict advantages in tripartite-to-bipartite SLOCC transformation when multiple copies are provided. In the asymptotic setting, we focus on determining the tripartite-to-bipartite SLOCC entanglement transformation rate. Computing this rate turns out to be equivalent to computing the asymptotic maximal Schmidt rank of the tripartite state, defined as the regularization of its maximal Schmidt rank. Despite the difficulty caused by the super-multiplicative property, we provide explicit formulas for evaluating the asymptotic maximal Schmidt ranks of two important families of tripartite pure states by resorting to certain results of the structure of matrix spaces, including the study of matrix semi-invariants. These formulas turn out to be powerful enough to give a sufficient and necessary condition to determine whether a given tripartite pure state can be transformed to the bipartite maximally entangled state under SLOCC, in the asymptotic setting. Applying the recent progress on the non-commutative rank problem, we can verify this condition in deterministic polynomial time.

The ab-initio density matrix renormalization group in practice.

PubMed

Olivares-Amaya, Roberto; Hu, Weifeng; Nakatani, Naoki; Sharma, Sandeep; Yang, Jun; Chan, Garnet Kin-Lic

2015-01-21

The ab-initio density matrix renormalization group (DMRG) is a tool that can be applied to a wide variety of interesting problems in quantum chemistry. Here, we examine the density matrix renormalization group from the vantage point of the quantum chemistry user. What kinds of problems is the DMRG well-suited to? What are the largest systems that can be treated at practical cost? What sort of accuracies can be obtained, and how do we reason about the computational difficulty in different molecules? By examining a diverse benchmark set of molecules: π-electron systems, benchmark main-group and transition metal dimers, and the Mn-oxo-salen and Fe-porphine organometallic compounds, we provide some answers to these questions, and show how the density matrix renormalization group is used in practice.

Density matrix renormalization group simulations of SU(N ) Heisenberg chains using standard Young tableaus: Fundamental representation and comparison with a finite-size Bethe ansatz

NASA Astrophysics Data System (ADS)

Nataf, Pierre; Mila, Frédéric

2018-04-01

We develop an efficient method to perform density matrix renormalization group simulations of the SU(N ) Heisenberg chain with open boundary conditions taking full advantage of the SU(N ) symmetry of the problem. This method is an extension of the method previously developed for exact diagonalizations and relies on a systematic use of the basis of standard Young tableaux. Concentrating on the model with the fundamental representation at each site (i.e., one particle per site in the fermionic formulation), we have benchmarked our results for the ground-state energy up to N =8 and up to 420 sites by comparing them with Bethe ansatz results on open chains, for which we have derived and solved the Bethe ansatz equations. The agreement for the ground-state energy is excellent for SU(3) (12 digits). It decreases with N , but it is still satisfactory for N =8 (six digits). Central charges c are also extracted from the entanglement entropy using the Calabrese-Cardy formula and agree with the theoretical values expected from the SU (N) 1 Wess-Zumino-Witten conformal field theories.

Development of edge effects around experimental ecosystem hotspots is affected by edge density and matrix type

USDA-ARS?s Scientific Manuscript database

Ecological edge effects are sensitive to landscape context. In particular, edge effects can be altered by matrix type and by the presence of other nearby edges. We experimentally altered patch configurations in an African savanna to determine how edge density and matrix type influence edge effect de...

Organizational behavior of human umbilical vein endothelial cells

PubMed Central

1982-01-01

Culture conditions that favor rapid multiplication of human umbilical vein endothelial cells (HUV-EC) also support long-term serial propagation of the cells. This is routinely achieved when HUV-EC are grown in Medium 199 (M-199) supplemented with fetal bovine serum (FBS) and endothelial cell growth factor (ECGF), on a human fibronectin (HFN) matrix. The HUV-EC can shift from a proliferative to an organized state when the in vitro conditions are changed from those favoring low density proliferation to those supporting high density survival. When ECGF and HFN are omitted, cultures fail to achieve confluence beyond the first or second passage: the preconfluent cultures organize into tubular structures after 4-6 wk. Some tubes become grossly visible and float in the culture medium, remaining tethered to the plastic dish at either end of the tube. On an ultrastructural level, the tubes consist of cells, held together by junctional complexes, arranged so as to form a lumen. The smallest lumens are formed by one cell folding over to form a junction with itself. The cells contain Weibel-Palade bodies and factor VIII-related antigen. The lumens contain granular, fibrillar and amorphous debris. Predigesting the HFN matrix with trypsin (10 min, 37 degrees C) or plasmin significantly accelerates tube formation. Thrombin and plasminogen activator had no apparent effect. Disruption of the largest tubes with trypsin/EDTA permits the cells to revert to a proliferative state if plated on HFN, in M-199, FBS, and ECGF. These observations indicate that culture conditions that do not favor proliferation permit attainment of a state of nonterminal differentiation (organization) by the endothelial cell. Furthermore, proteolytic modification of the HFN matrix may play an important role in endothelial organization. PMID:6813338

Phase diagram of the quantum Ising model with long-range interactions on an infinite-cylinder triangular lattice

NASA Astrophysics Data System (ADS)

Saadatmand, S. N.; Bartlett, S. D.; McCulloch, I. P.

2018-04-01

Obtaining quantitative ground-state behavior for geometrically-frustrated quantum magnets with long-range interactions is challenging for numerical methods. Here, we demonstrate that the ground states of these systems on two-dimensional lattices can be efficiently obtained using state-of-the-art translation-invariant variants of matrix product states and density-matrix renormalization-group algorithms. We use these methods to calculate the fully-quantitative ground-state phase diagram of the long-range interacting triangular Ising model with a transverse field on six-leg infinite-length cylinders and scrutinize the properties of the detected phases. We compare these results with those of the corresponding nearest neighbor model. Our results suggest that, for such long-range Hamiltonians, the long-range quantum fluctuations always lead to long-range correlations, where correlators exhibit power-law decays instead of the conventional exponential drops observed for short-range correlated gapped phases. Our results are relevant for comparisons with recent ion-trap quantum simulator experiments that demonstrate highly-controllable long-range spin couplings for several hundred ions.

Unveiling the nature of post-linear response Z-vector method for time-dependent density functional theory.

PubMed

Pastore, Mariachiara; Assfeld, Xavier; Mosconi, Edoardo; Monari, Antonio; Etienne, Thibaud

2017-07-14

We report a theoretical study on the analysis of the relaxed one-particle difference density matrix characterizing the passage from the ground to the excited state of a molecular system, as obtained from time-dependent density functional theory. In particular, this work aims at using the physics contained in the so-called Z-vector, which differentiates between unrelaxed and relaxed difference density matrices to analyze excited states' nature. For this purpose, we introduce novel quantum-mechanical quantities, based on the detachment/attachment methodology, for analysing the Z-vector transformation for different molecules and density functional theory functionals. A derivation pathway of these novel descriptors is reported, involving a numerical integration to be performed in the Euclidean space on the density functions. This topological analysis is then applied to two sets of chromophores, and the correlation between the level of theory and the behavior of our descriptors is properly rationalized. In particular, the effect of range-separation on the relaxation amplitude is discussed. The relaxation term is finally shown to be system-specific (for a given level of theory) and independent of the number of electrons (i.e., the relaxation amplitude is not simply the result of a collective phenomenon).

Density matrix renormalization group with efficient dynamical electron correlation through range separation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hedegård, Erik Donovan, E-mail: erik.hedegard@phys.chem.ethz.ch; Knecht, Stefan; Reiher, Markus, E-mail: markus.reiher@phys.chem.ethz.ch

2015-06-14

We present a new hybrid multiconfigurational method based on the concept of range-separation that combines the density matrix renormalization group approach with density functional theory. This new method is designed for the simultaneous description of dynamical and static electron-correlation effects in multiconfigurational electronic structure problems.

A matrix-based approach to solving the inverse Frobenius-Perron problem using sequences of density functions of stochastically perturbed dynamical systems

NASA Astrophysics Data System (ADS)

Nie, Xiaokai; Coca, Daniel

2018-01-01

The paper introduces a matrix-based approach to estimate the unique one-dimensional discrete-time dynamical system that generated a given sequence of probability density functions whilst subjected to an additive stochastic perturbation with known density.

A matrix-based approach to solving the inverse Frobenius-Perron problem using sequences of density functions of stochastically perturbed dynamical systems.

PubMed

Nie, Xiaokai; Coca, Daniel

2018-01-01

The paper introduces a matrix-based approach to estimate the unique one-dimensional discrete-time dynamical system that generated a given sequence of probability density functions whilst subjected to an additive stochastic perturbation with known density.

Binary synaptic connections based on memory switching in a-Si:H for artificial neural networks

NASA Technical Reports Server (NTRS)

Thakoor, A. P.; Lamb, J. L.; Moopenn, A.; Khanna, S. K.

1987-01-01

A scheme for nonvolatile associative electronic memory storage with high information storage density is proposed which is based on neural network models and which uses a matrix of two-terminal passive interconnections (synapses). It is noted that the massive parallelism in the architecture would require the ON state of a synaptic connection to be unusually weak (highly resistive). Memory switching using a-Si:H along with ballast resistors patterned from amorphous Ge-metal alloys is investigated for a binary programmable read only memory matrix. The fabrication of a 1600 synapse test array of uniform connection strengths and a-Si:H switching elements is discussed.

A feedforward artificial neural network based on quantum effect vector-matrix multipliers.

PubMed

Levy, H J; McGill, T C

1993-01-01

The vector-matrix multiplier is the engine of many artificial neural network implementations because it can simulate the way in which neurons collect weighted input signals from a dendritic arbor. A new technology for building analog weighting elements that is theoretically capable of densities and speeds far beyond anything that conventional VLSI in silicon could ever offer is presented. To illustrate the feasibility of such a technology, a small three-layer feedforward prototype network with five binary neurons and six tri-state synapses was built and used to perform all of the fundamental logic functions: XOR, AND, OR, and NOT.

Quantum electron-vibrational dynamics at finite temperature: Thermo field dynamics approach

NASA Astrophysics Data System (ADS)

Borrelli, Raffaele; Gelin, Maxim F.

2016-12-01

Quantum electron-vibrational dynamics in molecular systems at finite temperature is described using an approach based on the thermo field dynamics theory. This formulation treats temperature effects in the Hilbert space without introducing the Liouville space. A comparison with the theoretically equivalent density matrix formulation shows the key numerical advantages of the present approach. The solution of thermo field dynamics equations with a novel technique for the propagation of tensor trains (matrix product states) is discussed. Numerical applications to model spin-boson systems show that the present approach is a promising tool for the description of quantum dynamics of complex molecular systems at finite temperature.

Classical simulation of quantum many-body systems

NASA Astrophysics Data System (ADS)

Huang, Yichen

Classical simulation of quantum many-body systems is in general a challenging problem for the simple reason that the dimension of the Hilbert space grows exponentially with the system size. In particular, merely encoding a generic quantum many-body state requires an exponential number of bits. However, condensed matter physicists are mostly interested in local Hamiltonians and especially their ground states, which are highly non-generic. Thus, we might hope that at least some physical systems allow efficient classical simulation. Starting with one-dimensional (1D) quantum systems (i.e., the simplest nontrivial case), the first basic question is: Which classes of states have efficient classical representations? It turns out that this question is quantitatively related to the amount of entanglement in the state, for states with "little entanglement'' are well approximated by matrix product states (a data structure that can be manipulated efficiently on a classical computer). At a technical level, the mathematical notion for "little entanglement'' is area law, which has been proved for unique ground states in 1D gapped systems. We establish an area law for constant-fold degenerate ground states in 1D gapped systems and thus explain the effectiveness of matrix-product-state methods in (e.g.) symmetry breaking phases. This result might not be intuitively trivial as degenerate ground states in gapped systems can be long-range correlated. Suppose an efficient classical representation exists. How can one find it efficiently? The density matrix renormalization group is the leading numerical method for computing ground states in 1D quantum systems. However, it is a heuristic algorithm and the possibility that it may fail in some cases cannot be completely ruled out. Recently, a provably efficient variant of the density matrix renormalization group has been developed for frustration-free 1D gapped systems. We generalize this algorithm to all (i.e., possibly frustrated) 1D gapped systems. Note that the ground-state energy of 1D gapless Hamiltonians is computationally intractable even in the presence of translational invariance. It is tempting to extend methods and tools in 1D to two and higher dimensions (2+D), e.g., matrix product states are generalized to tensor network states. Since an area law for entanglement (if formulated properly) implies efficient matrix product state representations in 1D, an interesting question is whether a similar implication holds in 2+D. Roughly speaking, we show that an area law for entanglement (in any reasonable formulation) does not always imply efficient tensor network representations of the ground states of 2+D local Hamiltonians even in the presence of translational invariance. It should be emphasized that this result does not contradict with the common sense that in practice quantum states with more entanglement usually require more space to be stored classically; rather, it demonstrates that the relationship between entanglement and efficient classical representations is still far from being well understood. Excited eigenstates participate in the dynamics of quantum systems and are particularly relevant to the phenomenon of many-body localization (absence of transport at finite temperature in strongly correlated systems). We study the entanglement of excited eigenstates in random spin chains and expect that its singularities coincide with dynamical quantum phase transitions. This expectation is confirmed in the disordered quantum Ising chain using both analytical and numerical methods. Finally, we study the problem of generating ground states (possibly with topological order) in 1D gapped systems using quantum circuits. This is an interesting problem both in theory and in practice. It not only characterizes the essential difference between the entanglement patterns that give rise to trivial and nontrivial topological order, but also quantifies the difficulty of preparing quantum states with a quantum computer (in experiments).

Parallel scalability of Hartree-Fock calculations

NASA Astrophysics Data System (ADS)

Chow, Edmond; Liu, Xing; Smelyanskiy, Mikhail; Hammond, Jeff R.

2015-03-01

Quantum chemistry is increasingly performed using large cluster computers consisting of multiple interconnected nodes. For a fixed molecular problem, the efficiency of a calculation usually decreases as more nodes are used, due to the cost of communication between the nodes. This paper empirically investigates the parallel scalability of Hartree-Fock calculations. The construction of the Fock matrix and the density matrix calculation are analyzed separately. For the former, we use a parallelization of Fock matrix construction based on a static partitioning of work followed by a work stealing phase. For the latter, we use density matrix purification from the linear scaling methods literature, but without using sparsity. When using large numbers of nodes for moderately sized problems, density matrix computations are network-bandwidth bound, making purification methods potentially faster than eigendecomposition methods.

Coherent π-electron dynamics of (P)-2,2'-biphenol induced by ultrashort linearly polarized UV pulses: Angular momentum and ring current

NASA Astrophysics Data System (ADS)

Mineo, H.; Lin, S. H.; Fujimura, Y.

2013-02-01

The results of a theoretical investigation of coherent π-electron dynamics for nonplanar (P)-2,2'-biphenol induced by ultrashort linearly polarized UV pulses are presented. Expressions for the time-dependent coherent angular momentum and ring current are derived by using the density matrix method. The time dependence of these coherences is determined by the off-diagonal density matrix element, which can be obtained by solving the coupled equations of motion of the electronic-state density matrix. Dephasing effects on coherent angular momentum and ring current are taken into account within the Markov approximation. The magnitudes of the electronic angular momentum and current are expressed as the sum of expectation values of the corresponding operators in the two phenol rings (L and R rings). Here, L (R) denotes the phenol ring in the left (right)-hand side of (P)-2,2'-biphenol. We define the bond current between the nearest neighbor carbon atoms Ci and Cj as an electric current through a half plane perpendicular to the Ci-Cj bond. The bond current can be expressed in terms of the inter-atomic bond current. The inter-atomic bond current (bond current) depends on the position of the half plane on the bond and has the maximum value at the center. The coherent ring current in each ring is defined by averaging over the bond currents. Since (P)-2,2'-biphenol is nonplanar, the resultant angular momentum is not one-dimensional. Simulations of the time-dependent coherent angular momentum and ring current of (P)-2,2'-biphenol excited by ultrashort linearly polarized UV pulses are carried out using the molecular parameters obtained by the time-dependent density functional theory (TD-DFT) method. Oscillatory behaviors in the time-dependent angular momentum (ring current), which can be called angular momentum (ring current) quantum beats, are classified by the symmetry of the coherent state, symmetric or antisymmetric. The bond current of the bridge bond linking the L and R rings is zero for the symmetric coherent state, while it is nonzero for the antisymmetric coherent state. The magnitudes of ring current and ring current-induced magnetic field are also evaluated, and their possibility as a control parameter in ultrafast switching devices is discussed. The present results give a detailed description of the theoretical treatment reported in our previous paper [H. Mineo, M. Yamaki, Y. Teranish, M. Hayashi, S. H. Lin, and Y. Fujimura, J. Am. Chem. Soc. 134, 14279 (2012), 10.1021/ja3047848].

Coherent π-electron dynamics of (P)-2,2'-biphenol induced by ultrashort linearly polarized UV pulses: angular momentum and ring current.

PubMed

Mineo, H; Lin, S H; Fujimura, Y

2013-02-21

The results of a theoretical investigation of coherent π-electron dynamics for nonplanar (P)-2,2'-biphenol induced by ultrashort linearly polarized UV pulses are presented. Expressions for the time-dependent coherent angular momentum and ring current are derived by using the density matrix method. The time dependence of these coherences is determined by the off-diagonal density matrix element, which can be obtained by solving the coupled equations of motion of the electronic-state density matrix. Dephasing effects on coherent angular momentum and ring current are taken into account within the Markov approximation. The magnitudes of the electronic angular momentum and current are expressed as the sum of expectation values of the corresponding operators in the two phenol rings (L and R rings). Here, L (R) denotes the phenol ring in the left (right)-hand side of (P)-2,2'-biphenol. We define the bond current between the nearest neighbor carbon atoms Ci and Cj as an electric current through a half plane perpendicular to the Ci-Cj bond. The bond current can be expressed in terms of the inter-atomic bond current. The inter-atomic bond current (bond current) depends on the position of the half plane on the bond and has the maximum value at the center. The coherent ring current in each ring is defined by averaging over the bond currents. Since (P)-2,2'-biphenol is nonplanar, the resultant angular momentum is not one-dimensional. Simulations of the time-dependent coherent angular momentum and ring current of (P)-2,2'-biphenol excited by ultrashort linearly polarized UV pulses are carried out using the molecular parameters obtained by the time-dependent density functional theory (TD-DFT) method. Oscillatory behaviors in the time-dependent angular momentum (ring current), which can be called angular momentum (ring current) quantum beats, are classified by the symmetry of the coherent state, symmetric or antisymmetric. The bond current of the bridge bond linking the L and R rings is zero for the symmetric coherent state, while it is nonzero for the antisymmetric coherent state. The magnitudes of ring current and ring current-induced magnetic field are also evaluated, and their possibility as a control parameter in ultrafast switching devices is discussed. The present results give a detailed description of the theoretical treatment reported in our previous paper [H. Mineo, M. Yamaki, Y. Teranish, M. Hayashi, S. H. Lin, and Y. Fujimura, J. Am. Chem. Soc. 134, 14279 (2012)].

Electronic structure of Fe, Co, and Ni impurities in Pd

DOE Office of Scientific and Technical Information (OSTI.GOV)

van Acker, J.F.; Weijs, P.W.J.; Fuggle, J.C.

1988-11-15

A photoemission study of the valence bands of the dilute alloys PdFe, PdCo, and PdNi is presented. We use the Cooper minimum effect to estimate the local density of states on the impurity site. The behavior of transition-metal impurities in a transition-metal matrix is shown to be very different from their behavior in s-p metals. Our conclusion is that the Fe and Co 3d states are mixed with states throughout the Pd 4d band, while the Ni contribution to the spectra is dominated by a peak of (minority) 3d states near the Fermi level.

10-Qubit Entanglement and Parallel Logic Operations with a Superconducting Circuit

NASA Astrophysics Data System (ADS)

Song, Chao; Xu, Kai; Liu, Wuxin; Yang, Chui-ping; Zheng, Shi-Biao; Deng, Hui; Xie, Qiwei; Huang, Keqiang; Guo, Qiujiang; Zhang, Libo; Zhang, Pengfei; Xu, Da; Zheng, Dongning; Zhu, Xiaobo; Wang, H.; Chen, Y.-A.; Lu, C.-Y.; Han, Siyuan; Pan, Jian-Wei

2017-11-01

Here we report on the production and tomography of genuinely entangled Greenberger-Horne-Zeilinger states with up to ten qubits connecting to a bus resonator in a superconducting circuit, where the resonator-mediated qubit-qubit interactions are used to controllably entangle multiple qubits and to operate on different pairs of qubits in parallel. The resulting 10-qubit density matrix is probed by quantum state tomography, with a fidelity of 0.668 ±0.025 . Our results demonstrate the largest entanglement created so far in solid-state architectures and pave the way to large-scale quantum computation.

10-Qubit Entanglement and Parallel Logic Operations with a Superconducting Circuit.

PubMed

Song, Chao; Xu, Kai; Liu, Wuxin; Yang, Chui-Ping; Zheng, Shi-Biao; Deng, Hui; Xie, Qiwei; Huang, Keqiang; Guo, Qiujiang; Zhang, Libo; Zhang, Pengfei; Xu, Da; Zheng, Dongning; Zhu, Xiaobo; Wang, H; Chen, Y-A; Lu, C-Y; Han, Siyuan; Pan, Jian-Wei

2017-11-03

Here we report on the production and tomography of genuinely entangled Greenberger-Horne-Zeilinger states with up to ten qubits connecting to a bus resonator in a superconducting circuit, where the resonator-mediated qubit-qubit interactions are used to controllably entangle multiple qubits and to operate on different pairs of qubits in parallel. The resulting 10-qubit density matrix is probed by quantum state tomography, with a fidelity of 0.668±0.025. Our results demonstrate the largest entanglement created so far in solid-state architectures and pave the way to large-scale quantum computation.

Molecular properties of excited electronic state: Formalism, implementation, and applications of analytical second energy derivatives within the framework of the time-dependent density functional theory/molecular mechanics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zeng, Qiao; Liang, WanZhen, E-mail: liangwz@xmu.edu.cn; Liu, Jie

2014-05-14

This work extends our previous works [J. Liu and W. Z. Liang, J. Chem. Phys. 135, 014113 (2011); J. Liu and W. Z. Liang, J. Chem. Phys. 135, 184111 (2011)] on analytical excited-state energy Hessian within the framework of time-dependent density functional theory (TDDFT) to couple with molecular mechanics (MM). The formalism, implementation, and applications of analytical first and second energy derivatives of TDDFT/MM excited state with respect to the nuclear and electric perturbations are presented. Their performances are demonstrated by the calculations of adiabatic excitation energies, and excited-state geometries, harmonic vibrational frequencies, and infrared intensities for a number ofmore » benchmark systems. The consistent results with the full quantum mechanical method and other hybrid theoretical methods indicate the reliability of the current numerical implementation of developed algorithms. The computational accuracy and efficiency of the current analytical approach are also checked and the computational efficient strategies are suggested to speed up the calculations of complex systems with many MM degrees of freedom. Finally, we apply the current analytical approach in TDDFT/MM to a realistic system, a red fluorescent protein chromophore together with part of its nearby protein matrix. The calculated results indicate that the rearrangement of the hydrogen bond interactions between the chromophore and the protein matrix is responsible for the large Stokes shift.« less

Matrix product state representation of quasielectron wave functions

NASA Astrophysics Data System (ADS)

Kjäll, J.; Ardonne, E.; Dwivedi, V.; Hermanns, M.; Hansson, T. H.

2018-05-01

Matrix product state techniques provide a very efficient way to numerically evaluate certain classes of quantum Hall wave functions that can be written as correlators in two-dimensional conformal field theories. Important examples are the Laughlin and Moore-Read ground states and their quasihole excitations. In this paper, we extend the matrix product state techniques to evaluate quasielectron wave functions, a more complex task because the corresponding conformal field theory operator is not local. We use our method to obtain density profiles for states with multiple quasielectrons and quasiholes, and to calculate the (mutual) statistical phases of the excitations with high precision. The wave functions we study are subject to a known difficulty: the position of a quasielectron depends on the presence of other quasiparticles, even when their separation is large compared to the magnetic length. Quasielectron wave functions constructed using the composite fermion picture, which are topologically equivalent to the quasielectrons we study, have the same problem. This flaw is serious in that it gives wrong results for the statistical phases obtained by braiding distant quasiparticles. We analyze this problem in detail and show that it originates from an incomplete screening of the topological charges, which invalidates the plasma analogy. We demonstrate that this can be remedied in the case when the separation between the quasiparticles is large, which allows us to obtain the correct statistical phases. Finally, we propose that a modification of the Laughlin state, that allows for local quasielectron operators, should have good topological properties for arbitrary configurations of excitations.

A minimum drives automatic target definition procedure for multi-axis random control testing

NASA Astrophysics Data System (ADS)

Musella, Umberto; D'Elia, Giacomo; Carrella, Alex; Peeters, Bart; Mucchi, Emiliano; Marulo, Francesco; Guillaume, Patrick

2018-07-01

Multiple-Input Multiple-Output (MIMO) vibration control tests are able to closely replicate, via shakers excitation, the vibration environment that a structure needs to withstand during its operational life. This feature is fundamental to accurately verify the experienced stress state, and ultimately the fatigue life, of the tested structure. In case of MIMO random tests, the control target is a full reference Spectral Density Matrix in the frequency band of interest. The diagonal terms are the Power Spectral Densities (PSDs), representative for the acceleration operational levels, and the off-diagonal terms are the Cross Spectral Densities (CSDs). The specifications of random vibration tests are however often given in terms of PSDs only, coming from a legacy of single axis testing. Information about the CSDs is often missing. An accurate definition of the CSD profiles can further enhance the MIMO random testing practice, as these terms influence both the responses and the shaker's voltages (the so-called drives). The challenges are linked to the algebraic constraint that the full reference matrix must be positive semi-definite in the entire bandwidth, with no flexibility in modifying the given PSDs. This paper proposes a newly developed method that automatically provides the full reference matrix without modifying the PSDs, considered as test specifications. The innovative feature is the capability of minimizing the drives required to match the reference PSDs and, at the same time, to directly guarantee that the obtained full matrix is positive semi-definite. The drives minimization aims on one hand to reach the fixed test specifications without stressing the delicate excitation system; on the other hand it potentially allows to further increase the test levels. The detailed analytic derivation and implementation steps of the proposed method are followed by real-life testing considering different scenarios.

Direct evaluation of boson dynamics via finite-temperature time-dependent variation with multiple Davydov states.

PubMed

Fujihashi, Yuta; Wang, Lu; Zhao, Yang

2017-12-21

Recent advances in quantum optics allow for exploration of boson dynamics in dissipative many-body systems. However, the traditional descriptions of quantum dissipation using reduced density matrices are unable to capture explicit information of bath dynamics. In this work, efficient evaluation of boson dynamics is demonstrated by combining the multiple Davydov Ansatz with finite-temperature time-dependent variation, going beyond what state-of-the-art density matrix approaches are capable to offer for coupled electron-boson systems. To this end, applications are made to excitation energy transfer in photosynthetic systems, singlet fission in organic thin films, and circuit quantum electrodynamics in superconducting devices. Thanks to the multiple Davydov Ansatz, our analysis of boson dynamics leads to clear revelation of boson modes strongly coupled to electronic states, as well as in-depth description of polaron creation and destruction in the presence of thermal fluctuations.

Communication: CDFT-CI couplings can be unreliable when there is fractional charge transfer

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mavros, Michael G.; Van Voorhis, Troy, E-mail: tvan@mit.edu

2015-12-21

Constrained density functional theory with configuration interaction (CDFT-CI) is a useful, low-cost tool for the computational prediction of electronic couplings between pseudo-diabatic constrained electronic states. Such couplings are of paramount importance in electron transfer theory and transition state theory, among other areas of chemistry. Unfortunately, CDFT-CI occasionally fails significantly, predicting a coupling that does not decay exponentially with distance and/or overestimating the expected coupling by an order of magnitude or more. In this communication, we show that the eigenvalues of the difference density matrix between the two constrained states can be used as an a priori metric to determine whenmore » CDFT-CI are likely to be reliable: when the eigenvalues are near 0 or ±1, transfer of a whole electron is occurring, and CDFT-CI can be trusted. We demonstrate the utility of this metric with several illustrative examples.« less

Communication: CDFT-CI couplings can be unreliable when there is fractional charge transfer

NASA Astrophysics Data System (ADS)

Mavros, Michael G.; Van Voorhis, Troy

2015-12-01

Constrained density functional theory with configuration interaction (CDFT-CI) is a useful, low-cost tool for the computational prediction of electronic couplings between pseudo-diabatic constrained electronic states. Such couplings are of paramount importance in electron transfer theory and transition state theory, among other areas of chemistry. Unfortunately, CDFT-CI occasionally fails significantly, predicting a coupling that does not decay exponentially with distance and/or overestimating the expected coupling by an order of magnitude or more. In this communication, we show that the eigenvalues of the difference density matrix between the two constrained states can be used as an a priori metric to determine when CDFT-CI are likely to be reliable: when the eigenvalues are near 0 or ±1, transfer of a whole electron is occurring, and CDFT-CI can be trusted. We demonstrate the utility of this metric with several illustrative examples.

Towards a formal definition of static and dynamic electronic correlations.

PubMed

Benavides-Riveros, Carlos L; Lathiotakis, Nektarios N; Marques, Miguel A L

2017-05-24

Some of the most spectacular failures of density-functional and Hartree-Fock theories are related to an incorrect description of the so-called static electron correlation. Motivated by recent progress in the N-representability problem of the one-body density matrix for pure states, we propose a method to quantify the static contribution to the electronic correlation. By studying several molecular systems we show that our proposal correlates well with our intuition of static and dynamic electron correlation. Our results bring out the paramount importance of the occupancy of the highest occupied natural spin-orbital in such quantification.

The phonon-coupling model for Skyrme forces

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lyutorovich, N.; Tselyaev, V.; Speth, J., E-mail: J.Speth@fz-juelich.de

2016-11-15

A short review on the self-consistent RPA based on the energy-density functional of the Skyrme type is given. We also present an extension of the RPA where the coupling of phonons to the single-particle states is considered. Within this approach we present numerical results which are compared with data. The self-consistent approach is compared with the Landau–Migdal theory. Here we derive from the self-consistent ph interaction, the Landau–Migdal parameters as well as their density dependence. In the Appendix a new derivation of the reduced matrix elements of the ph interaction is presented.

Preliminary characterisation of new glass reference materials (GSA-1G, GSC-1G, GSD-1G and GSE-1G) by laser ablation-inductively coupled plasma-mass spectrometry using 193 nm, 213 nm and 266 nm wavelengths

USGS Publications Warehouse

Guillong, M.; Hametner, K.; Reusser, E.; Wilson, S.A.; Gunther, D.

2005-01-01

New glass reference materials GSA-1G, GSC-1G, GSD-1G and GSE-1G have been characterised using a prototype solid state laser ablation system capable of producing wavelengths of 193 nm, 213 nm and 266 nm. This system allowed comparison of the effects of different laser wavelengths under nearly identical ablation and ICP operating conditions. The wavelengths 213 nm and 266 nm were also used at higher energy densities to evaluate the influence of energy density on quantitative analysis. In addition, the glass reference materials were analysed using commercially available 266 nm Nd:YAG and 193 nm ArF excimer lasers. Laser ablation analysis was carried out using both single spot and scanning mode ablation. Using laser ablation ICP-MS, concentrations of fifty-eight elements were determined with external calibration to the NIST SRM 610 glass reference material. Instead of applying the more common internal standardisation procedure, the total concentration of all element oxide concentrations was normalised to 100%. Major element concentrations were compared with those determined by electron microprobe. In addition to NIST SRM 610 for external calibration, USGS BCR-2G was used as a more closely matrix-matched reference material in order to compare the effect of matrix-matched and non matrix-matched calibration on quantitative analysis. The results show that the various laser wavelengths and energy densities applied produced similar results, with the exception of scanning mode ablation at 266 nm without matrix-matched calibration where deviations up to 60% from the average were found. However, results acquired using a scanning mode with a matrix-matched calibration agreed with results obtained by spot analysis. The increased abundance of large particles produced when using a scanning ablation mode with NIST SRM 610, is responsible for elemental fractionation effects caused by incomplete vaporisation of large particles in the ICP.

Silicon quantum dots embedded in a SiO2 matrix: From structural study to carrier transport properties

NASA Astrophysics Data System (ADS)

Garcia-Castello, Nuria; Illera, Sergio; Guerra, Roberto; Prades, Joan Daniel; Ossicini, Stefano; Cirera, Albert

2013-08-01

We study the details of electronic transport related to the atomistic structure of silicon quantum dots embedded in a silicon dioxide matrix using ab initio calculations of the density of states. Several structural and composition features of quantum dots (QDs), such as diameter and amorphization level, are studied and correlated with transport under transfer Hamiltonian formalism. The current is strongly dependent on the QD density of states and on the conduction gap, both dependent on the dot diameter. In particular, as size increases, the available states inside the QD increase, while the QD band gap decreases due to relaxation of quantum confinement. Both effects contribute to increasing the current with the dot size. Besides, valence band offset between the band edges of the QD and the silica, and conduction band offset in a minor grade, increases with the QD diameter up to the theoretical value corresponding to planar heterostructures, thus decreasing the tunneling transmission probability and hence the total current. We discuss the influence of these parameters on electron and hole transport, evidencing a correlation between the electron (hole) barrier value and the electron (hole) current, and obtaining a general enhancement of the electron (hole) transport for larger (smaller) QD. Finally, we show that crystalline and amorphous structures exhibit enhanced probability of hole and electron current, respectively.

Double Gamow-Teller Transitions and its Relation to Neutrinoless β β Decay

NASA Astrophysics Data System (ADS)

Shimizu, Noritaka; Menéndez, Javier; Yako, Kentaro

2018-04-01

We study the double Gamow-Teller (DGT) strength distribution of 48Ca with state-of-the-art large-scale nuclear shell model calculations. Our analysis shows that the centroid energy of the DGT giant resonance depends mostly on the isovector pairing interaction, while the resonance width is more sensitive to isoscalar pairing. Pairing correlations are also key in neutrinoless β β (0 ν β β ) decay. We find a simple relation between the centroid energy of the 48Ca DGT giant resonance and the 0 ν β β decay nuclear matrix element. More generally, we observe a very good linear correlation between the DGT transition to the ground state of the final nucleus and the 0 ν β β decay matrix element. The correlation, which originates on the dominant short-range character of both transitions, extends to heavier systems including several β β emitters and also holds in energy-density functional results. Our findings suggest that DGT experiments can be a very valuable tool to obtain information on the value of 0 ν β β decay nuclear matrix elements.

Modified Hartree-Fock-Bogoliubov theory at finite temperature

NASA Astrophysics Data System (ADS)

Dinh Dang, Nguyen; Arima, Akito

2003-07-01

The modified Hartree-Fock-Bogoliubov (MHFB) theory at finite temperature is derived, which conserves the unitarity relation of the particle-density matrix. This is achieved by constructing a modified-quasiparticle-density matrix, where the fluctuation of the quasiparticle number is microscopically built in. This matrix can be directly obtained from the usual quasiparticle-density matrix by applying the secondary Bogoliubov transformation, which includes the quasiparticle-occupation number. It is shown that, in the limit of constant pairing parameter, the MHFB theory yields the previously obtained modified BCS (MBCS) equations. It is also proved that the modified quasiparticle-random-phase approximation, which is based on the MBCS quasiparticle excitations, conserves the Ikeda sum rule. The numerical calculations of the pairing gap, heat capacity, level density, and level-density parameter within the MBCS theory are carried out for 120Sn. The results show that the superfluid-normal phase transition is completely washed out. The applicability of the MBCS up to a temperature as high as T˜5 MeV is analyzed in detail.

Alternative dimensional reduction via the density matrix

NASA Astrophysics Data System (ADS)

de Carvalho, C. A.; Cornwall, J. M.; da Silva, A. J.

2001-07-01

We give graphical rules, based on earlier work for the functional Schrödinger equation, for constructing the density matrix for scalar and gauge fields in equilibrium at finite temperature T. More useful is a dimensionally reduced effective action (DREA) constructed from the density matrix by further functional integration over the arguments of the density matrix coupled to a source. The DREA is an effective action in one less dimension which may be computed order by order in perturbation theory or by dressed-loop expansions; it encodes all thermal matrix elements. We term the DREA procedure alternative dimensional reduction, to distinguish it from the conventional dimensionally reduced field theory (DRFT) which applies at infinite T. The DREA is useful because it gives a dimensionally reduced theory usable at any T including infinity, where it yields the DRFT, and because it does not and cannot have certain spurious infinities which sometimes occur in the density matrix itself or the conventional DRFT; these come from ln T factors at infinite temperature. The DREA can be constructed to all orders (in principle) and the only regularizations needed are those which control the ultraviolet behavior of the zero-T theory. An example of spurious divergences in the DRFT occurs in d=2+1φ4 theory dimensionally reduced to d=2. We study this theory and show that the rules for the DREA replace these ``wrong'' divergences in physical parameters by calculable powers of ln T; we also compute the phase transition temperature of this φ4 theory in one-loop order. Our density-matrix construction is equivalent to a construction of the Landau-Ginzburg ``coarse-grained free energy'' from a microscopic Hamiltonian.

Two-leg ladder systems with dipole–dipole Fermion interactions

NASA Astrophysics Data System (ADS)

Mosadeq, Hamid; Asgari, Reza

2018-05-01

The ground-state phase diagram of a two-leg fermionic dipolar ladder with inter-site interactions is studied using density matrix renormalization group (DMRG) techniques. We use a state-of-the-art implementation of the DMRG algorithm and finite size scaling to simulate large system sizes with high accuracy. We also consider two different model systems and explore stable phases in half and quarter filling factors. We find that in the half filling, the charge and spin gaps emerge in a finite value of the dipole–dipole and on-site interactions. In the quarter filling case, s-wave superconducting state, charge density wave, homogenous insulating and phase separation phases occur depend on the interaction values. Moreover, in the dipole–dipole interaction, the D-Mott phase emerges when the hopping terms along the chain and rung are the same, whereas, this phase has been only proposed for the anisotropic Hubbard model. In the half filling case, on the other hand, there is either charge-density wave or charged Mott order phase depends on the orientation of the dipole moments of the particles with respect to the ladder geometry.

Topological phase transition and the effect of Hubbard interactions on the one-dimensional topological Kondo insulator

NASA Astrophysics Data System (ADS)

Pillay, Jason C.; McCulloch, Ian P.

2018-05-01

The effect of a local Kondo coupling and Hubbard interaction on the topological phase of the one-dimensional topological Kondo insulator (TKI) is numerically investigated using the infinite matrix-product state density-matrix renormalization group algorithm. The ground state of the TKI is a symmetry-protected topological (SPT) phase protected by inversion symmetry. It is found that on its own, the Hubbard interaction that tends to force fermions into a one-charge per site order is insufficient to destroy the SPT phase. However, when the local Kondo Hamiltonian term that favors a topologically trivial ground state with a one-charge per site order is introduced, the Hubbard interaction assists in the destruction of the SPT phase. This topological phase transition occurs in the charge sector where the correlation length of the charge excitation diverges while the correlation length of the spin excitation remains finite. The critical exponents, central charge, and the phase diagram separating the SPT phase from the topologically trivial phase are presented.

Comparative study of heterogeneous magnetic state above TC in La0.82Sr0.18CoO3 cobaltite and La0.83Sr0.17MnO3 manganite

NASA Astrophysics Data System (ADS)

Ryzhov, V. A.; Lazuta, A. V.; Molkanov, P. L.; Khavronin, V. P.; Kurbakov, A. I.; Runov, V. V.; Mukovskii, Ya. M.; Pestun, A. E.; Privezentsev, R. V.

2012-10-01

The magnetic, transport and structural properties are studied for La0.83Sr0.17MnO3 and La0.82Sr0.18CoO3 single crystals with nearly the same doping and the metallic ground state. Their comparisons have shown that ferromagnetic clusters originate in the paramagnetic matrix below Т*>TC in both samples and exhibit similar properties. This suggests the possible universality of such phenomena in doped mixed-valence oxides of transition metals with the perovskite-type structure. The cluster density increases on cooling and plays an important role on the physical properties of these systems. The differences in cluster evolutions and scenarios of their insulator-metal transitions are related to different magnetic behaviors of the matrixes in these crystals that is mainly due to distinct spin states of the Mn3+ and Co3+ ions.

Growth model for uneven-aged loblolly pine stands : simulations and management implications

Treesearch

C.-R. Lin; J. Buongiorno; Jeffrey P. Prestemon; K. E. Skog

1998-01-01

A density-dependent matrix growth model of uneven-aged loblolly pine stands was developed with data from 991 permanent plots in the southern United States. The model predicts the number of pine, soft hardwood, and hard hardwood trees in 13 diameter classes, based on equations for ingrowth, upgrowth, and mortality. Projections of 6 to 10 years agreed with the growth...

On the equilibrium state of a small system with random matrix coupling to its environment

NASA Astrophysics Data System (ADS)

Lebowitz, J. L.; Pastur, L.

2015-07-01

We consider a random matrix model of interaction between a small n-level system, S, and its environment, a N-level heat reservoir, R. The interaction between S and R is modeled by a tensor product of a fixed n× n matrix and a N× N Hermitian random matrix. We show that under certain ‘macroscopicity’ conditions on R, the reduced density matrix of the system {{ρ }S}=T{{r}R}ρ S\\cup R(eq), is given by ρ S(c)˜ exp \\{-β {{H}S}\\}, where HS is the Hamiltonian of the isolated system. This holds for all strengths of the interaction and thus gives some justification for using ρ S(c) to describe some nano-systems, like biopolymers, in equilibrium with their environment (Seifert 2012 Rep. Prog. Phys. 75 126001). Our results extend those obtained previously in (Lebowitz and Pastur 2004 J. Phys. A: Math. Gen. 37 1517-34) (Lebowitz et al 2007 Contemporary Mathematics (Providence RI: American Mathematical Society) pp 199-218) for a special two-level system.

Neutrinoless ββ decay mediated by the exchange of light and heavy neutrinos: the role of nuclear structure correlations

NASA Astrophysics Data System (ADS)

Menéndez, J.

2018-01-01

Neutrinoless β β decay nuclear matrix elements calculated with the shell model and energy-density functional theory typically disagree by more than a factor of two in the standard scenario of light-neutrino exchange. In contrast, for a decay mediated by sterile heavy neutrinos the deviations are reduced to about 50%, an uncertainty similar to the one due to short-range effects. We compare matrix elements in the light- and heavy-neutrino-exchange channels, exploring the radial, momentum transfer and angular momentum-parity matrix element distributions, and considering transitions that involve correlated and uncorrelated nuclear states. We argue that the shorter-range heavy-neutrino exchange is less sensitive to collective nuclear correlations, and that discrepancies in matrix elements are mostly due to the treatment of long-range correlations in many-body calculations. Our analysis supports previous studies suggesting that isoscalar pairing correlations, which affect mostly the longer-range part of the neutrinoless β β decay operator, are partially responsible for the differences between nuclear matrix elements in the standard light-neutrino-exchange mechanism.

A density functional approach to ferrogels

NASA Astrophysics Data System (ADS)

Cremer, P.; Heinen, M.; Menzel, A. M.; Löwen, H.

2017-07-01

Ferrogels consist of magnetic colloidal particles embedded in an elastic polymer matrix. As a consequence, their structural and rheological properties are governed by a competition between magnetic particle-particle interactions and mechanical matrix elasticity. Typically, the particles are permanently fixed within the matrix, which makes them distinguishable by their positions. Over time, particle neighbors do not change due to the fixation by the matrix. Here we present a classical density functional approach for such ferrogels. We map the elastic matrix-induced interactions between neighboring colloidal particles distinguishable by their positions onto effective pairwise interactions between indistinguishable particles similar to a ‘pairwise pseudopotential’. Using Monte-Carlo computer simulations, we demonstrate for one-dimensional dipole-spring models of ferrogels that this mapping is justified. We then use the pseudopotential as an input into classical density functional theory of inhomogeneous fluids and predict the bulk elastic modulus of the ferrogel under various conditions. In addition, we propose the use of an ‘external pseudopotential’ when one switches from the viewpoint of a one-dimensional dipole-spring object to a one-dimensional chain embedded in an infinitely extended bulk matrix. Our mapping approach paves the way to describe various inhomogeneous situations of ferrogels using classical density functional concepts of inhomogeneous fluids.

Space charge in nanostructure resonances

NASA Astrophysics Data System (ADS)

Price, Peter J.

1996-10-01

In quantum ballistic propagation of electrons through a variety of nanostructures, resonance in the energy-dependent transmission and reflection probabilities generically is associated with (1) a quasi-level with a decay lifetime, and (2) a bulge in electron density within the structure. It can be shown that, to a good approximation, a simple formula in all cases connects the density of states for the latter to the energy dependence of the phase angles of the eigen values of the S-matrix governing the propagation. For both the Lorentzian resonances (normal or inverted) and for the Fano-type resonances, as a consequence of this eigen value formula, the space charge due to filled states over the energy range of a resonance is just equal (for each spin state) to one electron charge. The Coulomb interaction within this space charge is known to 'distort' the electrical characteristics of resonant nanostructures. In these systems, however, the exchange effect should effectively cancel the interaction between states with parallel spins, leaving only the anti-parallel spin contribution.

How measurement reversal could erroneously suggest the capability to discriminate the preparation basis of a quantum ensemble

NASA Astrophysics Data System (ADS)

Goyal, Sandeep K.; Singh, Rajeev; Ghosh, Sibasish

2016-01-01

Mixed states of a quantum system, represented by density operators, can be decomposed as a statistical mixture of pure states in a number of ways where each decomposition can be viewed as a different preparation recipe. However the fact that the density matrix contains full information about the ensemble makes it impossible to estimate the preparation basis for the quantum system. Here we present a measurement scheme to (seemingly) improve the performance of unsharp measurements. We argue that in some situations this scheme is capable of providing statistics from a single copy of the quantum system, thus making it possible to perform state tomography from a single copy. One of the by-products of the scheme is a way to distinguish between different preparation methods used to prepare the state of the quantum system. However, our numerical simulations disagree with our intuitive predictions. We show that a counterintuitive property of a biased classical random walk is responsible for the proposed mechanism not working.

Holon Wigner Crystal in a Lightly Doped Kagome Quantum Spin Liquid

DOE PAGES

Jiang, Hong -Chen; Devereaux, T.; Kivelson, S. A.

2017-08-07

We address the problem of a lightly doped spin liquid through a large-scale density-matrix renormalization group study of the t–J model on a kagome lattice with a small but nonzero concentration δ of doped holes. It is now widely accepted that the undoped (δ = 0) spin-1/2 Heisenberg antiferromagnet has a spin-liquid ground state. Theoretical arguments have been presented that light doping of such a spin liquid could give rise to a high temperature superconductor or an exotic topological Fermi liquid metal. Instead, we infer that the doped holes form an insulating charge-density wave state with one doped hole permore » unit cell, i.e., a Wigner crystal. Spin correlations remain short ranged, as in the spin-liquid parent state, from which we infer that the state is a crystal of spinless holons, rather than of holes. In conclusion, our results may be relevant to kagome lattice herbertsmithite upon doping.« less

Computing the Density Matrix in Electronic Structure Theory on Graphics Processing Units.

PubMed

Cawkwell, M J; Sanville, E J; Mniszewski, S M; Niklasson, Anders M N

2012-11-13

The self-consistent solution of a Schrödinger-like equation for the density matrix is a critical and computationally demanding step in quantum-based models of interatomic bonding. This step was tackled historically via the diagonalization of the Hamiltonian. We have investigated the performance and accuracy of the second-order spectral projection (SP2) algorithm for the computation of the density matrix via a recursive expansion of the Fermi operator in a series of generalized matrix-matrix multiplications. We demonstrate that owing to its simplicity, the SP2 algorithm [Niklasson, A. M. N. Phys. Rev. B2002, 66, 155115] is exceptionally well suited to implementation on graphics processing units (GPUs). The performance in double and single precision arithmetic of a hybrid GPU/central processing unit (CPU) and full GPU implementation of the SP2 algorithm exceed those of a CPU-only implementation of the SP2 algorithm and traditional matrix diagonalization when the dimensions of the matrices exceed about 2000 × 2000. Padding schemes for arrays allocated in the GPU memory that optimize the performance of the CUBLAS implementations of the level 3 BLAS DGEMM and SGEMM subroutines for generalized matrix-matrix multiplications are described in detail. The analysis of the relative performance of the hybrid CPU/GPU and full GPU implementations indicate that the transfer of arrays between the GPU and CPU constitutes only a small fraction of the total computation time. The errors measured in the self-consistent density matrices computed using the SP2 algorithm are generally smaller than those measured in matrices computed via diagonalization. Furthermore, the errors in the density matrices computed using the SP2 algorithm do not exhibit any dependence of system size, whereas the errors increase linearly with the number of orbitals when diagonalization is employed.

X ray attenuation measurements for high-temperature materials characterization and in-situ monitoring of damage accumulation. Ph.D. Thesis - Cleveland State Univ., 1991

NASA Technical Reports Server (NTRS)

Baaklini, George Y.

1992-01-01

The scope of this dissertation is to develop and apply x ray attenuation measurement systems that are capable of: (1) characterizing density variations in high-temperature materials, e.g., monolithic ceramics, ceramic and intermetallic matrix composites, and (2) noninvasively monitoring damage accumulation and failure sequences in ceramic matrix composites under room temperature tensile testing. This dissertation results in the development of: (1) a point scan digital radiography system, and (2) an in-situ x ray material testing system. Radiographic evaluation before, during, and after loading shows the effect of preexisting volume flaws on the fracture behavior of composites. Results show that x ray film radiography can monitor damage accumulation during tensile loading. Matrix cracking, fiber matrix debonding, fiber bridging, and fiber pullout are imaged throughout the tensile loading of the specimens. Further in-situ radiography is found to be a practical technique for estimating interfacial shear strength between the silicon carbide fibers and the reaction bonded silicon nitride matrix. It is concluded that pretest, in-situ, and post test x ray imaging can provide for greater understanding of ceramic matrix composite mechanical behavior.

Self-consistent predictor/corrector algorithms for stable and efficient integration of the time-dependent Kohn-Sham equation

NASA Astrophysics Data System (ADS)

Zhu, Ying; Herbert, John M.

2018-01-01

The "real time" formulation of time-dependent density functional theory (TDDFT) involves integration of the time-dependent Kohn-Sham (TDKS) equation in order to describe the time evolution of the electron density following a perturbation. This approach, which is complementary to the more traditional linear-response formulation of TDDFT, is more efficient for computation of broad-band spectra (including core-excited states) and for systems where the density of states is large. Integration of the TDKS equation is complicated by the time-dependent nature of the effective Hamiltonian, and we introduce several predictor/corrector algorithms to propagate the density matrix, one of which can be viewed as a self-consistent extension of the widely used modified-midpoint algorithm. The predictor/corrector algorithms facilitate larger time steps and are shown to be more efficient despite requiring more than one Fock build per time step, and furthermore can be used to detect a divergent simulation on-the-fly, which can then be halted or else the time step modified.

Broken Time-Reversal Symmetry in Strongly Correlated Ladder Structures

NASA Astrophysics Data System (ADS)

Troyer, Matthias

2004-03-01

A decade after the first detailed numerical investigations of strongly correlated ladder models, exotic and interesting phases are still being discovered. Besides charge and spin density wave states with broken translational symmetry, and resonating valence bond (RVB) type superconductivity, a time reversal symmetry borken phase was recently found at half filling [J.B. Marston et al., Phys. Rev. Lett 89, 056404 (2002)]. In this talk I will present our recent results of density matrix renormalization group (DMRG) calculations [Phys. Rev. Lett. 90, 186401 (2003)], where we provide, for the first time, in a doped strongly correlated system (two-leg ladder), a controlled theoretical demonstration of the existence of this state in which long-range ordered orbital currents are arranged in a staggered pattern. This phase, which we found to coexist with a charge density wave, is known in the literature under the names ``staggered flux phase'', ``orbital antiferromagnetism'' or ``d-density wave (DDW)''. This brings us closer to recent proposals that this order might be realized in the enigmatic pseudogap phase of the cuprate high temperature superconductors.

Decoherence can relax cosmic acceleration: an example

DOE Office of Scientific and Technical Information (OSTI.GOV)

Markkanen, Tommi, E-mail: tommi.markkanen@kcl.ac.uk

We investigate back reaction in de Sitter space in an approach where only states that are observationally accessible are included in the density matrix. Using the Bunch-Davies vacuum as the initial condition we find for a conformal scalar field and a cosmological constant that tracing over the unobservable states beyond the cosmological horizon leads to a thermal spectrum of particles and that such a configuration is unstable under semi-classical back reaction. It is concluded that this prescription results in an instability of de Sitter space with a gradually increasing horizon size.

Multireference Density Functional Theory with Generalized Auxiliary Systems for Ground and Excited States.

PubMed

Chen, Zehua; Zhang, Du; Jin, Ye; Yang, Yang; Su, Neil Qiang; Yang, Weitao

2017-09-21

To describe static correlation, we develop a new approach to density functional theory (DFT), which uses a generalized auxiliary system that is of a different symmetry, such as particle number or spin, from that of the physical system. The total energy of the physical system consists of two parts: the energy of the auxiliary system, which is determined with a chosen density functional approximation (DFA), and the excitation energy from an approximate linear response theory that restores the symmetry to that of the physical system, thus rigorously leading to a multideterminant description of the physical system. The electron density of the physical system is different from that of the auxiliary system and is uniquely determined from the functional derivative of the total energy with respect to the external potential. Our energy functional is thus an implicit functional of the physical system density, but an explicit functional of the auxiliary system density. We show that the total energy minimum and stationary states, describing the ground and excited states of the physical system, can be obtained by a self-consistent optimization with respect to the explicit variable, the generalized Kohn-Sham noninteracting density matrix. We have developed the generalized optimized effective potential method for the self-consistent optimization. Among options of the auxiliary system and the associated linear response theory, reformulated versions of the particle-particle random phase approximation (pp-RPA) and the spin-flip time-dependent density functional theory (SF-TDDFT) are selected for illustration of principle. Numerical results show that our multireference DFT successfully describes static correlation in bond dissociation and double bond rotation.

Many-body expansion of the Fock matrix in the fragment molecular orbital method

NASA Astrophysics Data System (ADS)

Fedorov, Dmitri G.; Kitaura, Kazuo

2017-09-01

A many-body expansion of the Fock matrix in the fragment molecular orbital method is derived up to three-body terms for restricted Hartree-Fock and density functional theory in the atomic orbital basis and compared to the expansion in the basis of fragment molecular orbitals (MOs). The physical nature of many-body corrections is revealed in terms of charge transfer terms. An improvement of the fragment MO expansion is proposed by adding exchange to the embedding. The accuracy of all developed methods is demonstrated in comparison to unfragmented results for polyalanines, a water cluster, Trp-cage (PDB: 1L2Y) and crambin (PDB: 1CRN) proteins, a zeolite cluster, a Si nano-wire, and a boron nitride ribbon. The physical nature of metallicity is discussed, and it is shown what kinds of metallic systems can be treated by fragment-based methods. The density of states is calculated for a fully closed and a partially open nano-ring of boron nitride with a diameter of 105 nm.

Beyond the single-file fluid limit using transfer matrix method: Exact results for confined parallel hard squares

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gurin, Péter; Varga, Szabolcs

2015-06-14

We extend the transfer matrix method of one-dimensional hard core fluids placed between confining walls for that case where the particles can pass each other and at most two layers can form. We derive an eigenvalue equation for a quasi-one-dimensional system of hard squares confined between two parallel walls, where the pore width is between σ and 3σ (σ is the side length of the square). The exact equation of state and the nearest neighbor distribution functions show three different structures: a fluid phase with one layer, a fluid phase with two layers, and a solid-like structure where the fluidmore » layers are strongly correlated. The structural transition between differently ordered fluids develops continuously with increasing density, i.e., no thermodynamic phase transition occurs. The high density structure of the system consists of clusters with two layers which are broken with particles staying in the middle of the pore.« less

Time Dependent Solution for the He I Line Ratio Electron Temperature and Density Diagnostic in TEXTOR and DIII-D

NASA Astrophysics Data System (ADS)

Munoz Burgos, J. M.; Schmitz, O.; Unterberg, E. A.; Loch, S. D.; Balance, C. P.

2010-11-01

We developed a time dependent solution for the He I line ratio diagnostic. Stationary solution is applied for L-mode at TEXTOR. The radial range is typically limited to a region near the separatrix due to metastable effects, and the atomic data used. We overcome this problem by applying a time dependent solution and thus avoid unphysical results. We use a new R-Matrix with Pseudostates and Convergence Cross-Coupling electron impact excitation and ionization atomic data set into the Collisional Radiative Model (CRM). We include contributions from higher Rydberg states into the CRM by means of the projection matrix. By applying this solution (to the region near the wall) and the stationary solution (near the separatrix), we triple the radial range of the current diagnostic. We explore the possibility of extending this approach to H-mode plasmas in DIII-D by estimating line emission profiles from electron temperature and density Thomson scattering data.

Five- and six-electron harmonium atoms: Highly accurate electronic properties and their application to benchmarking of approximate 1-matrix functionals

NASA Astrophysics Data System (ADS)

Cioslowski, Jerzy; Strasburger, Krzysztof

2018-04-01

Electronic properties of several states of the five- and six-electron harmonium atoms are obtained from large-scale calculations employing explicitly correlated basis functions. The high accuracy of the computed energies (including their components), natural spinorbitals, and their occupation numbers makes them suitable for testing, calibration, and benchmarking of approximate formalisms of quantum chemistry and solid state physics. In the case of the five-electron species, the availability of the new data for a wide range of the confinement strengths ω allows for confirmation and generalization of the previously reached conclusions concerning the performance of the presently known approximations for the electron-electron repulsion energy in terms of the 1-matrix that are at heart of the density matrix functional theory (DMFT). On the other hand, the properties of the three low-lying states of the six-electron harmonium atom, computed at ω = 500 and ω = 1000, uncover deficiencies of the 1-matrix functionals not revealed by previous studies. In general, the previously published assessment of the present implementations of DMFT being of poor accuracy is found to hold. Extending the present work to harmonically confined systems with even more electrons is most likely counterproductive as the steep increase in computational cost required to maintain sufficient accuracy of the calculated properties is not expected to be matched by the benefits of additional information gathered from the resulting benchmarks.

Coupled Cluster Method with Single and Double Excitations Tailored by Matrix Product State Wave Functions.

PubMed

Veis, Libor; Antalík, Andrej; Brabec, Jiří; Neese, Frank; Legeza, Örs; Pittner, Jiří

2016-10-03

In the past decade, the quantum chemical version of the density matrix renormalization group (DMRG) method has established itself as the method of choice for calculations of strongly correlated molecular systems. Despite its favorable scaling, it is in practice not suitable for computations of dynamic correlation. We present a novel method for accurate "post-DMRG" treatment of dynamic correlation based on the tailored coupled cluster (CC) theory in which the DMRG method is responsible for the proper description of nondynamic correlation, whereas dynamic correlation is incorporated through the framework of the CC theory. We illustrate the potential of this method on prominent multireference systems, in particular, N 2 and Cr 2 molecules and also oxo-Mn(Salen), for which we have performed the first post-DMRG computations in order to shed light on the energy ordering of the lowest spin states.

Finite-temperature dynamic structure factor of the spin-1 XXZ chain with single-ion anisotropy

NASA Astrophysics Data System (ADS)

Lange, Florian; Ejima, Satoshi; Fehske, Holger

2018-02-01

Improving matrix-product state techniques based on the purification of the density matrix, we are able to accurately calculate the finite-temperature dynamic response of the infinite spin-1 XXZ chain with single-ion anisotropy in the Haldane, large-D , and antiferromagnetic phases. Distinct thermally activated scattering processes make a significant contribution to the spectral weight in all cases. In the Haldane phase, intraband magnon scattering is prominent, and the on-site anisotropy causes the magnon to split into singlet and doublet branches. In the large-D phase response, the intraband signal is separated from an exciton-antiexciton continuum. In the antiferromagnetic phase, holons are the lowest-lying excitations, with a gap that closes at the transition to the Haldane state. At finite temperatures, scattering between domain-wall excitations becomes especially important and strongly enhances the spectral weight for momentum transfer π .

Strongly contracted canonical transformation theory

NASA Astrophysics Data System (ADS)

Neuscamman, Eric; Yanai, Takeshi; Chan, Garnet Kin-Lic

2010-01-01

Canonical transformation (CT) theory describes dynamic correlation in multireference systems with large active spaces. Here we discuss CT theory's intruder state problem and why our previous approach of overlap matrix truncation becomes infeasible for sufficiently large active spaces. We propose the use of strongly and weakly contracted excitation operators as alternatives for dealing with intruder states in CT theory. The performance of these operators is evaluated for the H2O, N2, and NiO molecules, with comparisons made to complete active space second order perturbation theory and Davidson-corrected multireference configuration interaction theory. Finally, using a combination of strongly contracted CT theory and orbital-optimized density matrix renormalization group theory, we evaluate the singlet-triplet gap of free base porphin using an active space containing all 24 out-of-plane 2p orbitals. Modeling dynamic correlation with an active space of this size is currently only possible using CT theory.

Entanglement and magnetism in high-spin graphene nanodisks

NASA Astrophysics Data System (ADS)

Hagymási, I.; Legeza, Ö.

2018-01-01

We investigate the ground-state properties of triangular graphene nanoflakes with zigzag edge configurations. The description of zero-dimensional nanostructures requires accurate many-body techniques since the widely used density-functional theory with local density approximation or Hartree-Fock methods cannot handle the strong quantum fluctuations. Applying the unbiased density-matrix renormalization group algorithm we calculate the magnetization and entanglement patterns with high accuracy for different interaction strengths and compare them to the mean-field results. With the help of quantum information analysis and subsystem density matrices we reveal that the edges are strongly entangled with each other. We also address the effect of electron and hole doping and demonstrate that the magnetic properties of triangular nanoflakes can be controlled by an electric field, which reveals features of flat-band ferromagnetism. This may open up new avenues in graphene based spintronics.

Entanglement between atomic thermal states and coherent or squeezed photons in a damping cavity

NASA Astrophysics Data System (ADS)

Yadollahi, F.; Safaiee, R.; Golshan, M. M.

2018-02-01

In the present study, the standard Jaynes-Cummings model, in a lossy cavity, is employed to characterize the entanglement between atoms and photons when the former is initially in a thermal state (mixed ensemble) while the latter is described by either coherent or squeezed distributions. The whole system is thus assumed to be in equilibrium with a heat reservoir at a finite temperature T, and the measure of negativity is used to determine the time evolution of atom-photon entanglement. To this end, the master equation for the density matrix, in the secular approximation, is solved and a partial transposition of the result is made. The degree of atom-photon entanglement is then numerically computed, through the negativity, as a function of time and temperature. To justify the behavior of atom-photon entanglement, moreover, we employ the so obtained total density matrix to compute and analyze the time evolution of the initial photonic coherent or squeezed probability distributions and the squeezing parameters. On more practical points, our results demonstrate that as the initial photon mean number increases, the atom-photon entanglement decays at a faster pace for the coherent distribution compared to the squeezed one. Moreover, it is shown that the degree of atom-photon entanglement is much higher and more stable for the squeezed distribution than that for the coherent one. Consequently, we conclude that the time intervals during which the atom-photon entanglement is distillable is longer for the squeezed distribution. It is also illustrated that as the temperature increases the rate of approaching separability is faster for the coherent initial distribution. The novel point of the present report is the calculation of dynamical density matrix (containing all physical information) for the combined system of atom-photon in a lossy cavity, as well as the corresponding negativity, at a finite temperature.

Quantitative (31)P NMR spectroscopy and (1)H MRI measurements of bone mineral and matrix density differentiate metabolic bone diseases in rat models.

PubMed

Cao, Haihui; Nazarian, Ara; Ackerman, Jerome L; Snyder, Brian D; Rosenberg, Andrew E; Nazarian, Rosalynn M; Hrovat, Mirko I; Dai, Guangping; Mintzopoulos, Dionyssios; Wu, Yaotang

2010-06-01

In this study, bone mineral density (BMD) of normal (CON), ovariectomized (OVX), and partially nephrectomized (NFR) rats was measured by (31)P NMR spectroscopy; bone matrix density was measured by (1)H water- and fat-suppressed projection imaging (WASPI); and the extent of bone mineralization (EBM) was obtained by the ratio of BMD/bone matrix density. The capability of these MR methods to distinguish the bone composition of the CON, OVX, and NFR groups was evaluated against chemical analysis (gravimetry). For cortical bone specimens, BMD of the CON and OVX groups was not significantly different; BMD of the NFR group was 22.1% (by (31)P NMR) and 17.5% (by gravimetry) lower than CON. For trabecular bone specimens, BMD of the OVX group was 40.5% (by (31)P NMR) and 24.6% (by gravimetry) lower than CON; BMD of the NFR group was 26.8% (by (31)P NMR) and 21.5% (by gravimetry) lower than CON. No significant change of cortical bone matrix density between CON and OVX was observed by WASPI or gravimetry; NFR cortical bone matrix density was 10.3% (by WASPI) and 13.9% (by gravimetry) lower than CON. OVX trabecular bone matrix density was 38.0% (by WASPI) and 30.8% (by gravimetry) lower than CON, while no significant change in NFR trabecular bone matrix density was observed by either method. The EBMs of OVX cortical and trabecular specimens were slightly higher than CON but not significantly different from CON. Importantly, EBMs of NFR cortical and trabecular specimens were 12.4% and 26.3% lower than CON by (31)P NMR/WASPI, respectively, and 4.0% and 11.9% lower by gravimetry. Histopathology showed evidence of osteoporosis in the OVX group and severe secondary hyperparathyroidism (renal osteodystrophy) in the NFR group. These results demonstrate that the combined (31)P NMR/WASPI method is capable of discerning the difference in EBM between animals with osteoporosis and those with impaired bone mineralization. Copyright 2010 Elsevier Inc. All rights reserved.

Detecting Damage in Ceramic Matrix Composites Using Electrical Resistance

NASA Technical Reports Server (NTRS)

Smith, Craig E.; Gyekenyesi, Andrew

2011-01-01

The majority of damage in SiC/SiC ceramic matrix composites subjected to monotonic tensile loads is in the form of distributed matrix cracks. These cracks initiate near stress concentrations, such as 90 deg fiber tows or large matrix pores and continue to accumulate with additional stress until matrix crack saturation is achieved. Such damage is difficult to detect with conventional nondestructive evaluation techniques (immersion ultrasonics, x-ray, etc.). Monitoring a specimen.s electrical resistance change provides an indirect approach for monitoring matrix crack density. Sylramic-iBN fiber- reinforced SiC composites with a melt infiltrated (MI) matrix were tensile tested at room temperature. Results showed an increase in resistance of more than 500% prior to fracture, which can be detected either in situ or post-damage. A relationship between resistance change and matrix crack density was also determined.

Detecting Cracks in Ceramic Matrix Composites by Electrical Resistance

NASA Technical Reports Server (NTRS)

Smith, Craig; Gyekenyesi, Andrew

2011-01-01

The majority of damage in SiC/SiC ceramic matrix composites subjected to monotonic tensile loads is in the form of distributed matrix cracks. These cracks initiate near stress concentrations, such as 90o fiber tows or large matrix pores and continue to accumulate with additional stress until matrix crack saturation is achieved. Such damage is difficult to detect with conventional nondestructive evaluation techniques (immersion ultrasonics, x-ray, etc.). Monitoring a specimen.s electrical resistance change provides an indirect approach for monitoring matrix crack density. Sylramic-iBN fiber- reinforced SiC composites with a melt infiltrated (MI) matrix were tensile tested at room temperature. Results showed an increase in resistance of more than 500% prior to fracture, which can be detected either in situ or post-damage. A relationship between resistance change and matrix crack density was also determined.

Molecular dynamics modeling of helium bubbles in austenitic steels

NASA Astrophysics Data System (ADS)

Jelea, A.

2018-06-01

The austenitic steel devices from pressurized water reactors are continuously subjected to neutron irradiation that produces crystalline point defects and helium atoms in the steel matrix. These species evolve into large defects such as dislocation loops and helium filled bubbles. This paper analyzes, through molecular dynamics simulations with recently developed interatomic potentials, the impact of the helium/steel interface on the helium behavior in nanosize bubbles trapped in an austenitic steel matrix. It is shown that the repulsive helium-steel interactions induce higher pressures in the bubble compared to bulk helium at the same temperature and average density. A new equation of state for helium is proposed in order to take into account these interface effects.

Random matrix approach to plasmon resonances in the random impedance network model of disordered nanocomposites

NASA Astrophysics Data System (ADS)

Olekhno, N. A.; Beltukov, Y. M.

2018-05-01

Random impedance networks are widely used as a model to describe plasmon resonances in disordered metal-dielectric and other two-component nanocomposites. In the present work, the spectral properties of resonances in random networks are studied within the framework of the random matrix theory. We have shown that the appropriate ensemble of random matrices for the considered problem is the Jacobi ensemble (the MANOVA ensemble). The obtained analytical expressions for the density of states in such resonant networks show a good agreement with the results of numerical simulations in a wide range of metal filling fractions 0

Quantum entanglement and spin control in silicon nanocrystal.

PubMed

Berec, Vesna

2012-01-01

Selective coherence control and electrically mediated exchange coupling of single electron spin between triplet and singlet states using numerically derived optimal control of proton pulses is demonstrated. We obtained spatial confinement below size of the Bohr radius for proton spin chain FWHM. Precise manipulation of individual spins and polarization of electron spin states are analyzed via proton induced emission and controlled population of energy shells in pure (29)Si nanocrystal. Entangled quantum states of channeled proton trajectories are mapped in transverse and angular phase space of (29)Si <100> axial channel alignment in order to avoid transversal excitations. Proton density and proton energy as impact parameter functions are characterized in single particle density matrix via discretization of diagonal and nearest off-diagonal elements. We combined high field and low densities (1 MeV/92 nm) to create inseparable quantum state by superimposing the hyperpolarizationed proton spin chain with electron spin of (29)Si. Quantum discretization of density of states (DOS) was performed by the Monte Carlo simulation method using numerical solutions of proton equations of motion. Distribution of gaussian coherent states is obtained by continuous modulation of individual spin phase and amplitude. Obtained results allow precise engineering and faithful mapping of spin states. This would provide the effective quantum key distribution (QKD) and transmission of quantum information over remote distances between quantum memory centers for scalable quantum communication network. Furthermore, obtained results give insights in application of channeled protons subatomic microscopy as a complete versatile scanning-probe system capable of both quantum engineering of charged particle states and characterization of quantum states below diffraction limit linear and in-depth resolution.PACS NUMBERS: 03.65.Ud, 03.67.Bg, 61.85.+p, 67.30.hj.

Energy density functional on a microscopic basis

NASA Astrophysics Data System (ADS)

Baldo, M.; Robledo, L.; Schuck, P.; Viñas, X.

2010-06-01

In recent years impressive progress has been made in the development of highly accurate energy density functionals, which allow us to treat medium-heavy nuclei. In this approach one tries to describe not only the ground state but also the first relevant excited states. In general, higher accuracy requires a larger set of parameters, which must be carefully chosen to avoid redundancy. Following this line of development, it is unavoidable that the connection of the functional with the bare nucleon-nucleon interaction becomes more and more elusive. In principle, the construction of a density functional from a density matrix expansion based on the effective nucleon-nucleon interaction is possible, and indeed the approach has been followed by few authors. However, to what extent a density functional based on such a microscopic approach can reach the accuracy of the fully phenomenological ones remains an open question. A related question is to establish which part of a functional can be actually derived by a microscopic approach and which part, in contrast, must be left as purely phenomenological. In this paper we discuss the main problems that are encountered when the microscopic approach is followed. To this purpose we will use the method we have recently introduced to illustrate the different aspects of these problems. In particular we will discuss the possible connection of the density functional with the nuclear matter equation of state and the distinct features of finite-size effect typical of nuclei.

Cosmological implications of quantum entanglement in the multiverse

NASA Astrophysics Data System (ADS)

Kanno, Sugumi

2015-12-01

We explore the cosmological implications of quantum entanglement between two causally disconnected universes in the multiverse. We first consider two causally separated de Sitter spaces with a state which is initially entangled. We derive the reduced density matrix of our universe and compute the spectrum of vacuum fluctuations. We then consider the same system with an initially non-entangled state. We find that due to quantum interference scale dependent modulations may enter the spectrum for the case of initially non-entangled state. This gives rise to the possibility that the existence of causally disconnected universes may be experimentally tested by analyzing correlators in detail.

Low-Density Parity-Check Code Design Techniques to Simplify Encoding

NASA Astrophysics Data System (ADS)

Perez, J. M.; Andrews, K.

2007-11-01

This work describes a method for encoding low-density parity-check (LDPC) codes based on the accumulate-repeat-4-jagged-accumulate (AR4JA) scheme, using the low-density parity-check matrix H instead of the dense generator matrix G. The use of the H matrix to encode allows a significant reduction in memory consumption and provides the encoder design a great flexibility. Also described are new hardware-efficient codes, based on the same kind of protographs, which require less memory storage and area, allowing at the same time a reduction in the encoding delay.

Resolution-of-identity stochastic time-dependent configuration interaction for dissipative electron dynamics in strong fields.

PubMed

Klinkusch, Stefan; Tremblay, Jean Christophe

2016-05-14

In this contribution, we introduce a method for simulating dissipative, ultrafast many-electron dynamics in intense laser fields. The method is based on the norm-conserving stochastic unraveling of the dissipative Liouville-von Neumann equation in its Lindblad form. The N-electron wave functions sampling the density matrix are represented in the basis of singly excited configuration state functions. The interaction with an external laser field is treated variationally and the response of the electronic density is included to all orders in this basis. The coupling to an external environment is included via relaxation operators inducing transition between the configuration state functions. Single electron ionization is represented by irreversible transition operators from the ionizing states to an auxiliary continuum state. The method finds its efficiency in the representation of the operators in the interaction picture, where the resolution-of-identity is used to reduce the size of the Hamiltonian eigenstate basis. The zeroth-order eigenstates can be obtained either at the configuration interaction singles level or from a time-dependent density functional theory reference calculation. The latter offers an alternative to explicitly time-dependent density functional theory which has the advantage of remaining strictly valid for strong field excitations while improving the description of the correlation as compared to configuration interaction singles. The method is tested on a well-characterized toy system, the excitation of the low-lying charge transfer state in LiCN.

Resolution-of-identity stochastic time-dependent configuration interaction for dissipative electron dynamics in strong fields

DOE Office of Scientific and Technical Information (OSTI.GOV)

Klinkusch, Stefan; Tremblay, Jean Christophe

In this contribution, we introduce a method for simulating dissipative, ultrafast many-electron dynamics in intense laser fields. The method is based on the norm-conserving stochastic unraveling of the dissipative Liouville-von Neumann equation in its Lindblad form. The N-electron wave functions sampling the density matrix are represented in the basis of singly excited configuration state functions. The interaction with an external laser field is treated variationally and the response of the electronic density is included to all orders in this basis. The coupling to an external environment is included via relaxation operators inducing transition between the configuration state functions. Single electronmore » ionization is represented by irreversible transition operators from the ionizing states to an auxiliary continuum state. The method finds its efficiency in the representation of the operators in the interaction picture, where the resolution-of-identity is used to reduce the size of the Hamiltonian eigenstate basis. The zeroth-order eigenstates can be obtained either at the configuration interaction singles level or from a time-dependent density functional theory reference calculation. The latter offers an alternative to explicitly time-dependent density functional theory which has the advantage of remaining strictly valid for strong field excitations while improving the description of the correlation as compared to configuration interaction singles. The method is tested on a well-characterized toy system, the excitation of the low-lying charge transfer state in LiCN.« less

Communication: Symmetrical quasi-classical analysis of linear optical spectroscopy

NASA Astrophysics Data System (ADS)

Provazza, Justin; Coker, David F.

2018-05-01

The symmetrical quasi-classical approach for propagation of a many degree of freedom density matrix is explored in the context of computing linear spectra. Calculations on a simple two state model for which exact results are available suggest that the approach gives a qualitative description of peak positions, relative amplitudes, and line broadening. Short time details in the computed dipole autocorrelation function result in exaggerated tails in the spectrum.

Implementation of rigorous renormalization group method for ground space and low-energy states of local Hamiltonians

NASA Astrophysics Data System (ADS)

Roberts, Brenden; Vidick, Thomas; Motrunich, Olexei I.

2017-12-01

The success of polynomial-time tensor network methods for computing ground states of certain quantum local Hamiltonians has recently been given a sound theoretical basis by Arad et al. [Math. Phys. 356, 65 (2017), 10.1007/s00220-017-2973-z]. The convergence proof, however, relies on "rigorous renormalization group" (RRG) techniques which differ fundamentally from existing algorithms. We introduce a practical adaptation of the RRG procedure which, while no longer theoretically guaranteed to converge, finds matrix product state ansatz approximations to the ground spaces and low-lying excited spectra of local Hamiltonians in realistic situations. In contrast to other schemes, RRG does not utilize variational methods on tensor networks. Rather, it operates on subsets of the system Hilbert space by constructing approximations to the global ground space in a treelike manner. We evaluate the algorithm numerically, finding similar performance to density matrix renormalization group (DMRG) in the case of a gapped nondegenerate Hamiltonian. Even in challenging situations of criticality, large ground-state degeneracy, or long-range entanglement, RRG remains able to identify candidate states having large overlap with ground and low-energy eigenstates, outperforming DMRG in some cases.

Canonical-ensemble state-averaged complete active space self-consistent field (SA-CASSCF) strategy for problems with more diabatic than adiabatic states: Charge-bond resonance in monomethine cyanines

DOE Office of Scientific and Technical Information (OSTI.GOV)

Olsen, Seth, E-mail: seth.olsen@uq.edu.au

2015-01-28

This paper reviews basic results from a theory of the a priori classical probabilities (weights) in state-averaged complete active space self-consistent field (SA-CASSCF) models. It addresses how the classical probabilities limit the invariance of the self-consistency condition to transformations of the complete active space configuration interaction (CAS-CI) problem. Such transformations are of interest for choosing representations of the SA-CASSCF solution that are diabatic with respect to some interaction. I achieve the known result that a SA-CASSCF can be self-consistently transformed only within degenerate subspaces of the CAS-CI ensemble density matrix. For uniformly distributed (“microcanonical”) SA-CASSCF ensembles, self-consistency is invariant tomore » any unitary CAS-CI transformation that acts locally on the ensemble support. Most SA-CASSCF applications in current literature are microcanonical. A problem with microcanonical SA-CASSCF models for problems with “more diabatic than adiabatic” states is described. The problem is that not all diabatic energies and couplings are self-consistently resolvable. A canonical-ensemble SA-CASSCF strategy is proposed to solve the problem. For canonical-ensemble SA-CASSCF, the equilibrated ensemble is a Boltzmann density matrix parametrized by its own CAS-CI Hamiltonian and a Lagrange multiplier acting as an inverse “temperature,” unrelated to the physical temperature. Like the convergence criterion for microcanonical-ensemble SA-CASSCF, the equilibration condition for canonical-ensemble SA-CASSCF is invariant to transformations that act locally on the ensemble CAS-CI density matrix. The advantage of a canonical-ensemble description is that more adiabatic states can be included in the support of the ensemble without running into convergence problems. The constraint on the dimensionality of the problem is relieved by the introduction of an energy constraint. The method is illustrated with a complete active space valence-bond (CASVB) analysis of the charge/bond resonance electronic structure of a monomethine cyanine: Michler’s hydrol blue. The diabatic CASVB representation is shown to vary weakly for “temperatures” corresponding to visible photon energies. Canonical-ensemble SA-CASSCF enables the resolution of energies and couplings for all covalent and ionic CASVB structures contributing to the SA-CASSCF ensemble. The CASVB solution describes resonance of charge- and bond-localized electronic structures interacting via bridge resonance superexchange. The resonance couplings can be separated into channels associated with either covalent charge delocalization or chemical bonding interactions, with the latter significantly stronger than the former.« less

Canonical-ensemble state-averaged complete active space self-consistent field (SA-CASSCF) strategy for problems with more diabatic than adiabatic states: charge-bond resonance in monomethine cyanines.

PubMed

Olsen, Seth

2015-01-28

This paper reviews basic results from a theory of the a priori classical probabilities (weights) in state-averaged complete active space self-consistent field (SA-CASSCF) models. It addresses how the classical probabilities limit the invariance of the self-consistency condition to transformations of the complete active space configuration interaction (CAS-CI) problem. Such transformations are of interest for choosing representations of the SA-CASSCF solution that are diabatic with respect to some interaction. I achieve the known result that a SA-CASSCF can be self-consistently transformed only within degenerate subspaces of the CAS-CI ensemble density matrix. For uniformly distributed ("microcanonical") SA-CASSCF ensembles, self-consistency is invariant to any unitary CAS-CI transformation that acts locally on the ensemble support. Most SA-CASSCF applications in current literature are microcanonical. A problem with microcanonical SA-CASSCF models for problems with "more diabatic than adiabatic" states is described. The problem is that not all diabatic energies and couplings are self-consistently resolvable. A canonical-ensemble SA-CASSCF strategy is proposed to solve the problem. For canonical-ensemble SA-CASSCF, the equilibrated ensemble is a Boltzmann density matrix parametrized by its own CAS-CI Hamiltonian and a Lagrange multiplier acting as an inverse "temperature," unrelated to the physical temperature. Like the convergence criterion for microcanonical-ensemble SA-CASSCF, the equilibration condition for canonical-ensemble SA-CASSCF is invariant to transformations that act locally on the ensemble CAS-CI density matrix. The advantage of a canonical-ensemble description is that more adiabatic states can be included in the support of the ensemble without running into convergence problems. The constraint on the dimensionality of the problem is relieved by the introduction of an energy constraint. The method is illustrated with a complete active space valence-bond (CASVB) analysis of the charge/bond resonance electronic structure of a monomethine cyanine: Michler's hydrol blue. The diabatic CASVB representation is shown to vary weakly for "temperatures" corresponding to visible photon energies. Canonical-ensemble SA-CASSCF enables the resolution of energies and couplings for all covalent and ionic CASVB structures contributing to the SA-CASSCF ensemble. The CASVB solution describes resonance of charge- and bond-localized electronic structures interacting via bridge resonance superexchange. The resonance couplings can be separated into channels associated with either covalent charge delocalization or chemical bonding interactions, with the latter significantly stronger than the former.

Effect of chiral symmetry on chaotic scattering from Majorana zero modes.

PubMed

Schomerus, H; Marciani, M; Beenakker, C W J

2015-04-24

In many of the experimental systems that may host Majorana zero modes, a so-called chiral symmetry exists that protects overlapping zero modes from splitting up. This symmetry is operative in a superconducting nanowire that is narrower than the spin-orbit scattering length, and at the Dirac point of a superconductor-topological insulator heterostructure. Here we show that chiral symmetry strongly modifies the dynamical and spectral properties of a chaotic scatterer, even if it binds only a single zero mode. These properties are quantified by the Wigner-Smith time-delay matrix Q=-iℏS^{†}dS/dE, the Hermitian energy derivative of the scattering matrix, related to the density of states by ρ=(2πℏ)^{-1}TrQ. We compute the probability distribution of Q and ρ, dependent on the number ν of Majorana zero modes, in the chiral ensembles of random-matrix theory. Chiral symmetry is essential for a significant ν dependence.

Relationship between diffusivity of water molecules inside hydrating tablets and their drug release behavior elucidated by magnetic resonance imaging.

PubMed

Kikuchi, Shingo; Onuki, Yoshinori; Kuribayashi, Hideto; Takayama, Kozo

2012-01-01

We reported previously that sustained release matrix tablets showed zero-order drug release without being affected by pH change. To understand drug release mechanisms more fully, we monitored the swelling and erosion of hydrating tablets using magnetic resonance imaging (MRI). Three different types of tablets comprised of polyion complex-forming materials and a hydroxypropyl methylcellulose (HPMC) were used. Proton density- and diffusion-weighted images of the hydrating tablets were acquired at intervals. Furthermore, apparent self-diffusion coefficient maps were generated from diffusion-weighted imaging to evaluate the state of hydrating tablets. Our findings indicated that water penetration into polyion complex tablets was faster than that into HPMC matrix tablets. In polyion complex tablets, water molecules were dispersed homogeneously and their diffusivity was relatively high, whereas in HPMC matrix tablets, water molecule movement was tightly restricted within the gel. An optimal tablet formulation determined in a previous study had water molecule penetration and diffusivity properties that appeared intermediate to those of polyion complex and HPMC matrix tablets; water molecules were capable of penetrating throughout the tablets and relatively high diffusivity was similar to that in the polyion complex tablet, whereas like the HPMC matrix tablet, it was well swollen. This study succeeded in characterizing the tablet hydration process. MRI provides profound insight into the state of water molecules in hydrating tablets; thus, it is a useful tool for understanding drug release mechanisms at a molecular level.

Geometrically induced surface polaritons in planar nanostructured metallic cavities

DOE Office of Scientific and Technical Information (OSTI.GOV)

Davids, P. S.; Intravia, F; Dalvit, Diego A.

2014-01-14

We examine the modal structure and dispersion of periodically nanostructured planar metallic cavities within the scattering matrix formulation. By nanostructuring a metallic grating in a planar cavity, artificial surface excitations or spoof plasmon modes are induced with dispersion determined by the periodicity and geometric characteristics of the grating. These spoof surface plasmon modes are shown to give rise to new cavity polaritonic modes at short mirror separations that modify the density of modes in nanostructured cavities. The increased modal density of states form cavity polarirons have a large impact on the fluctuation induced electromagnetic forces and enhanced hear transfer atmore » short separations.« less

Polymer Composite and Nanocomposite Dielectric Materials for Pulse Power Energy Storage †

PubMed Central

Barber, Peter; Balasubramanian, Shiva; Anguchamy, Yogesh; Gong, Shushan; Wibowo, Arief; Gao, Hongsheng; Ploehn, Harry J.; zur Loye, Hans-Conrad

2009-01-01

This review summarizes the current state of polymer composites used as dielectric materials for energy storage. The particular focus is on materials: polymers serving as the matrix, inorganic fillers used to increase the effective dielectric constant, and various recent investigations of functionalization of metal oxide fillers to improve compatibility with polymers. We review the recent literature focused on the dielectric characterization of composites, specifically the measurement of dielectric permittivity and breakdown field strength. Special attention is given to the analysis of the energy density of polymer composite materials and how the functionalization of the inorganic filler affects the energy density of polymer composite dielectric materials.

Energy-free machine learning force field for aluminum.

PubMed

Kruglov, Ivan; Sergeev, Oleg; Yanilkin, Alexey; Oganov, Artem R

2017-08-17

We used the machine learning technique of Li et al. (PRL 114, 2015) for molecular dynamics simulations. Atomic configurations were described by feature matrix based on internal vectors, and linear regression was used as a learning technique. We implemented this approach in the LAMMPS code. The method was applied to crystalline and liquid aluminum and uranium at different temperatures and densities, and showed the highest accuracy among different published potentials. Phonon density of states, entropy and melting temperature of aluminum were calculated using this machine learning potential. The results are in excellent agreement with experimental data and results of full ab initio calculations.

Exact steady state of a Kerr resonator with one- and two-photon driving and dissipation: Controllable Wigner-function multimodality and dissipative phase transitions

NASA Astrophysics Data System (ADS)

Bartolo, Nicola; Minganti, Fabrizio; Casteels, Wim; Ciuti, Cristiano

2016-09-01

We present exact results for the steady-state density matrix of a general class of driven-dissipative systems consisting of a nonlinear Kerr resonator in the presence of both coherent (one-photon) and parametric (two-photon) driving and dissipation. Thanks to the analytical solution, obtained via the complex P -representation formalism, we are able to explore any regime, including photon blockade, multiphoton resonant effects, and a mesoscopic regime with large photon density and quantum correlations. We show how the interplay between one- and two-photon driving provides a way to control the multimodality of the Wigner function in regimes where the semiclassical theory exhibits multistability. We also study the emergence of dissipative phase transitions in the thermodynamic limit of large photon numbers.

Truncated Calogero-Sutherland models

NASA Astrophysics Data System (ADS)

Pittman, S. M.; Beau, M.; Olshanii, M.; del Campo, A.

2017-05-01

A one-dimensional quantum many-body system consisting of particles confined in a harmonic potential and subject to finite-range two-body and three-body inverse-square interactions is introduced. The range of the interactions is set by truncation beyond a number of neighbors and can be tuned to interpolate between the Calogero-Sutherland model and a system with nearest and next-nearest neighbors interactions discussed by Jain and Khare. The model also includes the Tonks-Girardeau gas describing impenetrable bosons as well as an extension with truncated interactions. While the ground state wave function takes a truncated Bijl-Jastrow form, collective modes of the system are found in terms of multivariable symmetric polynomials. We numerically compute the density profile, one-body reduced density matrix, and momentum distribution of the ground state as a function of the range r and the interaction strength.

Levy Matrices and Financial Covariances

NASA Astrophysics Data System (ADS)

Burda, Zdzislaw; Jurkiewicz, Jerzy; Nowak, Maciej A.; Papp, Gabor; Zahed, Ismail

2003-10-01

In a given market, financial covariances capture the intra-stock correlations and can be used to address statistically the bulk nature of the market as a complex system. We provide a statistical analysis of three SP500 covariances with evidence for raw tail distributions. We study the stability of these tails against reshuffling for the SP500 data and show that the covariance with the strongest tails is robust, with a spectral density in remarkable agreement with random Lévy matrix theory. We study the inverse participation ratio for the three covariances. The strong localization observed at both ends of the spectral density is analogous to the localization exhibited in the random Lévy matrix ensemble. We discuss two competitive mechanisms responsible for the occurrence of an extensive and delocalized eigenvalue at the edge of the spectrum: (a) the Lévy character of the entries of the correlation matrix and (b) a sort of off-diagonal order induced by underlying inter-stock correlations. (b) can be destroyed by reshuffling, while (a) cannot. We show that the stocks with the largest scattering are the least susceptible to correlations, and likely candidates for the localized states. We introduce a simple model for price fluctuations which captures behavior of the SP500 covariances. It may be of importance for assets diversification.

Low-density resin impregnated ceramic article and method for making the same

NASA Technical Reports Server (NTRS)

Tran, Huy K. (Inventor); Henline, William D. (Inventor); Hsu, Ming-ta S. (Inventor); Rasky, Daniel J. (Inventor); Riccitiello, Salvatore R. (Inventor)

1997-01-01

A low-density resin impregnated ceramic article advantageously employed as a structural ceramic ablator comprising a matrix of ceramic fibers. The fibers of the ceramic matrix are coated with an organic resin film. The organic resin can be a thermoplastic resin or a cured thermosetting resin. In one embodiment, the resin is uniformly distributed within the ceramic article. In a second embodiment, the resin is distributed so as to provide a density gradient along at least one direction of the ceramic article. The resin impregnated ceramic article is prepared by providing a matrix of ceramic fibers; immersing the matrix of ceramic fibers in a solution of a solvent and an organic resin infiltrant; and removing the solvent to form a resin film on the ceramic fibers.

Self-Avoiding Walks on the Random Lattice and the Random Hopping Model on a Cayley Tree

NASA Astrophysics Data System (ADS)

Kim, Yup

Using a field theoretic method based on the replica trick, it is proved that the three-parameter renormalization group for an n-vector model with quenched randomness reduces to a two-parameter one in the limit n (--->) 0 which corresponds to self-avoiding walks (SAWs). This is also shown by the explicit calculation of the renormalization group recursion relations to second order in (epsilon). From this reduction we find that SAWs on the random lattice are in the same universality class as SAWs on the regular lattice. By analogy with the case of the n-vector model with cubic anisotropy in the limit n (--->) 1, the fixed-point structure of the n-vector model with randomness is analyzed in the SAW limit, so that a physical interpretation of the unphysical fixed point is given. Corrections of the values of critical exponents of the unphysical fixed point published previously is also given. Next we formulate an integral equation and recursion relations for the configurationally averaged one particle Green's function of the random hopping model on a Cayley tree of coordination number ((sigma) + 1). This formalism is tested by applying it successfully to the nonrandom model. Using this scheme for 1 << (sigma) < (INFIN) we calculate the density of states of this model with a Gaussian distribution of hopping matrix elements in the range of energy E('2) > E(,c)('2), where E(,c) is a critical energy described below. The singularity in the Green's function which occurs at energy E(,1)('(0)) for (sigma) = (INFIN) is shifted to complex energy E(,1) (on the unphysical sheet of energy E) for small (sigma)('-1). This calculation shows that the density of states is smooth function of energy E around the critical energy E(,c) = Re E(,1) in accord with Wegner's theorem. In this formulation the density of states has no sharp phase transition on the real axis of E because E(,1) has developed an imaginary part. Using the Lifschitz argument, we calculate the density of states near the band edge for the model when the hopping matrix elements are governed by a bounded probability distribution. It is also shown within the dynamical system language that the density of states of the model with a bounded distribution never vanishes inside the band and we suggest a theoretical mechanism for the formation of energy bands.

Equivalence principle for quantum systems: dephasing and phase shift of free-falling particles

NASA Astrophysics Data System (ADS)

Anastopoulos, C.; Hu, B. L.

2018-02-01

We ask the question of how the (weak) equivalence principle established in classical gravitational physics should be reformulated and interpreted for massive quantum objects that may also have internal degrees of freedom (dof). This inquiry is necessary because even elementary concepts like a classical trajectory are not well defined in quantum physics—trajectories originating from quantum histories become viable entities only under stringent decoherence conditions. From this investigation we posit two logically and operationally distinct statements of the equivalence principle for quantum systems. Version A: the probability distribution of position for a free-falling particle is the same as the probability distribution of a free particle, modulo a mass-independent shift of its mean. Version B: any two particles with the same velocity wave-function behave identically in free fall, irrespective of their masses. Both statements apply to all quantum states, including those without a classical correspondence, and also for composite particles with quantum internal dof. We also investigate the consequences of the interaction between internal and external dof induced by free fall. For a class of initial states, we find dephasing occurs for the translational dof, namely, the suppression of the off-diagonal terms of the density matrix, in the position basis. We also find a gravitational phase shift in the reduced density matrix of the internal dof that does not depend on the particle’s mass. For classical states, the phase shift has a natural classical interpretation in terms of gravitational red-shift and special relativistic time-dilation.

Development of a poly(dimethylacrylamide) based matrix material for solid phase high density peptide array synthesis employing a laser based material transfer

NASA Astrophysics Data System (ADS)

Ridder, Barbara; Foertsch, Tobias C.; Welle, Alexander; Mattes, Daniela S.; von Bojnicic-Kninski, Clemens M.; Loeffler, Felix F.; Nesterov-Mueller, Alexander; Meier, Michael A. R.; Breitling, Frank

2016-12-01

Poly(dimethylacrylamide) (PDMA) based matrix materials were developed for laser-based in situ solid phase peptide synthesis to produce high density arrays. In this specific array synthesis approach, amino acid derivatives are embedded into a matrix material, serving as a ;solid; solvent material at room temperature. Then, a laser pulse transfers this mixture to the target position on a synthesis slide, where the peptide array is synthesized. Upon heating above the glass transition temperature of the matrix material, it softens, allowing diffusion of the amino acid derivatives to the synthesis surface and serving as a solvent for peptide bond formation. Here, we synthesized PDMA six-arm star polymers, offering the desired matrix material properties, using atom transfer radical polymerization. With the synthesized polymers as matrix material, we structured and synthesized arrays with combinatorial laser transfer. With densities of up to 20,000 peptide spots per cm2, the resolution could be increased compared to the commercially available standard matrix material. Time-of-Flight Secondary Ion Mass Spectrometry experiments revealed the penetration behavior of an amino acid derivative into the prepared acceptor synthesis surface and the effectiveness of the washing protocols.

Decay of correlations between cross-polarized electromagnetic waves in a two-dimensional random medium.

PubMed

Gorodnichev, E E

2018-04-01

The problem of multiple scattering of polarized light in a two-dimensional medium composed of fiberlike inhomogeneities is studied. The attenuation lengths for the density matrix elements are calculated. For a highly absorbing medium it is found that, as the sample thickness increases, the intensity of waves polarized along the fibers decays faster than the other density matrix elements. With further increase in the sample thickness, the off-diagonal elements which are responsible for correlations between the cross-polarized waves disappear. In the asymptotic limit of very thick samples the scattered light proves to be polarized perpendicular to the fibers. The difference in the attenuation lengths between the density matrix elements results in a nonmonotonic depth dependence of the degree of polarization. In the opposite case of a weakly absorbing medium, the off-diagonal element of the density matrix and, correspondingly, the correlations between the cross-polarized fields are shown to decay faster than the intensity of waves polarized along and perpendicular to the fibers.

Joint refinement model for the spin resolved one-electron reduced density matrix of YTiO3 using magnetic structure factors and magnetic Compton profiles data.

PubMed

Gueddida, Saber; Yan, Zeyin; Kibalin, Iurii; Voufack, Ariste Bolivard; Claiser, Nicolas; Souhassou, Mohamed; Lecomte, Claude; Gillon, Béatrice; Gillet, Jean-Michel

2018-04-28

In this paper, we propose a simple cluster model with limited basis sets to reproduce the unpaired electron distributions in a YTiO 3 ferromagnetic crystal. The spin-resolved one-electron-reduced density matrix is reconstructed simultaneously from theoretical magnetic structure factors and directional magnetic Compton profiles using our joint refinement algorithm. This algorithm is guided by the rescaling of basis functions and the adjustment of the spin population matrix. The resulting spin electron density in both position and momentum spaces from the joint refinement model is in agreement with theoretical and experimental results. Benefits brought from magnetic Compton profiles to the entire spin density matrix are illustrated. We studied the magnetic properties of the YTiO 3 crystal along the Ti-O 1 -Ti bonding. We found that the basis functions are mostly rescaled by means of magnetic Compton profiles, while the molecular occupation numbers are mainly modified by the magnetic structure factors.

Effect of bidispersity in grafted chain length on grafted chain conformations and potential of mean force between polymer grafted nanoparticles in a homopolymer matrix.

PubMed

Nair, Nitish; Wentzel, Nathaniel; Jayaraman, Arthi

2011-05-21

In efforts to produce polymeric materials with tailored physical properties, significant interest has grown around the ability to control the spatial organization of nanoparticles in polymer nanocomposites. One way to achieve controlled particle arrangement is by grafting the nanoparticle surface with polymers that are compatible with the matrix, thus manipulating the interfacial interactions between the nanoparticles and the polymer matrix. Previous work has shown that the molecular weight of the grafted polymer, both at high grafting density and low grafting density, plays a key role in dictating the effective inter-particle interactions in a polymer matrix. At high grafting density nanoparticles disperse (aggregate) if the graft molecular weight is higher (lower) than the matrix molecular weight. At low grafting density the longer grafts can better shield the nanoparticle surface from direct particle-particle contacts than the shorter grafts and lead to the dispersion of the grafted particles in the matrix. Despite the importance of graft molecular weight, and evidence of non-trivial effects of polydispersity of chains grafted on flat surfaces, most theoretical work on polymer grafted nanoparticles has only focused on monodisperse grafted chains. In this paper, we focus on how bidispersity in grafted chain lengths affects the grafted chain conformations and inter-particle interactions in an implicit solvent and in a dense homopolymer polymer matrix. We first present the effects of bidispersity on grafted chain conformations in a single polymer grafted particle using purely Monte Carlo (MC) simulations. This is followed by calculations of the potential of mean force (PMF) between two grafted particles in a polymer matrix using a self-consistent Polymer Reference Interaction Site Model theory-Monte Carlo simulation approach. Monte Carlo simulations of a single polymer grafted particle in an implicit solvent show that in the bidisperse polymer grafted particles with an equal number of short and long grafts at low to medium grafting density, the short grafts are in a more coiled up conformation (lower radius of gyration) than their monodisperse counterparts to provide a larger free volume to the longer grafts so they can gain conformational entropy. The longer grafts do not show much difference in conformation from their monodisperse counterparts at low grafting density, but at medium grafting density the longer grafts exhibit less stretched conformations (lower radius of gyration) as compared to their monodisperse counterparts. In the presence of an explicit homopolymer matrix, the longer grafts are more compressed by the matrix homopolymer chains than the short grafts. We observe that the potential of mean force between bidisperse grafted particles has features of the PMF of monodisperse grafted particles with short grafts and monodisperse grafted particles with long grafts. The value of the PMF at contact is governed by the short grafts and values at large inter-particle distances are governed by the longer grafts. Further comparison of the PMF for bidisperse and monodisperse polymer grafted particles in a homopolymer matrix at varying parameters shows that the effects of matrix chain length, matrix packing fraction, grafting density, and particle curvature on the PMF between bidisperse polymer grafted particles are similar to those seen between monodisperse polymer grafted particles. © 2011 American Institute of Physics.

The time-dependent density matrix renormalisation group method

NASA Astrophysics Data System (ADS)

Ma, Haibo; Luo, Zhen; Yao, Yao

2018-04-01

Substantial progress of the time-dependent density matrix renormalisation group (t-DMRG) method in the recent 15 years is reviewed in this paper. By integrating the time evolution with the sweep procedures in density matrix renormalisation group (DMRG), t-DMRG provides an efficient tool for real-time simulations of the quantum dynamics for one-dimensional (1D) or quasi-1D strongly correlated systems with a large number of degrees of freedom. In the illustrative applications, the t-DMRG approach is applied to investigate the nonadiabatic processes in realistic chemical systems, including exciton dissociation and triplet fission in polymers and molecular aggregates as well as internal conversion in pyrazine molecule.

Long-range corrected density functional through the density matrix expansion based semilocal exchange hole.

PubMed

Patra, Bikash; Jana, Subrata; Samal, Prasanjit

2018-03-28

The exchange hole, which is one of the principal constituents of the density functional formalism, can be used to design accurate range-separated hybrid functionals in association with appropriate correlation. In this regard, the exchange hole derived from the density matrix expansion has gained attention due to its fulfillment of some of the desired exact constraints. Thus, the new long-range corrected density functional proposed here combines the meta generalized gradient approximation level exchange functional designed from the density matrix expansion based exchange hole coupled with the ab initio Hartree-Fock exchange through the range separation of the Coulomb interaction operator using the standard error function technique. Then, in association with the Lee-Yang-Parr correlation functional, the assessment and benchmarking of the above newly constructed range-separated functional with various well-known test sets shows its reasonable performance for a broad range of molecular properties, such as thermochemistry, non-covalent interaction and barrier heights of the chemical reactions.

Structure of low-lying states of {sup 10,11}C from proton elastic and inelastic scattering

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jouanne, C.; Lapoux, V.; Auger, F.

2005-07-01

To probe the ground state and transition densities, elastic and inelastic scattering on a proton target were measured in inverse kinematics for the unstable {sup 10}C and {sup 11}C nuclei at 45.3 and 40.6 MeV/nucleon, respectively. The detection of the recoil proton was performed by the MUST telescope array, in coincidence with a wall of scintillators for the quasiprojectile. The differential cross sections for elastic and inelastic scattering to the first excited states are compared to the optical model calculations performed within the framework of the microscopic nucleon-nucleus Jeukenne-Lejeune-Mahaux potential. Elastic scattering is sensitive to the matter-root-mean square radius foundmore » to be 2.42{+-}0.1 and 2.33{+-}0.1 fm, for {sup 10,11}C, respectively. The transition densities from cluster and mean-field models are tested, and the cluster model predicts the correct order of magnitude of cross sections for the transitions of both isotopes. Using the Bohr-Mottelson prescription, a profile for the {sup 10}C transition density from the 0{sup +} ground to the 2{sub 1}{sup +} state is deduced from the data. The corresponding neutron transition matrix element is extracted: M{sub n}=5.51{+-}1.09 fm{sup 2}.« less

Measurement of differential cross sections and spin density matrix elements along with a partial wave analysis for gammap → po using CLAS at Jefferson Lab

NASA Astrophysics Data System (ADS)

Williams, Mike

This work presents measurements of differential cross sections, dsigma/dcos qwCM , and spin density matrix elements, r0MM' , for the reaction gammap → po in the energy range 1.72 GeV< s <2.84 GeV. The data were collected at Jefferson Lab, using the CLAS detector, as part of the g11a run period in 2004. Our r0MM' measurements vastly increase the precision of the world's data and extend the large angle measurements by over 400 MeV in s . Our data confirms that for s < 2.1 GeV, the forward angle (small |t|) production amplitude is dominated by t-channel pi0 exchange. At higher energies, existing non-resonant models do a poor job of describing our data. In particular, u-channel models fail to reproduce our highest energy backwards r0MM' measurements. A mass-independent partial wave analysis has also been performed. Near threshold, the dominant resonance contributions extracted are the **** F15 (1680) and *** D 13(1700). Together with the t-channel pi0 exchange, these three waves provide a remarkably good description of our differential cross section and spin density matrix element measurements for s < 2 GeV. Strong, but not conclusive, evidence for the **** G17(2190) has also been extracted. Improved non-resonant models may be necessary to irrefutably show whether this state contributes to o photoproduction. Evidence for missing resonances is suggestive, but inconclusive without theoretical input.

Variational Two-Particle Density Matrix Calculation for the Hubbard Model Below Half Filling Using Spin-Adapted Lifting Conditions

NASA Astrophysics Data System (ADS)

Verstichel, Brecht; van Aggelen, Helen; Poelmans, Ward; Van Neck, Dimitri

2012-05-01

The variational determination of the two-particle density matrix is an interesting, but not yet fully explored technique that allows us to obtain ground-state properties of a quantum many-body system without reference to an N-particle wave function. The one-dimensional fermionic Hubbard model has been studied before with this method, using standard two- and three-index conditions on the density matrix [J. R. Hammond , Phys. Rev. A 73, 062505 (2006)PLRAAN1050-294710.1103/PhysRevA.73.062505], while a more recent study explored so-called subsystem constraints [N. Shenvi , Phys. Rev. Lett. 105, 213003 (2010)PRLTAO0031-900710.1103/PhysRevLett.105.213003]. These studies reported good results even with only standard two-index conditions, but have always been limited to the half-filled lattice. In this Letter, we establish the fact that the two-index approach fails for other fillings. In this case, a subset of three-index conditions is absolutely needed to describe the correct physics in the strong-repulsion limit. We show that applying lifting conditions [J. R. Hammond , Phys. Rev. APLRAAN1050-2947 71, 062503 (2005)10.1103/PhysRevA.71.062503] is the most economical way to achieve this, while still avoiding the computationally much heavier three-index conditions. A further extension to spin-adapted lifting conditions leads to increased accuracy in the intermediate repulsion regime. At the same time, we establish the feasibility of such studies to the more complicated phase diagram in two-dimensional Hubbard models.

The origin of anisotropy and high density of states in the electronic structure of Cr2GeC by means of polarized soft x-ray spectroscopy and ab initio calculations

NASA Astrophysics Data System (ADS)

Magnuson, Martin; Mattesini, Maurizio; Bugnet, Matthieu; Eklund, Per

2015-10-01

The anisotropy in the electronic structure of the inherently nanolaminated ternary phase Cr2GeC is investigated by bulk-sensitive and element selective soft x-ray absorption/emission spectroscopy. The angle-resolved absorption/emission measurements reveal differences between the in-plane and out-of-plane bonding at the (0001) interfaces of Cr2GeC. The Cr L 2, 3, C K, and Ge M 1, M 2, 3 emission spectra are interpreted with first-principles density-functional theory (DFT) including core-to-valence dipole transition matrix elements. For the Ge 4s states, the x-ray emission measurements reveal two orders of magnitude higher intensity at the Fermi level than DFT within the General Gradient Approximation (GGA) predicts. We provide direct evidence of anisotropy in the electronic structure and the orbital occupation that should affect the thermal expansion coefficient and transport properties. As shown in this work, hybridization and redistribution of intensity from the shallow 3d core levels to the 4s valence band explain the large Ge density of states at the Fermi level.

The origin of anisotropy and high density of states in the electronic structure of Cr2GeC by means of polarized soft x-ray spectroscopy and ab initio calculations.

PubMed

Magnuson, Martin; Mattesini, Maurizio; Bugnet, Matthieu; Eklund, Per

2015-10-21

The anisotropy in the electronic structure of the inherently nanolaminated ternary phase Cr2GeC is investigated by bulk-sensitive and element selective soft x-ray absorption/emission spectroscopy. The angle-resolved absorption/emission measurements reveal differences between the in-plane and out-of-plane bonding at the (0001) interfaces of Cr2GeC. The Cr L(2, 3), C K, and Ge M1, M(2, 3) emission spectra are interpreted with first-principles density-functional theory (DFT) including core-to-valence dipole transition matrix elements. For the Ge 4s states, the x-ray emission measurements reveal two orders of magnitude higher intensity at the Fermi level than DFT within the General Gradient Approximation (GGA) predicts. We provide direct evidence of anisotropy in the electronic structure and the orbital occupation that should affect the thermal expansion coefficient and transport properties. As shown in this work, hybridization and redistribution of intensity from the shallow 3d core levels to the 4s valence band explain the large Ge density of states at the Fermi level.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pratap, Surender; Sarkar, Niladri, E-mail: niladri@pilani.bits-pilani.ac.in

Self-Consistent Quantum Method using Schrodinger-Poisson equations have been used for determining the Channel electron density of Nano-Scale MOSFETs for 6nm and 9nm thick channels. The 6nm thick MOSFET show the peak of the electron density at the middle where as the 9nm thick MOSFET shows the accumulation of the electrons at the oxide/semiconductor interface. The electron density in the channel is obtained from the diagonal elements of the density matrix; [ρ]=[1/(1+exp(β(H − μ)))] A Tridiagonal Hamiltonian Matrix [H] is constructed for the oxide/channel/oxide 1D structure for the dual gate MOSFET. This structure is discretized and Finite-Difference method is used formore » constructing the matrix equation. The comparison of these results which are obtained by Quantum methods are done with Semi-Classical methods.« less

Stress fluctuations in fracture networks from theoretical and numerical models

NASA Astrophysics Data System (ADS)

Davy, P.; Darcel, C.; Mas Ivars, D.; Le Goc, R.

2017-12-01

We analyze the spatial fluctuations of stress in a simple tridimensional model constituted by a population of disc-shaped fractures embedded in an elastic matrix with uniform and isotropic properties. The fluctuations arise from the classical stress enhancement at fracture tips and stress shadowing around fracture centers that are amplified or decreased by the interactions between close-by fractures. The distribution of local stresses is calculated at the elementary mesh scale with the 3DEC numerical program based on the distinct element method. As expected, the stress distributions vary with fracture density, the larger is the density, the wider is the distribution. For freely slipping fractures, it is mainly controlled by the percolation parameter p (i.e., the total volume of spheres surrounding fractures). For stresses smaller than the remote deviatoric stress, the distribution depends only on for the range of density that has been studied. For large stresses, the distribution decreases exponentially when increasing stress, with a characteristic stress that increases with entailing a widening of the stress distribution. We extend the analysis to fractures with plane resistance defined by an elastic shear stiffness ks and a slip Coulomb threshold. A consequence of the fracture plane resistance is to lower the stress perturbation in the surrounding matrix by a factor that depends on the ratio between ks and a fracture-matrix stiffness km mainly dependent on the ratio between Young modulus and fracture size. km is also the ratio between the remote shear stress and the displacement across the fracture plane in the case of freely slipping fractures. A complete analytical derivation of the expressions of the stress perturbations and of the fracture displacements is obtained and checked with numerical simulations. In the limit ks >> km, the stress perturbation tends to 0 and the stress state is spatially uniform. The analysis allows us to quantify the intensity of the stress fluctuations in fractured rocks as a function of both the fracture network characteristics (density and size distribution), and the mechanical properties (fracture shear stiffness vs matrix elastic properties).

Simple expression for the quantum Fisher information matrix

NASA Astrophysics Data System (ADS)

Šafránek, Dominik

2018-04-01

Quantum Fisher information matrix (QFIM) is a cornerstone of modern quantum metrology and quantum information geometry. Apart from optimal estimation, it finds applications in description of quantum speed limits, quantum criticality, quantum phase transitions, coherence, entanglement, and irreversibility. We derive a surprisingly simple formula for this quantity, which, unlike previously known general expression, does not require diagonalization of the density matrix, and is provably at least as efficient. With a minor modification, this formula can be used to compute QFIM for any finite-dimensional density matrix. Because of its simplicity, it could also shed more light on the quantum information geometry in general.

Feedback control of nonlinear quantum systems: a rule of thumb.

PubMed

Jacobs, Kurt; Lund, Austin P

2007-07-13

We show that in the regime in which feedback control is most effective - when measurements are relatively efficient, and feedback is relatively strong - then, in the absence of any sharp inhomogeneity in the noise, it is always best to measure in a basis that does not commute with the system density matrix than one that does. That is, it is optimal to make measurements that disturb the state one is attempting to stabilize.

Local Charge Injection and Extraction on Surface-Modified Al2O3 Nanoparticles in LDPE.

PubMed

Borgani, Riccardo; Pallon, Love K H; Hedenqvist, Mikael S; Gedde, Ulf W; Haviland, David B

2016-09-14

We use a recently developed scanning probe technique to image with high spatial resolution the injection and extraction of charge around individual surface-modified aluminum oxide nanoparticles embedded in a low-density polyethylene (LDPE) matrix. We find that the experimental results are consistent with a simple band structure model where localized electronic states are available in the band gap (trap states) in the vicinity of the nanoparticles. This work offers experimental support to a previously proposed mechanism for enhanced insulating properties of nanocomposite LDPE and provides a powerful experimental tool to further investigate such properties.

Proton clouds to measure long-range contacts between nonexchangeable side chain protons in solid-state NMR.

PubMed

Sinnige, Tessa; Daniëls, Mark; Baldus, Marc; Weingarth, Markus

2014-03-26

We show that selective labeling of proteins with protonated amino acids embedded in a perdeuterated matrix, dubbed 'proton clouds', provides general access to long-range contacts between nonexchangeable side chain protons in proton-detected solid-state NMR, which is important to study protein tertiary structure. Proton-cloud labeling significantly improves spectral resolution by simultaneously reducing proton line width and spectral crowding despite a high local proton density in clouds. The approach is amenable to almost all canonical amino acids. Our method is demonstrated on ubiquitin and the β-barrel membrane protein BamA.

Processing and properties of SiC whisker reinforced Si sub 3 N sub 4 ceramic matrix composites

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nunn, S.D.

1991-01-01

Silicon carbide whiskers reinforced silicon nitride ceramic matrix composites were pressureless sintered to high density by liquid phase sintering. Important processing parameters included: whisker dispersion by ultrasonic shear homogenization, particle refinement by attrition milling, pressure slip casting to obtain high greed densities, and sintering in a protective powder bed to limit decomposition. Composites with a {beta}20-Si{sub 3}N{sub 4} solid solution matrix containing 20 vol.% SiC whiskers were sintered to 98-100% theoretical density; composites having a Si{sub 3}N{sub 4} matrix containing YAG sintering aid were sintered to 98% of the theoretical density with 20 vol.% SiC whiskers, and 94% density withmore » 30 vol.% SiC whiskers. Analysis of the pressureless sintered composites revealed orientation of the SiC whiskers and the Si{sub 3}N{sub 4} matrix grains. The mechanical properties of hot pressed Si{sub 3}N{sub 4} composites reinforced with 20 vol.% SiC whiskers were shown to depend on the characteristics of the intergranular phase. Variations in the properties of the composites were analyzed in terms of the amount and morphology of the secondary phase, and the development of internal residual stresses due to the thermal expansion mismatch between the sintering aid phase at the grain boundaries.« less

Computer simulation of the matrix-inclusion interphase in bulk metallic glass based nanocomposites

NASA Astrophysics Data System (ADS)

Kokotin, V.; Hermann, H.; Eckert, J.

2011-10-01

Atomistic models for matrix-inclusion systems are generated. Analyses of the systems show that interphase layers of finite thickness appear interlinking the surface of the nanocrystalline inclusion and the embedding amorphous matrix. In a first approximation, the interphase is characterized as an amorphous structure with a density slightly reduced compared to that of the matrix. This result holds for both monatomic hard sphere systems and a Cu47.5Zr47.5Al5 alloy simulated by molecular dynamics (MD). The elastic shear and bulk modulus of the interphase are calculated by simulated deformation of the MD systems. Both moduli diminish with decreasing density but the shear modulus is more sensitive against density reduction by one order of magnitude. This result explains recent observations of shear band initiation at the amorphous-crystalline interface during plastic deformation.

Multivariate Granger causality: an estimation framework based on factorization of the spectral density matrix

PubMed Central

Wen, Xiaotong; Rangarajan, Govindan; Ding, Mingzhou

2013-01-01

Granger causality is increasingly being applied to multi-electrode neurophysiological and functional imaging data to characterize directional interactions between neurons and brain regions. For a multivariate dataset, one might be interested in different subsets of the recorded neurons or brain regions. According to the current estimation framework, for each subset, one conducts a separate autoregressive model fitting process, introducing the potential for unwanted variability and uncertainty. In this paper, we propose a multivariate framework for estimating Granger causality. It is based on spectral density matrix factorization and offers the advantage that the estimation of such a matrix needs to be done only once for the entire multivariate dataset. For any subset of recorded data, Granger causality can be calculated through factorizing the appropriate submatrix of the overall spectral density matrix. PMID:23858479

Towards a multiconfigurational method of increments

NASA Astrophysics Data System (ADS)

Fertitta, E.; Koch, D.; Paulus, B.; Barcza, G.; Legeza, Ö.

2018-06-01

The method of increments (MoI) allows one to successfully calculate cohesive energies of bulk materials with high accuracy, but it encounters difficulties when calculating dissociation curves. The reason is that its standard formalism is based on a single Hartree-Fock (HF) configuration whose orbitals are localised and used for the many-body expansion. In situations where HF does not allow a size-consistent description of the dissociation, the MoI cannot be guaranteed to yield proper results either. Herein, we address the problem by employing a size-consistent multiconfigurational reference for the MoI formalism. This leads to a matrix equation where a coupling derived by the reference itself is employed. In principle, such an approach allows one to evaluate approximate values for the ground as well as excited states energies. While the latter are accurate close to the avoided crossing only, the ground state results are very promising for the whole dissociation curve, as shown by the comparison with density matrix renormalisation group benchmarks. We tested this two-state constant-coupling MoI on beryllium rings of different sizes and studied the error introduced by the constant coupling.

Electronic structure properties of deep defects in hBN

NASA Astrophysics Data System (ADS)

Dev, Pratibha; Prdm Collaboration

In recent years, the search for room-temperature solid-state qubit (quantum bit) candidates has revived interest in the study of deep-defect centers in semiconductors. The charged NV-center in diamond is the best known amongst these defects. However, as a host material, diamond poses several challenges and so, increasingly, there is an interest in exploring deep defects in alternative semiconductors such as hBN. The layered structure of hBN makes it a scalable platform for quantum applications, as there is a greater potential for controlling the location of the deep defect in the 2D-matrix through careful experiments. Using density functional theory-based methods, we have studied the electronic and structural properties of several deep defects in hBN. Native defects within hBN layers are shown to have high spin ground states that should survive even at room temperature, making them interesting solid-state qubit candidates in a 2D matrix. Partnership for Reduced Dimensional Material (PRDM) is part of the NSF sponsored Partnerships for Research and Education in Materials (PREM).

Evolution of the entanglement of the N00N-type of states in a coupled two cavity system via an adiabatic approximation

NASA Astrophysics Data System (ADS)

Chakrabarti, R.; Sreekumari, G.; Yogesh, V.

2018-06-01

We study a system of two cavities each encapsulating a qubit and an oscillator degrees of freedom. An ultrastrong interaction between the qubit and the oscillator is assumed, and the photons are allowed to hop between the cavities. A partition of the time scale between the fast-moving oscillator and the slow moving qubit allows us to set up an adiabatic approximation procedure where we employ the delocalized degrees of freedom to diagonalize the Hamiltonian. The time evolution of the N00N-type initial states now furnishes, for instance, the reduced density matrix of a bipartite system of two qubits. For a macroscopic size of the N00N component of the initial state the sudden death of the entanglement between the qubits and its continued null value are prominently manifest as the information percolates to the qubits after long intervals. For the low photon numbers of the initial states the dynamics produces almost maximally entangled two-qubit states, which by utilizing the Hilbert–Schmidt distance between the density matrices, are observed to be nearly pure generalized Bell states.

Simple Derivation of the Lindblad Equation

ERIC Educational Resources Information Center

Pearle, Philip

2012-01-01

The Lindblad equation is an evolution equation for the density matrix in quantum theory. It is the general linear, Markovian, form which ensures that the density matrix is Hermitian, trace 1, positive and completely positive. Some elementary examples of the Lindblad equation are given. The derivation of the Lindblad equation presented here is…

Inverting pump-probe spectroscopy for state tomography of excitonic systems.

PubMed

Hoyer, Stephan; Whaley, K Birgitta

2013-04-28

We propose a two-step protocol for inverting ultrafast spectroscopy experiments on a molecular aggregate to extract the time-evolution of the excited state density matrix. The first step is a deconvolution of the experimental signal to determine a pump-dependent response function. The second step inverts this response function to obtain the quantum state of the system, given a model for how the system evolves following the probe interaction. We demonstrate this inversion analytically and numerically for a dimer model system, and evaluate the feasibility of scaling it to larger molecular aggregates such as photosynthetic protein-pigment complexes. Our scheme provides a direct alternative to the approach of determining all Hamiltonian parameters and then simulating excited state dynamics.

Microscopically based energy density functionals for nuclei using the density matrix expansion. II. Full optimization and validation

NASA Astrophysics Data System (ADS)

Navarro Pérez, R.; Schunck, N.; Dyhdalo, A.; Furnstahl, R. J.; Bogner, S. K.

2018-05-01

Background: Energy density functional methods provide a generic framework to compute properties of atomic nuclei starting from models of nuclear potentials and the rules of quantum mechanics. Until now, the overwhelming majority of functionals have been constructed either from empirical nuclear potentials such as the Skyrme or Gogny forces, or from systematic gradient-like expansions in the spirit of the density functional theory for atoms. Purpose: We seek to obtain a usable form of the nuclear energy density functional that is rooted in the modern theory of nuclear forces. We thus consider a functional obtained from the density matrix expansion of local nuclear potentials from chiral effective field theory. We propose a parametrization of this functional carefully calibrated and validated on selected ground-state properties that is suitable for large-scale calculations of nuclear properties. Methods: Our energy functional comprises two main components. The first component is a non-local functional of the density and corresponds to the direct part (Hartree term) of the expectation value of local chiral potentials on a Slater determinant. Contributions to the mean field and the energy of this term are computed by expanding the spatial, finite-range components of the chiral potential onto Gaussian functions. The second component is a local functional of the density and is obtained by applying the density matrix expansion to the exchange part (Fock term) of the expectation value of the local chiral potential. We apply the UNEDF2 optimization protocol to determine the coupling constants of this energy functional. Results: We obtain a set of microscopically constrained functionals for local chiral potentials from leading order up to next-to-next-to-leading order with and without three-body forces and contributions from Δ excitations. These functionals are validated on the calculation of nuclear and neutron matter, nuclear mass tables, single-particle shell structure in closed-shell nuclei, and the fission barrier of 240Pu. Quantitatively, they perform noticeably better than the more phenomenological Skyrme functionals. Conclusions: The inclusion of higher-order terms in the chiral perturbation expansion seems to produce a systematic improvement in predicting nuclear binding energies while the impact on other observables is not really significant. This result is especially promising since all the fits have been performed at the single-reference level of the energy density functional approach, where important collective correlations such as center-of-mass correction, rotational correction, or zero-point vibrational energies have not been taken into account yet.

Superfluidity, Bose-Einstein condensation, and structure in one-dimensional Luttinger liquids

NASA Astrophysics Data System (ADS)

Vranješ Markić, L.; Vrcan, H.; Zuhrianda, Z.; Glyde, H. R.

2018-01-01

We report diffusion Monte Carlo (DMC) and path integral Monte Carlo (PIMC) calculations of the properties of a one-dimensional (1D) Bose quantum fluid. The equation of state, the superfluid fraction ρS/ρ0 , the one-body density matrix n (x ) , the pair distribution function g (x ) , and the static structure factor S (q ) are evaluated. The aim is to test Luttinger liquid (LL) predictions for 1D fluids over a wide range of fluid density and LL parameter K . The 1D Bose fluid examined is a single chain of 4He atoms confined to a line in the center of a narrow nanopore. The atoms cannot exchange positions in the nanopore, the criterion for 1D. The fluid density is varied from the spinodal density where the 1D liquid is unstable to droplet formation to the density of bulk liquid 4He. In this range, K varies from K >2 at low density, where a robust superfluid is predicted, to K <0.5 , where fragile 1D superflow and solidlike peaks in S (q ) are predicted. For uniform pore walls, the ρS/ρ0 scales as predicted by LL theory. The n (x ) and g (x ) show long range oscillations and decay with x as predicted by LL theory. The amplitude of the oscillations is large at high density (small K ) and small at low density (large K ). The K values obtained from different properties agree well verifying the internal structure of LL theory. In the presence of disorder, the ρS/ρ0 does not scale as predicted by LL theory. A single vJ parameter in the LL theory that recovers LL scaling was not found. The one body density matrix (OBDM) in disorder is well predicted by LL theory. The "dynamical" superfluid fraction, ρSD/ρ0 , is determined. The physics of the deviation from LL theory in disorder and the "dynamical" ρSD/ρ0 are discussed.

Anodization Mechanism on SiC Nanoparticle Reinforced Al Matrix Composites Produced by Power Metallurgy.

PubMed

Ferreira, Sonia C; Conde, Ana; Arenas, María A; Rocha, Luis A; Velhinho, Alexandre

2014-12-19

Specimens of aluminum-based composites reinforced by silicon carbide nanoparticles (Al/SiC np ) produced by powder metallurgy (PM) were anodized under voltage control in tartaric-sulfuric acid (TSA). In this work, the influence of the amount of SiC np on the film growth during anodizing was investigated. The current density versus time response and the morphology of the porous alumina film formed at the composite surface are compared to those concerning a commercial aluminum alloy (AA1050) anodized under the same conditions. The processing method of the aluminum alloys influences the efficiency of the anodizing process, leading to a lower thicknesses for the unreinforced Al-PM alloy regarding the AA1050. The current density versus time response is strongly dependent on the amount of SiC np . The current peaks and the steady-state current density recorded at each voltage step increases with the SiC np volume fraction due to the oxidation of the SiC np . The formation mechanism of the anodic film on Al/SiC np composites is different from that occurring in AA1050, partly due the heterogeneous distribution of the reinforcement particles in the metallic matrix, but also to the entrapment of SiC np in the anodic film.

Anodization Mechanism on SiC Nanoparticle Reinforced Al Matrix Composites Produced by Power Metallurgy

PubMed Central

Ferreira, Sonia C.; Conde, Ana; Arenas, María A.; Rocha, Luis A.; Velhinho, Alexandre

2014-01-01

Specimens of aluminum-based composites reinforced by silicon carbide nanoparticles (Al/SiCnp) produced by powder metallurgy (PM) were anodized under voltage control in tartaric-sulfuric acid (TSA). In this work, the influence of the amount of SiCnp on the film growth during anodizing was investigated. The current density versus time response and the morphology of the porous alumina film formed at the composite surface are compared to those concerning a commercial aluminum alloy (AA1050) anodized under the same conditions. The processing method of the aluminum alloys influences the efficiency of the anodizing process, leading to a lower thicknesses for the unreinforced Al-PM alloy regarding the AA1050. The current density versus time response is strongly dependent on the amount of SiCnp. The current peaks and the steady-state current density recorded at each voltage step increases with the SiCnp volume fraction due to the oxidation of the SiCnp. The formation mechanism of the anodic film on Al/SiCnp composites is different from that occurring in AA1050, partly due the heterogeneous distribution of the reinforcement particles in the metallic matrix, but also to the entrapment of SiCnp in the anodic film. PMID:28788295

Quasistatic antiferromagnetism in the quantum wells of SmTiO3/SrTiO3 heterostructures

NASA Astrophysics Data System (ADS)

Need, Ryan F.; Marshall, Patrick B.; Kenney, Eric; Suter, Andreas; Prokscha, Thomas; Salman, Zaher; Kirby, Brian J.; Stemmer, Susanne; Graf, Michael J.; Wilson, Stephen D.

2018-03-01

High carrier density quantum wells embedded within a Mott insulating matrix present a rich arena for exploring unconventional electronic phase behavior ranging from non-Fermi-liquid transport and signatures of quantum criticality to pseudogap formation. Probing the proposed connection between unconventional magnetotransport and incipient electronic order within these quantum wells has however remained an enduring challenge due to the ultra-thin layer thicknesses required. Here we address this challenge by exploring the magnetic properties of high-density SrTiO3 quantum wells embedded within the antiferromagnetic Mott insulator SmTiO3 via muon spin relaxation and polarized neutron reflectometry measurements. The one electron per planar unit cell acquired by the nominal d0 band insulator SrTiO3 when embedded within a d1 Mott SmTiO3 matrix exhibits slow magnetic fluctuations that begin to freeze into a quasistatic spin state below a critical temperature T*. The appearance of this quasistatic well magnetism coincides with the previously reported opening of a pseudogap in the tunneling spectra of high carrier density wells inside this film architecture. Our data suggest a common origin of the pseudogap phase behavior in this quantum critical oxide heterostructure with those observed in bulk Mott materials close to an antiferromagnetic instability.

Density-based cluster algorithms for the identification of core sets

NASA Astrophysics Data System (ADS)

Lemke, Oliver; Keller, Bettina G.

2016-10-01

The core-set approach is a discretization method for Markov state models of complex molecular dynamics. Core sets are disjoint metastable regions in the conformational space, which need to be known prior to the construction of the core-set model. We propose to use density-based cluster algorithms to identify the cores. We compare three different density-based cluster algorithms: the CNN, the DBSCAN, and the Jarvis-Patrick algorithm. While the core-set models based on the CNN and DBSCAN clustering are well-converged, constructing core-set models based on the Jarvis-Patrick clustering cannot be recommended. In a well-converged core-set model, the number of core sets is up to an order of magnitude smaller than the number of states in a conventional Markov state model with comparable approximation error. Moreover, using the density-based clustering one can extend the core-set method to systems which are not strongly metastable. This is important for the practical application of the core-set method because most biologically interesting systems are only marginally metastable. The key point is to perform a hierarchical density-based clustering while monitoring the structure of the metric matrix which appears in the core-set method. We test this approach on a molecular-dynamics simulation of a highly flexible 14-residue peptide. The resulting core-set models have a high spatial resolution and can distinguish between conformationally similar yet chemically different structures, such as register-shifted hairpin structures.

Generalized Gibbs ensembles for quantum field theories

NASA Astrophysics Data System (ADS)

Essler, F. H. L.; Mussardo, G.; Panfil, M.

2015-05-01

We consider the nonequilibrium dynamics in quantum field theories (QFTs). After being prepared in a density matrix that is not an eigenstate of the Hamiltonian, such systems are expected to relax locally to a stationary state. In the presence of local conservation laws, these stationary states are believed to be described by appropriate generalized Gibbs ensembles. Here we demonstrate that in order to obtain a correct description of the stationary state, it is necessary to take into account conservation laws that are not (ultra)local in the usual sense of QFTs, but fulfill a significantly weaker form of locality. We discuss the implications of our results for integrable QFTs in one spatial dimension.

Dynamic current susceptibility as a probe of Majorana bound states in nanowire-based Josephson junctions

NASA Astrophysics Data System (ADS)

Trif, Mircea; Dmytruk, Olesia; Bouchiat, Hélène; Aguado, Ramón; Simon, Pascal

2018-02-01

We theoretically study a Josephson junction based on a semiconducting nanowire subject to a time-dependent flux bias. We establish a general density-matrix approach for the dynamical response of the Majorana junction and calculate the resulting flux-dependent susceptibility using both microscopic and effective low-energy descriptions for the nanowire. We find that the diagonal component of the susceptibility, associated with the dynamics of the Majorana state populations, dominates over the standard Kubo contribution for a wide range of experimentally relevant parameters. The diagonal term, explored, in this Rapid Communication, in the context of Majorana physics, allows probing accurately the presence of Majorana bound states in the junction.

Nonlocal polarization interferometer for entanglement detection

DOE PAGES

Williams, Brian P.; Humble, Travis S.; Grice, Warren P.

2014-10-30

We report a nonlocal interferometer capable of detecting entanglement and identifying Bell states statistically. This is possible due to the interferometer's unique correlation dependence on the antidiagonal elements of the density matrix, which have distinct bounds for separable states and unique values for the four Bell states. The interferometer consists of two spatially separated balanced Mach-Zehnder or Sagnac interferometers that share a polarization-entangled source. Correlations between these interferometers exhibit nonlocal interference, while single-photon interference is suppressed. This interferometer also allows for a unique version of the Clauser-Horne-Shimony-Holt Bell test where the local reality is the photon polarization. In conclusion, wemore » present the relevant theory and experimental results.« less

Bound States and the Third Harmonic Generation in an Electric Field Biased Semi-parabolic Quantum Well

NASA Astrophysics Data System (ADS)

Zhang, Li; Xie, Hong-Jing

2003-11-01

Within the framework of the compact density matrix approach, the third-harmonic generation (THG) in an electric-field-biased semi-parabolic quantum well (QW) has been deduced and investigated. Via variant of displacement harmonic oscillation, the exact electronic states in the semi-parabolic QW with an applied electric field have also been obtained and discussed. Numerical results on typical GaAs material reveal that, electric fields and confined potential frequency of semi-parabolic QW have obvious influences on the energy levels of electronic states and the THG in the semi-parabolic QW systems. The project supported in part by Guangdong Provincial Natural Science Foundation of China

Analysis of the progressive failure of brittle matrix composites

NASA Technical Reports Server (NTRS)

Thomas, David J.

1995-01-01

This report investigates two of the most common modes of localized failures, namely, periodic fiber-bridged matrix cracks and transverse matrix cracks. A modification of Daniels' bundle theory is combined with Weibull's weakest link theory to model the statistical distribution of the periodic matrix cracking strength for an individual layer. Results of the model predictions are compared with experimental data from the open literature. Extensions to the model are made to account for possible imperfections within the layer (i.e., nonuniform fiber lengths, irregular crack spacing, and degraded in-situ fiber properties), and the results of these studies are presented. A generalized shear-lag analysis is derived which is capable of modeling the development of transverse matrix cracks in material systems having a general multilayer configuration and under states of full in-plane load. A method for computing the effective elastic properties for the damaged layer at the global level is detailed based upon the solution for the effects of the damage at the local level. This methodology is general in nature and is therefore also applicable to (0(sub m)/90(sub n))(sub s) systems. The characteristic stress-strain response for more general cases is shown to be qualitatively correct (experimental data is not available for a quantitative evaluation), and the damage evolution is recorded in terms of the matrix crack density as a function of the applied strain. Probabilistic effects are introduced to account for the statistical nature of the material strengths, thus allowing cumulative distribution curves for the probability of failure to be generated for each of the example laminates. Additionally, Oh and Finney's classic work on fracture location in brittle materials is extended and combined with the shear-lag analysis. The result is an analytical form for predicting the probability density function for the location of the next transverse crack occurrence within a crack bounded region. The results of this study verified qualitatively the validity of assuming a uniform crack spacing (as was done in the shear-lag model).

Multiresolution quantum chemistry in multiwavelet bases: excited states from time-dependent Hartree–Fock and density functional theory via linear response

DOE PAGES

Yanai, Takeshi; Fann, George I.; Beylkin, Gregory; ...

2015-02-25

Using the fully numerical method for time-dependent Hartree–Fock and density functional theory (TD-HF/DFT) with the Tamm–Dancoff (TD) approximation we use a multiresolution analysis (MRA) approach to present our findings. From a reformulation with effective use of the density matrix operator, we obtain a general form of the HF/DFT linear response equation in the first quantization formalism. It can be readily rewritten as an integral equation with the bound-state Helmholtz (BSH) kernel for the Green's function. The MRA implementation of the resultant equation permits excited state calculations without virtual orbitals. Moreover, the integral equation is efficiently and adaptively solved using amore » numerical multiresolution solver with multiwavelet bases. Our implementation of the TD-HF/DFT methods is applied for calculating the excitation energies of H 2, Be, N 2, H 2O, and C 2H 4 molecules. The numerical errors of the calculated excitation energies converge in proportion to the residuals of the equation in the molecular orbitals and response functions. The energies of the excited states at a variety of length scales ranging from short-range valence excitations to long-range Rydberg-type ones are consistently accurate. It is shown that the multiresolution calculations yield the correct exponential asymptotic tails for the response functions, whereas those computed with Gaussian basis functions are too diffuse or decay too rapidly. Finally, we introduce a simple asymptotic correction to the local spin-density approximation (LSDA) so that in the TDDFT calculations, the excited states are correctly bound.« less

Chiral Luttinger liquids and a generalized Luttinger's theorem in fractional quantum Hall edges via finite-entanglement scaling

NASA Astrophysics Data System (ADS)

Varjas, Daniel; Zaletel, Michael; Moore, Joel

2014-03-01

We use bosonic field theories and the infinite system density matrix renormalization group (iDMRG) method to study infinite strips of fractional quantum Hall (FQH) states starting from microscopic Hamiltonians. Finite-entanglement scaling allows us to accurately measure chiral central charge, edge mode exponents and momenta without finite-size errors. We analyze states in the first and second level of the standard hierarchy and compare our results to predictions of the chiral Luttinger liquid (χLL) theory. The results confirm the universality of scaling exponents in chiral edges and demonstrate that renormalization is subject to universal relations in the non-chiral case. We prove a generalized Luttinger's theorem involving all singularities in the momentum-resolved density, which naturally arises when mapping Landau levels on a cylinder to a fermion chain and deepens our understanding of non-Fermi liquids in 1D.

Chiral Luttinger liquids and a generalized Luttinger theorem in fractional quantum Hall edges via finite-entanglement scaling

NASA Astrophysics Data System (ADS)

Varjas, Dániel; Zaletel, Michael P.; Moore, Joel E.

2013-10-01

We use bosonic field theories and the infinite system density matrix renormalization group method to study infinite strips of fractional quantum Hall states starting from microscopic Hamiltonians. Finite-entanglement scaling allows us to accurately measure chiral central charge, edge-mode exponents, and momenta without finite-size errors. We analyze states in the first and second levels of the standard hierarchy and compare our results to predictions of the chiral Luttinger liquid theory. The results confirm the universality of scaling exponents in chiral edges and demonstrate that renormalization is subject to universal relations in the nonchiral case. We prove a generalized Luttinger theorem involving all singularities in the momentum-resolved density, which naturally arises when mapping Landau levels on a cylinder to a fermion chain and deepens our understanding of non-Fermi liquids in one dimension.

Scaling for hard-sphere colloidal glasses near jamming

NASA Astrophysics Data System (ADS)

Zargar, Rojman; DeGiuli, Eric; Bonn, Daniel

2016-12-01

Hard-sphere colloids are model systems in which to study the glass transition and universal properties of amorphous solids. Using covariance matrix analysis to determine the vibrational modes, we experimentally measure here the scaling behavior of the density of states, shear modulus, and mean-squared displacement (MSD) in a hard-sphere colloidal glass. Scaling the frequency with the boson-peak frequency, we find that the density of states at different volume fractions all collapse on a single master curve, which obeys a power law in terms of the scaled frequency. Below the boson peak, the exponent is consistent with theoretical results obtained by real-space and phase-space approaches to understanding amorphous solids. We find that the shear modulus and the MSD are nearly inversely proportional, and show a singular power-law dependence on the distance from random close packing. Our results are in very good agreement with the theoretical predictions.

Manipulating sonic band gaps at will: vibrational density of states in three-dimensional acoustic metamaterial composites

NASA Astrophysics Data System (ADS)

Terao, Takamichi

2018-04-01

Vibrational properties of elastic composites containing a mass-in-mass microstructure embedded in a solid matrix are numerically studied. Using a lattice model, we investigate the vibrational density of states in three-dimensional composite structures where resonant particles are randomly dispersed. By dispersing such particles in the system, a sonic band gap appears. It is confirmed that this band gap can be introduced in a desired frequency regime by changing the parameters of resonant particles and the frequency width of this band gap can be controlled by varying the concentration of the resonant particles to be dispersed. In addition, multiple sonic band gaps can be realized using different species of resonant particles. These results enable us to suggest an alternative method to fabricate devices that can inhibit the propagation of elastic waves with specific frequencies using acoustic metamaterials.

Neural network based feed-forward high density associative memory

NASA Technical Reports Server (NTRS)

Daud, T.; Moopenn, A.; Lamb, J. L.; Ramesham, R.; Thakoor, A. P.

1987-01-01

A novel thin film approach to neural-network-based high-density associative memory is described. The information is stored locally in a memory matrix of passive, nonvolatile, binary connection elements with a potential to achieve a storage density of 10 to the 9th bits/sq cm. Microswitches based on memory switching in thin film hydrogenated amorphous silicon, and alternatively in manganese oxide, have been used as programmable read-only memory elements. Low-energy switching has been ascertained in both these materials. Fabrication and testing of memory matrix is described. High-speed associative recall approaching 10 to the 7th bits/sec and high storage capacity in such a connection matrix memory system is also described.

Polyaniline-CuO hybrid nanocomposite with enhanced electrical conductivity

NASA Astrophysics Data System (ADS)

de Souza, Vânia S.; da Frota, Hidembergue O.; Sanches, Edgar A.

2018-02-01

A hybrid nanocomposite based on a polymer matrix constituted of Polyaniline Emeraldine-salt form (PANI-ES) reinforced by copper oxide II (CuO) particles was obtained by in situ polymerization. Structural, morphological and electrical properties of the pure materials and nanocomposite form were investigated. The presence of CuO particles in the nanocomposite material affected the natural alignment of the polymer chains. XRD technique allowed the visualization of the polymer amorphization in the nanocomposite form, suggesting an interaction between both phases. The FTIR spectra confirmed this molecular interaction due to the blue shift of the characteristic absorption peaks of PANI-ES in the nanocomposite form. SEM images revealed that the polymer nanofiber morphology was no longer observed in the nanocomposite. The CuO spherical particles are randomly dispersed in the polymer matrix. The density functional theory plus the Coulomb interaction method revealed a charge transfer from PANI to CuO slab. Moreover, the density of states (DOS) has revealed that the nanocomposite behaves as a metal. In agreement, the electrical conductivity showed an increase of 60% in the nanocomposite material.

Phase dilemma in natural orbital functional theory from the N-representability perspective

NASA Astrophysics Data System (ADS)

Mitxelena, Ion; Rodriguez-Mayorga, Mauricio; Piris, Mario

2018-06-01

Any rigorous approach to first-order reduced density matrix ( Γ) functional theory faces the phase dilemma, that is, having to deal with a large number of possible combinations of signs in terms of the electron-electron interaction energy. This problem was discovered by reducing a ground-state energy generated from an approximate N-particle wavefunction into a functional of Γ, known as the top-down method. Here, we show that the phase dilemma also appears in the bottom-up method, in which the functional E[ Γ] is generated by progressive inclusion of N-representability conditions on the reconstructed two-particle reduced density matrix. It is shown that an adequate choice of signs is essential to accurately describe model systems with strong non-dynamic (static) electron correlation, specifically, the one-dimensional Hubbard model with periodic boundary conditions and hydrogen rings. For the latter, the Piris natural orbital functional 7 (PNOF7), with phases equal to -1 for the inter-pair energy terms containing the exchange-time-inversion integrals, agrees with exact diagonalization results.

Crossover between superconductivity and magnetism in SrRuO3 mesocrystal embedded YBa2Cu3O7-x heterostructures.

PubMed

Suresh, Vandrangi; Lin, Jheng-Cyuan; Liu, Heng-Jui; Zhang, Zaoli; Chiang, Ping-Chih; Hsun, Yu-Ching; Chen, Yi-Chun; Lin, Jiunn-Yuan; Chu, Ying-Hao

2016-11-03

The competition between superconductivity and ferromagnetism poses great challenges and has attracted renewed interest for applications in novel spintronic devices. In order to emphasize their interactions, we fabricated a heterostructure composed of superconducting YBa 2 Cu 3 O 7-δ (YBCO) film embedded with itinerant ferromagnetic SrRuO 3 (SRO) mesocrystals. Starting from a doping concentration of 10 vol% of SRO mesocrystal in a YBCO matrix, corresponding to the density of SRO nanocrystals ∼5 × 10 9 cm -2 , which exhibits the typical characteristic of a metal-superconductor transition, and then increasing the magnetic interactions as a function of SRO embedment, the electronic correlation and the interplay between superconductivity and magnetism throughout the temperature regime were investigated. A metal-insulator transition in the normal state of YBCO and a crossover between superconductivity and magnetism at low temperatures were found upon increasing the density of nano-size SRO crystallites in the YBCO matrix as a consequence of competing interactions between these two ordered phases.

Hydrogen Permeability of Polymer Matrix Composites at Cryogenic Temperatures

NASA Technical Reports Server (NTRS)

Grenoble, Ray W.; Gates, Thomas S

2005-01-01

This paper presents experimental methods and results of an ongoing study of the correlation between damage state and hydrogen gas permeability of laminated composite materials under mechanical strains and thermal loads. A specimen made from IM-7/977-2 composite material has been mechanically cycled at room temperature to induce microcrack damage. Crack density and tensile modulus were observed as functions of number of cycles. Damage development was found to occur most quickly in the off-axis plies near the outside of the laminate. Permeability measurements were made after 170,000 cycles and 430,000 cycles. Leak rate was found to depend on applied mechanical strain, crack density, and test temperature.

Exchange Coupling Interactions from the Density Matrix Renormalization Group and N-Electron Valence Perturbation Theory: Application to a Biomimetic Mixed-Valence Manganese Complex.

PubMed

Roemelt, Michael; Krewald, Vera; Pantazis, Dimitrios A

2018-01-09

The accurate description of magnetic level energetics in oligonuclear exchange-coupled transition-metal complexes remains a formidable challenge for quantum chemistry. The density matrix renormalization group (DMRG) brings such systems for the first time easily within reach of multireference wave function methods by enabling the use of unprecedentedly large active spaces. But does this guarantee systematic improvement in predictive ability and, if so, under which conditions? We identify operational parameters in the use of DMRG using as a test system an experimentally characterized mixed-valence bis-μ-oxo/μ-acetato Mn(III,IV) dimer, a model for the oxygen-evolving complex of photosystem II. A complete active space of all metal 3d and bridge 2p orbitals proved to be the smallest meaningful starting point; this is readily accessible with DMRG and greatly improves on the unrealistic metal-only configuration interaction or complete active space self-consistent field (CASSCF) values. Orbital optimization is critical for stabilizing the antiferromagnetic state, while a state-averaged approach over all spin states involved is required to avoid artificial deviations from isotropic behavior that are associated with state-specific calculations. Selective inclusion of localized orbital subspaces enables probing the relative contributions of different ligands and distinct superexchange pathways. Overall, however, full-valence DMRG-CASSCF calculations fall short of providing a quantitative description of the exchange coupling owing to insufficient recovery of dynamic correlation. Quantitatively accurate results can be achieved through a DMRG implementation of second order N-electron valence perturbation theory (NEVPT2) in conjunction with a full-valence metal and ligand active space. Perspectives for future applications of DMRG-CASSCF/NEVPT2 to exchange coupling in oligonuclear clusters are discussed.

Muscle-tendon units localization and activation level analysis based on high-density surface EMG array and NMF algorithm

NASA Astrophysics Data System (ADS)

Huang, Chengjun; Chen, Xiang; Cao, Shuai; Zhang, Xu

2016-12-01

Objective. Some skeletal muscles can be subdivided into smaller segments called muscle-tendon units (MTUs). The purpose of this paper is to propose a framework to locate the active region of the corresponding MTUs within a single skeletal muscle and to analyze the activation level varieties of different MTUs during a dynamic motion task. Approach. Biceps brachii and gastrocnemius were selected as targeted muscles and three dynamic motion tasks were designed and studied. Eight healthy male subjects participated in the data collection experiments, and 128-channel surface electromyographic (sEMG) signals were collected with a high-density sEMG electrode grid (a grid consists of 8 rows and 16 columns). Then the sEMG envelopes matrix was factorized into a matrix of weighting vectors and a matrix of time-varying coefficients by nonnegative matrix factorization algorithm. Main results. The experimental results demonstrated that the weightings vectors, which represent invariant pattern of muscle activity across all channels, could be used to estimate the location of MTUs and the time-varying coefficients could be used to depict the variation of MTUs activation level during dynamic motion task. Significance. The proposed method provides one way to analyze in-depth the functional state of MTUs during dynamic tasks and thus can be employed on multiple noteworthy sEMG-based applications such as muscle force estimation, muscle fatigue research and the control of myoelectric prostheses. This work was supported by the National Nature Science Foundation of China under Grant 61431017 and 61271138.

Quantum confinement effects on electronic photomobilities at nanostructured semiconductor surfaces: Si(111) without and with adsorbed Ag clusters

NASA Astrophysics Data System (ADS)

Hembree, Robert H.; Vazhappilly, Tijo; Micha, David A.

2017-12-01

The conductivity of holes and electrons photoexcited in Si slabs is affected by the slab thickness and by adsorbates. The mobilities of those charged carriers depend on how many layers compose the slab, and this has important scientific and technical consequences for the understanding of photovoltaic materials. A previously developed general computational procedure combining density matrix and electronic band structure treatments has been applied to extensive calculations of mobilities of photoexcited electrons and holes at Si(111) nanostructured surfaces with varying slab thickness and for varying photon energies, to investigate the expected change in mobility magnitudes as the slab thickness is increased. Results have been obtained with and without adsorbed silver clusters for comparison of their optical and photovoltaic properties. Band states were generated using a modified ab initio density functional treatment with the PBE exchange and correlation density functionals and with periodic boundary conditions for large atomic supercells. An energy gap correction was applied to the unoccupied orbital energies of each band structure by running more accurate HSE hybrid functional calculations for a Si(111) slab. Photoexcited state populations for slabs with 6, 8, 10, and 12 layers were generated using a steady state reduced density matrix including dissipative effects due to energy exchange with excitons and phonons in the medium. Mobilities have been calculated from the derivatives of voltage-driven electronic energies with respect to electronic momentum, for each energy band and for the average over bands. Results show two clear trends: (a) adding Ag increases the hole photomobilities and (b) decreasing the slab thickness increases hole photomobilities. The increased hole populations in 6- and 8-layer systems and the large increase in hole mobility for these thinner slabs can be interpreted as a quantum confinement effect of hole orbitals. As the slab thickness increases to ten and twelve layers, the effect of silver adsorbates decreases leading to smaller relative enhancements to the conduction electron and hole mobilities, but the addition of the silver nanoclusters still increases the absorbance of light and the mobility of holes compared to their mobilities in the pure Si slabs.

Three-dimensional matrix fiber alignment modulates cell migration and MT1-MMP utility by spatially and temporally directing protrusions

NASA Astrophysics Data System (ADS)

Fraley, Stephanie I.; Wu, Pei-Hsun; He, Lijuan; Feng, Yunfeng; Krisnamurthy, Ranjini; Longmore, Gregory D.; Wirtz, Denis

2015-10-01

Multiple attributes of the three-dimensional (3D) extracellular matrix (ECM) have been independently implicated as regulators of cell motility, including pore size, crosslink density, structural organization, and stiffness. However, these parameters cannot be independently varied within a complex 3D ECM protein network. We present an integrated, quantitative study of these parameters across a broad range of complex matrix configurations using self-assembling 3D collagen and show how each parameter relates to the others and to cell motility. Increasing collagen density resulted in a decrease and then an increase in both pore size and fiber alignment, which both correlated significantly with cell motility but not bulk matrix stiffness within the range tested. However, using the crosslinking enzyme Transglutaminase II to alter microstructure independently of density revealed that motility is most significantly predicted by fiber alignment. Cellular protrusion rate, protrusion orientation, speed of migration, and invasion distance showed coupled biphasic responses to increasing collagen density not predicted by 2D models or by stiffness, but instead by fiber alignment. The requirement of matrix metalloproteinase (MMP) activity was also observed to depend on microstructure, and a threshold of MMP utility was identified. Our results suggest that fiber topography guides protrusions and thereby MMP activity and motility.

Quantum chi-squared and goodness of fit testing

DOE Office of Scientific and Technical Information (OSTI.GOV)

Temme, Kristan; Verstraete, Frank

2015-01-15

A quantum mechanical hypothesis test is presented for the hypothesis that a certain setup produces a given quantum state. Although the classical and the quantum problems are very much related to each other, the quantum problem is much richer due to the additional optimization over the measurement basis. A goodness of fit test for i.i.d quantum states is developed and a max-min characterization for the optimal measurement is introduced. We find the quantum measurement which leads both to the maximal Pitman and Bahadur efficiencies, and determine the associated divergence rates. We discuss the relationship of the quantum goodness of fitmore » test to the problem of estimating multiple parameters from a density matrix. These problems are found to be closely related and we show that the largest error of an optimal strategy, determined by the smallest eigenvalue of the Fisher information matrix, is given by the divergence rate of the goodness of fit test.« less

Fully nonlocal inelastic scattering computations for spectroscopical transmission electron microscopy methods

NASA Astrophysics Data System (ADS)

Rusz, Ján; Lubk, Axel; Spiegelberg, Jakob; Tyutyunnikov, Dmitry

2017-12-01

The complex interplay of elastic and inelastic scattering amenable to different levels of approximation constitutes the major challenge for the computation and hence interpretation of TEM-based spectroscopical methods. The two major approaches to calculate inelastic scattering cross sections of fast electrons on crystals—Yoshioka-equations-based forward propagation and the reciprocal wave method—are founded in two conceptually differing schemes—a numerical forward integration of each inelastically scattered wave function, yielding the exit density matrix, and a computation of inelastic scattering matrix elements using elastically scattered initial and final states (double channeling). Here, we compare both approaches and show that the latter is computationally competitive to the former by exploiting analytical integration schemes over multiple excited states. Moreover, we show how to include full nonlocality of the inelastic scattering event, neglected in the forward propagation approaches, at no additional computing costs in the reciprocal wave method. Detailed simulations show in some cases significant errors due to the z -locality approximation and hence pitfalls in the interpretation of spectroscopical TEM results.

Collagen Matrix Density Drives the Metabolic Shift in Breast Cancer Cells.

PubMed

Morris, Brett A; Burkel, Brian; Ponik, Suzanne M; Fan, Jing; Condeelis, John S; Aguirre-Ghiso, Julio A; Castracane, James; Denu, John M; Keely, Patricia J

2016-11-01

Increased breast density attributed to collagen I deposition is associated with a 4-6 fold increased risk of developing breast cancer. Here, we assessed cellular metabolic reprogramming of mammary carcinoma cells in response to increased collagen matrix density using an in vitro 3D model. Our initial observations demonstrated changes in functional metabolism in both normal mammary epithelial cells and mammary carcinoma cells in response to changes in matrix density. Further, mammary carcinoma cells grown in high density collagen matrices displayed decreased oxygen consumption and glucose metabolism via the tricarboxylic acid (TCA) cycle compared to cells cultured in low density matrices. Despite decreased glucose entry into the TCA cycle, levels of glucose uptake, cell viability, and ROS were not different between high and low density matrices. Interestingly, under high density conditions the contribution of glutamine as a fuel source to drive the TCA cycle was significantly enhanced. These alterations in functional metabolism mirrored significant changes in the expression of metabolic genes involved in glycolysis, oxidative phosphorylation, and the serine synthesis pathway. This study highlights the broad importance of the collagen microenvironment to cellular expression profiles, and shows that changes in density of the collagen microenvironment can modulate metabolic shifts of cancer cells. Copyright © 2016 The Authors. Published by Elsevier B.V. All rights reserved.

Constructing diabatic states from adiabatic states: Extending generalized Mulliken-Hush to multiple charge centers with Boys localization

NASA Astrophysics Data System (ADS)

Subotnik, Joseph E.; Yeganeh, Sina; Cave, Robert J.; Ratner, Mark A.

2008-12-01

This article shows that, although Boys localization is usually applied to single-electron orbitals, the Boys method itself can be applied to many electron molecular states. For the two-state charge-transfer problem, we show analytically that Boys localization yields the same charge-localized diabatic states as those found by generalized Mulliken-Hush theory. We suggest that for future work in electron transfer, where systems have more than two charge centers, one may benefit by using a variant of Boys localization to construct diabatic potential energy surfaces and extract electronic coupling matrix elements. We discuss two chemical examples of Boys localization and propose a generalization of the Boys algorithm for creating diabatic states with localized spin density that should be useful for Dexter triplet-triplet energy transfer.

Constructing diabatic states from adiabatic states: extending generalized Mulliken-Hush to multiple charge centers with boys localization.

PubMed

Subotnik, Joseph E; Yeganeh, Sina; Cave, Robert J; Ratner, Mark A

2008-12-28

This article shows that, although Boys localization is usually applied to single-electron orbitals, the Boys method itself can be applied to many electron molecular states. For the two-state charge-transfer problem, we show analytically that Boys localization yields the same charge-localized diabatic states as those found by generalized Mulliken-Hush theory. We suggest that for future work in electron transfer, where systems have more than two charge centers, one may benefit by using a variant of Boys localization to construct diabatic potential energy surfaces and extract electronic coupling matrix elements. We discuss two chemical examples of Boys localization and propose a generalization of the Boys algorithm for creating diabatic states with localized spin density that should be useful for Dexter triplet-triplet energy transfer.

Propensity, Probability, and Quantum Theory

NASA Astrophysics Data System (ADS)

Ballentine, Leslie E.

2016-08-01

Quantum mechanics and probability theory share one peculiarity. Both have well established mathematical formalisms, yet both are subject to controversy about the meaning and interpretation of their basic concepts. Since probability plays a fundamental role in QM, the conceptual problems of one theory can affect the other. We first classify the interpretations of probability into three major classes: (a) inferential probability, (b) ensemble probability, and (c) propensity. Class (a) is the basis of inductive logic; (b) deals with the frequencies of events in repeatable experiments; (c) describes a form of causality that is weaker than determinism. An important, but neglected, paper by P. Humphreys demonstrated that propensity must differ mathematically, as well as conceptually, from probability, but he did not develop a theory of propensity. Such a theory is developed in this paper. Propensity theory shares many, but not all, of the axioms of probability theory. As a consequence, propensity supports the Law of Large Numbers from probability theory, but does not support Bayes theorem. Although there are particular problems within QM to which any of the classes of probability may be applied, it is argued that the intrinsic quantum probabilities (calculated from a state vector or density matrix) are most naturally interpreted as quantum propensities. This does not alter the familiar statistical interpretation of QM. But the interpretation of quantum states as representing knowledge is untenable. Examples show that a density matrix fails to represent knowledge.

Energy spectrum and electrical conductivity of graphene with a nitrogen impurity

NASA Astrophysics Data System (ADS)

Repetskii, S. P.; Vyshivanaya, I. G.; Skotnikov, V. A.; Yatsenyuk, A. A.

2015-04-01

The electronic structure of graphene with a nitrogen impurity has been studied based on the model of tight binding using exchange-correlation potentials in the density-functional theory. Wave functions of 2 s and 2 p states of neutral noninteracting carbon atoms have been chosen as the basis. When studying the matrix elements of the Hamiltonian, the first three coordination shells have been taken into account. It has been established that the hybridization of electron-energy bands leads to the splitting of the electron energy spectrum near the Fermi level. Due to the overlap of the energy bands, the arising gap behaves as a quasi-gap, in which the density of the electron levels is much lower than in the rest of the spectrum. It has been established that the conductivity of graphene decreases with increasing nitrogen concentration. Since the increase in the nitrogen concentration leads to an increase in the density of states at the Fermi level, the decrease in the conductivity is due to a sharper decrease in the time of relaxation of the electron sates.

An accurate and linear-scaling method for calculating charge-transfer excitation energies and diabatic couplings

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pavanello, Michele; Van Voorhis, Troy; Visscher, Lucas

2013-02-07

Quantum-mechanical methods that are both computationally fast and accurate are not yet available for electronic excitations having charge transfer character. In this work, we present a significant step forward towards this goal for those charge transfer excitations that take place between non-covalently bound molecules. In particular, we present a method that scales linearly with the number of non-covalently bound molecules in the system and is based on a two-pronged approach: The molecular electronic structure of broken-symmetry charge-localized states is obtained with the frozen density embedding formulation of subsystem density-functional theory; subsequently, in a post-SCF calculation, the full-electron Hamiltonian and overlapmore » matrix elements among the charge-localized states are evaluated with an algorithm which takes full advantage of the subsystem DFT density partitioning technique. The method is benchmarked against coupled-cluster calculations and achieves chemical accuracy for the systems considered for intermolecular separations ranging from hydrogen-bond distances to tens of Angstroms. Numerical examples are provided for molecular clusters comprised of up to 56 non-covalently bound molecules.« less

An accurate and linear-scaling method for calculating charge-transfer excitation energies and diabatic couplings.

PubMed

Pavanello, Michele; Van Voorhis, Troy; Visscher, Lucas; Neugebauer, Johannes

2013-02-07

Quantum-mechanical methods that are both computationally fast and accurate are not yet available for electronic excitations having charge transfer character. In this work, we present a significant step forward towards this goal for those charge transfer excitations that take place between non-covalently bound molecules. In particular, we present a method that scales linearly with the number of non-covalently bound molecules in the system and is based on a two-pronged approach: The molecular electronic structure of broken-symmetry charge-localized states is obtained with the frozen density embedding formulation of subsystem density-functional theory; subsequently, in a post-SCF calculation, the full-electron Hamiltonian and overlap matrix elements among the charge-localized states are evaluated with an algorithm which takes full advantage of the subsystem DFT density partitioning technique. The method is benchmarked against coupled-cluster calculations and achieves chemical accuracy for the systems considered for intermolecular separations ranging from hydrogen-bond distances to tens of Ångstroms. Numerical examples are provided for molecular clusters comprised of up to 56 non-covalently bound molecules.

Landscape attributes as drivers of the geographical variation in density of Sapajus nigritus Kerr, 1792, a primate endemic to the Atlantic Forest

NASA Astrophysics Data System (ADS)

Hendges, Carla D.; Melo, Geruza L.; Gonçalves, Alberto S.; Cerezer, Felipe O.; Cáceres, Nilton C.

2017-10-01

Neotropical primates are among the most well studied forest mammals concerning their population densities. However, few studies have evaluated the factors that influence the spatial variation in the population density of primates, which limits the possibility of inferences towards this animal group, especially at the landscape-level. Here, we compiled density data of Sapajus nigritus from 21 forest patches of the Brazilian Atlantic Forest. We tested the effects of climatic variables (temperature, precipitation), landscape attributes (number of patches, mean inter-patch isolation distance, matrix modification index) and patch size on the population density using linear models and the Akaike information criterion. Our findings showed that the density of S. nigritus is influenced by landscape attributes, particularly by fragmentation and matrix modification. Overall, moderately fragmented landscapes and those surrounded by matrices with intermediate indexes of temporal modification (i.e., crop plantations, forestry) are related to high densities of this species. These results support the assumptions that ecologically flexible species respond positively to forest fragmentation. However, the non-linear relationship between S. nigritus density and number of patches suggests that even the species that are most tolerant to forest cover changes seem to respond positively only at an intermediate level of habitat fragmentation, being dependent of both a moderate degree of forest cover and a high quality matrix. The results we found here can be a common response to fragmentation for those forest dweller species that are able to use the matrix as complementary foraging sites.

Metrics of cellular and vascular infiltration of human acellular dermal matrix in ventral hernia repairs.

PubMed

Campbell, Kristin Turza; Burns, Nadja K; Ensor, Joe; Butler, Charles E

2012-04-01

Human acellular dermal matrix is used for ventral hernia repair, as it resists infection and remodels by means of surrounding tissue. However, the tissue source and impact of basement membrane on cell and vessel infiltration have not been determined. The authors hypothesized that musculofascia would be the primary tissue source of cells and vessels infiltrating into human acellular dermal matrix and that the basement membrane would inhibit infiltration. Fifty-six guinea pigs underwent inlay human acellular dermal matrix ventral hernia repair with the basement membrane oriented toward or away from the peritoneum. At postoperative weeks 1, 2, or 4, repair sites were completely excised. Histologic and immunohistochemical analyses were performed to quantify cell and vessel density within repair-site zones, including interface (lateral, beneath musculofascia) and center (beneath subcutaneous fat) zones. Cell and vessel quantities were compared as functions of zone, basement membrane orientation, and time. Cellular and vascular infiltration increased over time universally. The interface demonstrated greater mean cell density than the center (weeks 1 and 2, p = 0.01 and p < 0.0001, respectively). Cell density was greater with the basement membrane oriented toward the peritoneum at week 4 (p = 0.02). The interface zone had greater mean vessel density than the center zone at week 4 (p < 0.0001). Orienting the basement membrane toward the peritoneum increased vessel density at week 4 (p = 0.0004). Cellular and vascular infiltration into human acellular dermal matrix for ventral hernia repairs was greater from musculofascia than from subcutaneous fat, and the basement membrane inhibited cellular and vascular infiltration. Human acellular dermal matrix should be placed adjacent to the best vascularizing tissue to improve fibrovascular incorporation.

Matrix density effects on the mechanical properties of SiC fiber-reinforced silicon nitride matrix properties

NASA Technical Reports Server (NTRS)

Bhatt, Ramakrishna T.; Kiser, Lames D.

1990-01-01

The room temperature mechanical properties were measured for SiC fiber reinforced reaction-bonded silicon nitride composites (SiC/RBSN) of different densities. The composites consisted of approx. 30 vol percent uniaxially aligned 142 micron diameter SiC fibers (Textron SCS-6) in a reaction-bonded Si3N4 matrix. The composite density was varied by changing the consolidation pressure during RBSN processing and by hot isostatically pressing the SiC/RBSN composites. Results indicate that as the consolidation pressure was increased from 27 to 138 MPa, the average pore size of the nitrided composites decreased from 0.04 to 0.02 microns and the composite density increased from 2.07 to 2.45 gm/cc. Nonetheless, these improvements resulted in only small increases in the first matrix cracking stress, primary elastic modulus, and ultimate tensile strength values of the composites. In contrast, HIP consolidation of SiC/RBSN resulted in a fully dense material whose first matrix cracking stress and elastic modulus were approx. 15 and 50 percent higher, respectively, and ultimate tensile strength values were approx. 40 percent lower than those for unHIPed SiC/RBSN composites. The modulus behavior for all specimens can be explained by simple rule-of-mixture theory. Also, the loss in ultimate strength for the HIPed composites appears to be related to a degradation in fiber strength at the HIP temperature. However, the density effect on matrix fracture strength was much less than would be expected based on typical monolithic Si3N4 behavior, suggesting that composite theory is indeed operating. Possible practical implications of these observations are discussed.

Approximating local observables on projected entangled pair states

NASA Astrophysics Data System (ADS)

Schwarz, M.; Buerschaper, O.; Eisert, J.

2017-06-01

Tensor network states are for good reasons believed to capture ground states of gapped local Hamiltonians arising in the condensed matter context, states which are in turn expected to satisfy an entanglement area law. However, the computational hardness of contracting projected entangled pair states in two- and higher-dimensional systems is often seen as a significant obstacle when devising higher-dimensional variants of the density-matrix renormalization group method. In this work, we show that for those projected entangled pair states that are expected to provide good approximations of such ground states of local Hamiltonians, one can compute local expectation values in quasipolynomial time. We therefore provide a complexity-theoretic justification of why state-of-the-art numerical tools work so well in practice. We finally turn to the computation of local expectation values on quantum computers, providing a meaningful application for a small-scale quantum computer.

Increased extracellular matrix density decreases MCF10A breast cell acinus formation in 3D culture conditions.

PubMed

Lance, Amanda; Yang, Chih-Chao; Swamydas, Muthulekha; Dean, Delphine; Deitch, Sandy; Burg, Karen J L; Dréau, Didier

2016-01-01

The extracellular matrix (ECM) contributes to the generation and dynamic of normal breast tissue, in particular to the generation of polarized acinar and ductal structures. In vitro 3D culture conditions, including variations in the composition of the ECM, have been shown to directly influence the formation and organization of acinus-like and duct-like structures. Furthermore, the density of the ECM appears to also play a role in the normal mammary tissue and tumour formation. Here we show that the density of the ECM directly influences the number, organization and function of breast acini. Briefly, non-malignant human breast MCF10A cells were incubated in increasing densities of a Matrigel®-collagen I matrix. Elastic moduli near and distant to the acinus structures were measured by atomic force microscopy, and the number of acinus structures was determined. Immunochemistry was used to investigate the expression levels of E-cadherin, laminin, matrix metalloproteinase-14 and ß-casein in MCF10A cells. The modulus of the ECM was significantly increased near the acinus structures and the number of acinus structures decreased with the increase in Matrigel-collagen I density. As evaluated by the expression of laminin, the organization of the acinus structures present was altered as the density of the ECM increased. Increases in both E-cadherin and MMP14 expression by MCF10A cells as ECM density increased were also observed. In contrast, MCF10A cells expressed lower ß-casein levels as the ECM density increased. Taken together, these observations highlight the key role of ECM density in modulating the number, organization and function of breast acini. Copyright © 2013 John Wiley & Sons, Ltd.

A density matrix-based method for the linear-scaling calculation of dynamic second- and third-order properties at the Hartree-Fock and Kohn-Sham density functional theory levels.

PubMed

Kussmann, Jörg; Ochsenfeld, Christian

2007-11-28

A density matrix-based time-dependent self-consistent field (D-TDSCF) method for the calculation of dynamic polarizabilities and first hyperpolarizabilities using the Hartree-Fock and Kohn-Sham density functional theory approaches is presented. The D-TDSCF method allows us to reduce the asymptotic scaling behavior of the computational effort from cubic to linear for systems with a nonvanishing band gap. The linear scaling is achieved by combining a density matrix-based reformulation of the TDSCF equations with linear-scaling schemes for the formation of Fock- or Kohn-Sham-type matrices. In our reformulation only potentially linear-scaling matrices enter the formulation and efficient sparse algebra routines can be employed. Furthermore, the corresponding formulas for the first hyperpolarizabilities are given in terms of zeroth- and first-order one-particle reduced density matrices according to Wigner's (2n+1) rule. The scaling behavior of our method is illustrated for first exemplary calculations with systems of up to 1011 atoms and 8899 basis functions.

Band gap engineering in finite elongated graphene nanoribbon heterojunctions: Tight-binding model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tayo, Benjamin O.

2015-08-15

A simple model based on the divide and conquer rule and tight-binding (TB) approximation is employed for studying the role of finite size effect on the electronic properties of elongated graphene nanoribbon (GNR) heterojunctions. In our model, the GNR heterojunction is divided into three parts: a left (L) part, middle (M) part, and right (R) part. The left part is a GNR of width W{sub L}, the middle part is a GNR of width W{sub M}, and the right part is a GNR of width W{sub R}. We assume that the left and right parts of the GNR heterojunction interactmore » with the middle part only. Under this approximation, the Hamiltonian of the system can be expressed as a block tridiagonal matrix. The matrix elements of the tridiagonal matrix are computed using real space nearest neighbor orthogonal TB approximation. The electronic structure of the GNR heterojunction is analyzed by computing the density of states. We demonstrate that for heterojunctions for which W{sub L} = W{sub R}, the band gap of the system can be tuned continuously by varying the length of the middle part, thus providing a new approach to band gap engineering in GNRs. Our TB results were compared with calculations employing divide and conquer rule in combination with density functional theory (DFT) and were found to agree nicely.« less

Density Control of Multi-Agent Systems with Safety Constraints: A Markov Chain Approach

NASA Astrophysics Data System (ADS)

Demirer, Nazli

The control of systems with autonomous mobile agents has been a point of interest recently, with many applications like surveillance, coverage, searching over an area with probabilistic target locations or exploring an area. In all of these applications, the main goal of the swarm is to distribute itself over an operational space to achieve mission objectives specified by the density of swarm. This research focuses on the problem of controlling the distribution of multi-agent systems considering a hierarchical control structure where the whole swarm coordination is achieved at the high-level and individual vehicle/agent control is managed at the low-level. High-level coordination algorithms uses macroscopic models that describes the collective behavior of the whole swarm and specify the agent motion commands, whose execution will lead to the desired swarm behavior. The low-level control laws execute the motion to follow these commands at the agent level. The main objective of this research is to develop high-level decision control policies and algorithms to achieve physically realizable commanding of the agents by imposing mission constraints on the distribution. We also make some connections with decentralized low-level motion control. This dissertation proposes a Markov chain based method to control the density distribution of the whole system where the implementation can be achieved in a decentralized manner with no communication between agents since establishing communication with large number of agents is highly challenging. The ultimate goal is to guide the overall density distribution of the system to a prescribed steady-state desired distribution while satisfying desired transition and safety constraints. Here, the desired distribution is determined based on the mission requirements, for example in the application of area search, the desired distribution should match closely with the probabilistic target locations. The proposed method is applicable for both systems with a single agent and systems with large number of agents due to the probabilistic nature, where the probability distribution of each agent's state evolves according to a finite-state and discrete-time Markov chain (MC). Hence, designing proper decision control policies requires numerically tractable solution methods for the synthesis of Markov chains. The synthesis problem has the form of a Linear Matrix Inequality Problem (LMI), with LMI formulation of the constraints. To this end, we propose convex necessary and sufficient conditions for safety constraints in Markov chains, which is a novel result in the Markov chain literature. In addition to LMI-based, offline, Markov matrix synthesis method, we also propose a QP-based, online, method to compute a time-varying Markov matrix based on the real-time density feedback. Both problems are convex optimization problems that can be solved in a reliable and tractable way, utilizing existing tools in the literature. A Low Earth Orbit (LEO) swarm simulations are presented to validate the effectiveness of the proposed algorithms. Another problem tackled as a part of this research is the generalization of the density control problem to autonomous mobile agents with two control modes: ON and OFF. Here, each mode consists of a (possibly overlapping) finite set of actions, that is, there exist a set of actions for the ON mode and another set for the OFF mode. We give formulation for a new Markov chain synthesis problem, with additional measurements for the state transitions, where a policy is designed to ensure desired safety and convergence properties for the underlying Markov chain.

Lithium-coated polymeric matrix as a minimum volume-change and dendrite-free lithium metal anode

PubMed Central

Liu, Yayuan; Lin, Dingchang; Liang, Zheng; Zhao, Jie; Yan, Kai; Cui, Yi

2016-01-01

Lithium metal is the ideal anode for the next generation of high-energy-density batteries. Nevertheless, dendrite growth, side reactions and infinite relative volume change have prevented it from practical applications. Here, we demonstrate a promising metallic lithium anode design by infusing molten lithium into a polymeric matrix. The electrospun polyimide employed is stable against highly reactive molten lithium and, via a conformal layer of zinc oxide coating to render the surface lithiophilic, molten lithium can be drawn into the matrix, affording a nano-porous lithium electrode. Importantly, the polymeric backbone enables uniform lithium stripping/plating, which successfully confines lithium within the matrix, realizing minimum volume change and effective dendrite suppression. The porous electrode reduces the effective current density; thus, flat voltage profiles and stable cycling of more than 100 cycles is achieved even at a high current density of 5 mA cm−2 in both carbonate and ether electrolyte. The advantages of the porous, polymeric matrix provide important insights into the design principles of lithium metal anodes. PMID:26987481

Lithium-coated polymeric matrix as a minimum volume-change and dendrite-free lithium metal anode

DOE PAGES

Liu, Yayuan; Lin, Dingchang; Liang, Zheng; ...

2016-03-18

Lithium metal is the ideal anode for the next generation of high-energy-density batteries. Nevertheless, dendrite growth, side reactions and infinite relative volume change have prevented it from practical applications. Here, we demonstrate a promising metallic lithium anode design by infusing molten lithium into a polymeric matrix. The electrospun polyimide employed is stable against highly reactive molten lithium and, via a conformal layer of zinc oxide coating to render the surface lithiophilic, molten lithium can be drawn into the matrix, affording a nano-porous lithium electrode. Importantly, the polymeric backbone enables uniform lithium stripping/plating, which successfully confines lithium within the matrix, realizingmore » minimum volume change and effective dendrite suppression. The porous electrode reduces the effective current density; thus, flat voltage profiles and stable cycling of more than 100 cycles is achieved even at a high current density of 5 mA cm -2 in both carbonate and ether electrolyte. Furthermore, the advantages of the porous, polymeric matrix provide important insights into the design principles of lithium metal anodes.« less

Lithium-coated polymeric matrix as a minimum volume-change and dendrite-free lithium metal anode

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liu, Yayuan; Lin, Dingchang; Liang, Zheng

Lithium metal is the ideal anode for the next generation of high-energy-density batteries. Nevertheless, dendrite growth, side reactions and infinite relative volume change have prevented it from practical applications. Here, we demonstrate a promising metallic lithium anode design by infusing molten lithium into a polymeric matrix. The electrospun polyimide employed is stable against highly reactive molten lithium and, via a conformal layer of zinc oxide coating to render the surface lithiophilic, molten lithium can be drawn into the matrix, affording a nano-porous lithium electrode. Importantly, the polymeric backbone enables uniform lithium stripping/plating, which successfully confines lithium within the matrix, realizingmore » minimum volume change and effective dendrite suppression. The porous electrode reduces the effective current density; thus, flat voltage profiles and stable cycling of more than 100 cycles is achieved even at a high current density of 5 mA cm -2 in both carbonate and ether electrolyte. Furthermore, the advantages of the porous, polymeric matrix provide important insights into the design principles of lithium metal anodes.« less

Stockholder projector analysis: A Hilbert-space partitioning of the molecular one-electron density matrix with orthogonal projectors

NASA Astrophysics Data System (ADS)

Vanfleteren, Diederik; Van Neck, Dimitri; Bultinck, Patrick; Ayers, Paul W.; Waroquier, Michel

2012-01-01

A previously introduced partitioning of the molecular one-electron density matrix over atoms and bonds [D. Vanfleteren et al., J. Chem. Phys. 133, 231103 (2010)] is investigated in detail. Orthogonal projection operators are used to define atomic subspaces, as in Natural Population Analysis. The orthogonal projection operators are constructed with a recursive scheme. These operators are chemically relevant and obey a stockholder principle, familiar from the Hirshfeld-I partitioning of the electron density. The stockholder principle is extended to density matrices, where the orthogonal projectors are considered to be atomic fractions of the summed contributions. All calculations are performed as matrix manipulations in one-electron Hilbert space. Mathematical proofs and numerical evidence concerning this recursive scheme are provided in the present paper. The advantages associated with the use of these stockholder projection operators are examined with respect to covalent bond orders, bond polarization, and transferability.

Communication: A difference density picture for the self-consistent field ansatz.

PubMed

Parrish, Robert M; Liu, Fang; Martínez, Todd J

2016-04-07

We formulate self-consistent field (SCF) theory in terms of an interaction picture where the working variable is the difference density matrix between the true system and a corresponding superposition of atomic densities. As the difference density matrix directly represents the electronic deformations inherent in chemical bonding, this "difference self-consistent field (dSCF)" picture provides a number of significant conceptual and computational advantages. We show that this allows for a stable and efficient dSCF iterative procedure with wholly single-precision Coulomb and exchange matrix builds. We also show that the dSCF iterative procedure can be performed with aggressive screening of the pair space. These approximations are tested and found to be accurate for systems with up to 1860 atoms and >10 000 basis functions, providing for immediate overall speedups of up to 70% in the heavily optimized TeraChem SCF implementation.

Communication: A difference density picture for the self-consistent field ansatz

NASA Astrophysics Data System (ADS)

Parrish, Robert M.; Liu, Fang; Martínez, Todd J.

2016-04-01

We formulate self-consistent field (SCF) theory in terms of an interaction picture where the working variable is the difference density matrix between the true system and a corresponding superposition of atomic densities. As the difference density matrix directly represents the electronic deformations inherent in chemical bonding, this "difference self-consistent field (dSCF)" picture provides a number of significant conceptual and computational advantages. We show that this allows for a stable and efficient dSCF iterative procedure with wholly single-precision Coulomb and exchange matrix builds. We also show that the dSCF iterative procedure can be performed with aggressive screening of the pair space. These approximations are tested and found to be accurate for systems with up to 1860 atoms and >10 000 basis functions, providing for immediate overall speedups of up to 70% in the heavily optimized TeraChem SCF implementation.

Modeling Biophysical and Biological Properties From the Characteristics of the Molecular Electron Density, Electron Localization and Delocalization Matrices, and the Electrostatic Potential

PubMed Central

Matta*, Chérif F

2014-01-01

The electron density and the electrostatic potential are fundamentally related to the molecular hamiltonian, and hence are the ultimate source of all properties in the ground- and excited-states. The advantages of using molecular descriptors derived from these fundamental scalar fields, both accessible from theory and from experiment, in the formulation of quantitative structure-to-activity and structure-to-property relationships, collectively abbreviated as QSAR, are discussed. A few such descriptors encode for a wide variety of properties including, for example, electronic transition energies, pKa's, rates of ester hydrolysis, NMR chemical shifts, DNA dimers binding energies, π-stacking energies, toxicological indices, cytotoxicities, hepatotoxicities, carcinogenicities, partial molar volumes, partition coefficients (log P), hydrogen bond donor capacities, enzyme–substrate complementarities, bioisosterism, and regularities in the genetic code. Electronic fingerprinting from the topological analysis of the electron density is shown to be comparable and possibly superior to Hammett constants and can be used in conjunction with traditional bulk and liposolubility descriptors to accurately predict biological activities. A new class of descriptors obtained from the quantum theory of atoms in molecules' (QTAIM) localization and delocalization indices and bond properties, cast in matrix format, is shown to quantify transferability and molecular similarity meaningfully. Properties such as “interacting quantum atoms (IQA)” energies which are expressible into an interaction matrix of two body terms (and diagonal one body “self” terms, as IQA energies) can be used in the same manner. The proposed QSAR-type studies based on similarity distances derived from such matrix representatives of molecular structure necessitate extensive investigation before their utility is unequivocally established. © 2014 The Author and the Journal of Computational Chemistry Published by Wiley Periodicals, Inc. PMID:24777743

Universality and Thouless energy in the supersymmetric Sachdev-Ye-Kitaev model

NASA Astrophysics Data System (ADS)

García-García, Antonio M.; Jia, Yiyang; Verbaarschot, Jacobus J. M.

2018-05-01

We investigate the supersymmetric Sachdev-Ye-Kitaev (SYK) model, N Majorana fermions with infinite range interactions in 0 +1 dimensions. We have found that, close to the ground state E ≈0 , discrete symmetries alter qualitatively the spectral properties with respect to the non-supersymmetric SYK model. The average spectral density at finite N , which we compute analytically and numerically, grows exponentially with N for E ≈0 . However the chiral condensate, which is normalized with respect the total number of eigenvalues, vanishes in the thermodynamic limit. Slightly above E ≈0 , the spectral density grows exponentially with the energy. Deep in the quantum regime, corresponding to the first O (N ) eigenvalues, the average spectral density is universal and well described by random matrix ensembles with chiral and superconducting discrete symmetries. The dynamics for E ≈0 is investigated by level fluctuations. Also in this case we find excellent agreement with the prediction of chiral and superconducting random matrix ensembles for eigenvalue separations smaller than the Thouless energy, which seems to scale linearly with N . Deviations beyond the Thouless energy, which describes how ergodicity is approached, are universally characterized by a quadratic growth of the number variance. In the time domain, we have found analytically that the spectral form factor g (t ), obtained from the connected two-level correlation function of the unfolded spectrum, decays as 1 /t2 for times shorter but comparable to the Thouless time with g (0 ) related to the coefficient of the quadratic growth of the number variance. Our results provide further support that quantum black holes are ergodic and therefore can be classified by random matrix theory.

Propagation of Circularly Polarized Light Through a Two-Dimensional Random Medium

NASA Astrophysics Data System (ADS)

Gorodnichev, E. E.

2017-12-01

The problem of small-angle multiple-scattering of circularly polarized light in a two-dimensional medium with large fiberlike inhomogeneities is studied. The attenuation lengths for elements the density matrix are calculated. It is found that with increasing the sample thickness the intensity of waves polarized along the fibers decays faster than the other density matrix elements. With further increase in the thickness, the off-diagonal element which is responsible for correlation between the cross-polarized waves dissapears. In the case of very thick samples the scattered field proves to be polarized perpendicular to the fibers. It is shown that the difference in the attenuation lengths of the density matrix elements results in a non-monotonic depth dependence of the degree of polarization.

Highly Flexible and Conductive Cellulose-Mediated PEDOT:PSS/MWCNT Composite Films for Supercapacitor Electrodes.

PubMed

Zhao, Dawei; Zhang, Qi; Chen, Wenshuai; Yi, Xin; Liu, Shouxin; Wang, Qingwen; Liu, Yixing; Li, Jian; Li, Xianfeng; Yu, Haipeng

2017-04-19

Recent improvements in flexible electronics have increased the need to develop flexible and lightweight power sources. However, current flexible electrodes are limited by low capacitance, poor mechanical properties, and lack of cycling stability. In this article, we describe an ionic liquid-processed supramolecular assembly of cellulose and 3,4-ethylenedioxythiophene for the formation of a flexible and conductive cellulose/poly(3,4-ethylenedioxythiophene) PEDOT:poly(styrene sulfonate) (PSS) composite matrix. On this base, multiwalled carbon nanotubes (MWCNTs) were incorporated into the matrix to fabricate an MWCNT-reinforced cellulose/PEDOT:PSS film (MCPP), which exhibited favorable flexibility and conductivity. The MCPP-based electrode displayed comprehensively excellent electrochemical properties, such as a low resistance of 0.45 Ω, a high specific capacitance of 485 F g -1 at 1 A g -1 , and good cycling stability, with a capacity retention of 95% after 2000 cycles at 2 A g -1 . An MCPP-based symmetric solid-state supercapacitor with Ni foam as the current collector and PVA/KOH gel as the electrolyte exhibited a specific capacitance of 380 F g -1 at 0.25 A g -1 and achieved a maximum energy density of 13.2 Wh kg -1 (0.25 A g -1 ) with a power density of 0.126 kW kg -1 or an energy density of 4.86 Wh kg -1 at 10 A g -1 , corresponding to a high power density of 4.99 kW kg -1 . Another kind of MCPP-based solid-state supercapacitor without the Ni foam showed excellent flexibility and a high volumetric capacitance of 50.4 F cm -3 at 0.05 A cm -3 . Both the electrodes and the supercapacitors were environmentally stable and could be operated under remarkable deformation or high temperature without damage to their structural integrity or a significant decrease in capacitive performance. Overall, this work provides a strategy for the fabrication of flexible and conductive energy-storage films with ionic liquid-processed cellulose as a medium.

Absolute empirical rate coefficient for the excitation of the 117.6 nm line in C III

NASA Astrophysics Data System (ADS)

Gardner, L. D.; Daw, A. N.; Janzen, P. H.; Atkins, N.; Kohl, J. L.

2005-05-01

We have measured the absolute cross sections for electron impact excitation (EIE) of C2+ (2s2p 3P° - 2p2 3P) for energies from below threshold to 17 eV above and derived EIE rate coefficients required for astrophysical applications. The uncertainty in the rate coefficient at a typical solar temperature of formation of C2+ is less than ± 6 %. Ions are produced in a 5 GHz Electron Cyclotron Resonance (ECR) ion source, extracted, formed into a beam, and transported to a collision chamber where they collide with electrons from an electron beam inclined at 45 degrees. The beams are modulated and the radiation from the decay of the excited ions at λ 117.6 nm is detected synchronously using an absolutely calibrated optical system that subtends slightly over π steradians. The fractional population of the C2+ metastable state in the incident ion beam has been determined experimentally to be 0.42 ± 0.03 (1.65 σ). At the reported ± 15 % total experimental uncertainty level (1.65 σ), the measured structure and absolute scale of the cross section are in fairly good agreement with 6-term close-coupling R-matrix calculations and 90-term R-matrix with pseudo-states calculations, although some minor differences are seen just above threshold. As density-sensitive line intensity ratios vary by only about a factor of 5 as the density changes by nearly a factor of 100, even a 30 % uncertainty in the excitation rate can lead to a factor of 3 error in density. This work is supported by NASA Supporting Research and Technology grants NAG5- 9516 and NAG5-12863 in Solar and Heliospheric Physics and by the Smithsonian Astrophysical Observatory.

Single-Sided Noinvasive Inspection of Multielement Sample Using Fan-Beam Multiplexed Compton Scatter Tomography

DTIC Science & Technology

2000-05-01

a vector , ρ "# represents the set of voxel densities sorted into a vector , and ( )A ρ $# "# represents a 8 mapping of the voxel densities to...density vector in equation (4) suggests that solving for ρ "# by direct inversion is not possible, calling for an iterative technique beginning with...the vector of measured spectra, and D is the diagonal matrix of the inverse of the variances. The diagonal matrix provides weighting terms, which

Communication: spin-boson model with diagonal and off-diagonal coupling to two independent baths: ground-state phase transition in the deep sub-Ohmic regime.

PubMed

Zhao, Yang; Yao, Yao; Chernyak, Vladimir; Zhao, Yang

2014-04-28

We investigate a spin-boson model with two boson baths that are coupled to two perpendicular components of the spin by employing the density matrix renormalization group method with an optimized boson basis. It is revealed that in the deep sub-Ohmic regime there exists a novel second-order phase transition between two types of doubly degenerate states, which is reduced to one of the usual types for nonzero tunneling. In addition, it is found that expectation values of the spin components display jumps at the phase boundary in the absence of bias and tunneling.

Light-matter interaction in doped microcavities

NASA Astrophysics Data System (ADS)

Averkiev, N. S.; Glazov, M. M.

2007-07-01

We discuss theoretically the light-matter coupling in a microcavity containing a quantum well with a two-dimensional electron gas. The high density limit where the bound exciton states are absent is considered. The matrix element of an interband optical absorption demonstrates the Mahan singularity [Phys. Rev. B153, 882 (1967); 163, 612 (1967)] due to strong Coulomb effect between the electrons and a photocreated hole. We extend the nonlocal dielectric response theory to calculate the quantum well reflection and transmission coefficients as well as the microcavity transmission spectra. The new eigenmodes of the system are discussed. Their implications for the steady state and time-resolved spectroscopy experiments are analyzed.

Laser-assisted photothermal imprinting of nanocomposite

NASA Astrophysics Data System (ADS)

Lu, Y.; Shao, D. B.; Chen, S. C.

2004-08-01

We report on a laser-assisted photothermal imprinting method for directly patterning carbon nanofiber-reinforced polyethylene nanocomposite. A single laser pulse from a solid state Nd :YAG laser (10ns pluse, 532 and 355nm wavelengths) is used to melt/soften a thin skin layer of the polymer nanocomposite. Meanwhile, a fused quartz mold with micro sized surface relief structures is pressed against the surface of the composite. Successful pattern transfer is realized upon releasing the quartz mold. Although polyethylene is transparent to the laser beam, the carbon nanofibers in the high density polyethylene (HDPE) matrix absorb the laser energy and convert it into heat. Numerical heat conduction simulation shows the HDPE matrix is partially melted or softened, allowing for easier imprinting of the relief pattern of the quartz mold.

Estimating Density and Temperature Dependence of Juvenile Vital Rates Using a Hidden Markov Model

PubMed Central

McElderry, Robert M.

2017-01-01

Organisms in the wild have cryptic life stages that are sensitive to changing environmental conditions and can be difficult to survey. In this study, I used mark-recapture methods to repeatedly survey Anaea aidea (Nymphalidae) caterpillars in nature, then modeled caterpillar demography as a hidden Markov process to assess if temporal variability in temperature and density influence the survival and growth of A. aidea over time. Individual encounter histories result from the joint likelihood of being alive and observed in a particular stage, and I have included hidden states by separating demography and observations into parallel and independent processes. I constructed a demographic matrix containing the probabilities of all possible fates for each stage, including hidden states, e.g., eggs and pupae. I observed both dead and live caterpillars with high probability. Peak caterpillar abundance attracted multiple predators, and survival of fifth instars declined as per capita predation rate increased through spring. A time lag between predator and prey abundance was likely the cause of improved fifth instar survival estimated at high density. Growth rates showed an increase with temperature, but the preferred model did not include temperature. This work illustrates how state-space models can include unobservable stages and hidden state processes to evaluate how environmental factors influence vital rates of cryptic life stages in the wild. PMID:28505138

Matrix density alters zyxin phosphorylation, which limits peripheral process formation and extension in endothelial cells invading 3D collagen matrices.

PubMed

Abbey, Colette A; Bayless, Kayla J

2014-09-01

This study was designed to determine the optimal conditions required for known pro-angiogenic stimuli to elicit successful endothelial sprouting responses. We used an established, quantifiable model of endothelial cell (EC) sprout initiation where ECs were tested for invasion in low (1 mg/mL) and high density (5 mg/mL) 3D collagen matrices. Sphingosine 1-phosphate (S1P) alone, or S1P combined with stromal derived factor-1α (SDF) and phorbol ester (TPA), elicited robust sprouting responses. The ability of these factors to stimulate sprouting was more effective in higher density collagen matrices. S1P stimulation resulted in a significant increase in invasion distance, and with the exception of treatment groups containing phorbol ester, invasion distance was longer in 1mg/mL compared to 5mg/mL collagen matrices. Closer examination of cell morphology revealed that increasing matrix density and supplementing with SDF and TPA enhanced the formation of multicellular structures more closely resembling capillaries. TPA enhanced the frequency and size of lumen formation and correlated with a robust increase in phosphorylation of p42/p44 Erk kinase, while S1P and SDF did not. Also, a higher number of significantly longer extended processes formed in 5mg/mL compared to 1mg/mL collagen matrices. Because collagen matrices at higher density have been reported to be stiffer, we tested for changes in the mechanosensitive protein, zyxin. Interestingly, zyxin phosphorylation levels inversely correlated with matrix density, while levels of total zyxin did not change significantly. Immunofluorescence and localization studies revealed that total zyxin was distributed evenly throughout invading structures, while phosphorylated zyxin was slightly more intense in extended peripheral processes. Silencing zyxin expression increased extended process length and number of processes, while increasing zyxin levels decreased extended process length. Altogether these data indicate that ECs integrate signals from multiple exogenous factors, including changes in matrix density, to accomplish successful sprouting responses. We show here for the first time that zyxin limited the formation and extension of fine peripheral processes used by ECs for matrix interrogation, providing a molecular explanation for altered EC responses to high and low density collagen matrices. Copyright © 2014 International Society of Matrix Biology. Published by Elsevier B.V. All rights reserved.

Simple model for molecular scattering

NASA Astrophysics Data System (ADS)

Mehta, Nirav; Ticknor, Christopher; Hazzard, Kaden

2017-04-01

The collisions of ultracold molecules are qualitatively different from the collisions of ultracold atoms due to the high density of bimolecular resonances near the collision energy. We present results from a simple N-channel scattering model with square-well channel potentials and constant channel couplings (inside the well) designed to reproduce essential features of chaotic molecular scattering. The potential depths and channel splittings are tuned to reproduce the appropriate density of states for the short-range bimolecular collision complex (BCC), which affords a direct comparison of the resulting level-spacing distribution to that expected from random matrix theory (RMT), namely the so-called Wigner surmise. The density of states also sets the scale for the rate of dissociation from the BCC to free molecules, as approximated by transition state theory (TST). Our model affords a semi-analytic solution for the scattering amplitude in the open channel, and a determinantal equation for the eigenenergies of the short-ranged BCC. It is likely the simplest finite-ranged scattering model that can be compared to expectations from the approximations of RMT, and TST. The validity of these approximations has implications for the many-channel Hubbard model recently developed. This research was funded in part by the National Science Foundation under Grant No. NSF PHY-1125915.

Demonstration of entanglement of electrostatically coupled singlet-triplet qubits.

PubMed

Shulman, M D; Dial, O E; Harvey, S P; Bluhm, H; Umansky, V; Yacoby, A

2012-04-13

Quantum computers have the potential to solve certain problems faster than classical computers. To exploit their power, it is necessary to perform interqubit operations and generate entangled states. Spin qubits are a promising candidate for implementing a quantum processor because of their potential for scalability and miniaturization. However, their weak interactions with the environment, which lead to their long coherence times, make interqubit operations challenging. We performed a controlled two-qubit operation between singlet-triplet qubits using a dynamically decoupled sequence that maintains the two-qubit coupling while decoupling each qubit from its fluctuating environment. Using state tomography, we measured the full density matrix of the system and determined the concurrence and the fidelity of the generated state, providing proof of entanglement.

On the mixing time in the Wang-Landau algorithm

NASA Astrophysics Data System (ADS)

Fadeeva, Marina; Shchur, Lev

2018-01-01

We present preliminary results of the investigation of the properties of the Markov random walk in the energy space generated by the Wang-Landau probability. We build transition matrix in the energy space (TMES) using the exact density of states for one-dimensional and two-dimensional Ising models. The spectral gap of TMES is inversely proportional to the mixing time of the Markov chain. We estimate numerically the dependence of the mixing time on the lattice size, and extract the mixing exponent.

Role of small-norm components in extended random-phase approximation

NASA Astrophysics Data System (ADS)

Tohyama, Mitsuru

2017-09-01

The role of the small-norm amplitudes in extended random-phase approximation (RPA) theories such as the particle-particle and hole-hole components of one-body amplitudes and the two-body amplitudes other than two-particle/two-hole components are investigated for the one-dimensional Hubbard model using an extended RPA derived from the time-dependent density matrix theory. It is found that these amplitudes cannot be neglected in strongly interacting regions where the effects of ground-state correlations are significant.

Floating matrix tablets based on low density foam powder: effects of formulation and processing parameters on drug release.

PubMed

Streubel, A; Siepmann, J; Bodmeier, R

2003-01-01

The aim of this study was to develop and physicochemically characterize single unit, floating controlled drug delivery systems consisting of (i). polypropylene foam powder, (ii). matrix-forming polymer(s), (iii). drug, and (iv). filler (optional). The highly porous foam powder provided low density and, thus, excellent in vitro floating behavior of the tablets. All foam powder-containing tablets remained floating for at least 8 h in 0.1 N HCl at 37 degrees C. Different types of matrix-forming polymers were studied: hydroxypropyl methylcellulose (HPMC), polyacrylates, sodium alginate, corn starch, carrageenan, gum guar and gum arabic. The tablets eroded upon contact with the release medium, and the relative importance of drug diffusion, polymer swelling and tablet erosion for the resulting release patterns varied significantly with the type of matrix former. The release rate could effectively be modified by varying the "matrix-forming polymer/foam powder" ratio, the initial drug loading, the tablet geometry (radius and height), the type of matrix-forming polymer, the use of polymer blends and the addition of water-soluble or water-insoluble fillers (such as lactose or microcrystalline cellulose). The floating behavior of the low density drug delivery systems could successfully be combined with accurate control of the drug release patterns.

Nonlinear optical microscopy reveals invading endothelial cells anisotropically alter three-dimensional collagen matrices

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lee, P.-F.; Yeh, Alvin T.; Bayless, Kayla J.

The interactions between endothelial cells (ECs) and the extracellular matrix (ECM) are fundamental in mediating various steps of angiogenesis, including cell adhesion, migration and sprout formation. Here, we used a noninvasive and non-destructive nonlinear optical microscopy (NLOM) technique to optically image endothelial sprouting morphogenesis in three-dimensional (3D) collagen matrices. We simultaneously captured signals from collagen fibers and endothelial cells using second harmonic generation (SHG) and two-photon excited fluorescence (TPF), respectively. Dynamic 3D imaging revealed EC interactions with collagen fibers along with quantifiable alterations in collagen matrix density elicited by EC movement through and morphogenesis within the matrix. Specifically, we observedmore » increased collagen density in the area between bifurcation points of sprouting structures and anisotropic increases in collagen density around the perimeter of lumenal structures, but not advancing sprout tips. Proteinase inhibition studies revealed membrane-associated matrix metalloproteinase were utilized for sprout advancement and lumen expansion. Rho-associated kinase (p160ROCK) inhibition demonstrated that the generation of cell tension increased collagen matrix alterations. This study followed sprouting ECs within a 3D matrix and revealed that the advancing structures recognize and significantly alter their extracellular environment at the periphery of lumens as they progress.« less

Improved Dielectric Properties and Energy Storage Density of Poly(vinylidene fluoride-co-hexafluoropropylene) Nanocomposite with Hydantoin Epoxy Resin Coated BaTiO3.

PubMed

Luo, Hang; Zhang, Dou; Jiang, Chao; Yuan, Xi; Chen, Chao; Zhou, Kechao

2015-04-22

Energy storage materials are urgently demanded in modern electric power supply and renewable energy systems. The introduction of inorganic fillers to polymer matrix represents a promising avenue for the development of high energy density storage materials, which combines the high dielectric constant of inorganic fillers with supernal dielectric strength of polymer matrix. However, agglomeration and phase separation of inorganic fillers in the polymer matrix remain the key barriers to promoting the practical applications of the composites for energy storage. Here, we developed a low-cost and environmentally friendly route to modifying BaTiO3 (BT) nanoparticles by a kind of water-soluble hydantoin epoxy resin. The modified BT nanoparticles exhibited homogeneous dispersion in the ferroelectric polymer poly(vinylidene fluoride-co-hexafluoropropylene) (P(VDF-HFP)) matrix and strong interfacial adhesion with the polymer matrix. The dielectric constants of the nanocomposites increased significantly with the increase of the coated BT loading, while the dielectric loss of the nanocomposites was still as low as that of the pure P(VDF-HFP). The energy storage density of the nanocomposites was largely enhanced with the coated BT loading at the same electric field. The nanocomposite with 20 vol % BT exhibited an estimated maximum energy density of 8.13 J cm(-3), which was much higher than that of pure P(VDF-HFP) and other dielectric polymers. The findings of this research could provide a feasible approach to produce high energy density materials for practical application in energy storage.

Derivation of an eigenvalue probability density function relating to the Poincaré disk

NASA Astrophysics Data System (ADS)

Forrester, Peter J.; Krishnapur, Manjunath

2009-09-01

A result of Zyczkowski and Sommers (2000 J. Phys. A: Math. Gen. 33 2045-57) gives the eigenvalue probability density function for the top N × N sub-block of a Haar distributed matrix from U(N + n). In the case n >= N, we rederive this result, starting from knowledge of the distribution of the sub-blocks, introducing the Schur decomposition and integrating over all variables except the eigenvalues. The integration is done by identifying a recursive structure which reduces the dimension. This approach is inspired by an analogous approach which has been recently applied to determine the eigenvalue probability density function for random matrices A-1B, where A and B are random matrices with entries standard complex normals. We relate the eigenvalue distribution of the sub-blocks to a many-body quantum state, and to the one-component plasma, on the pseudosphere.

An efficient method for quantum transport simulations in the time domain

NASA Astrophysics Data System (ADS)

Wang, Y.; Yam, C.-Y.; Frauenheim, Th.; Chen, G. H.; Niehaus, T. A.

2011-11-01

An approximate method based on adiabatic time dependent density functional theory (TDDFT) is presented, that allows for the description of the electron dynamics in nanoscale junctions under arbitrary time dependent external potentials. The density matrix of the device region is propagated according to the Liouville-von Neumann equation. The semi-infinite leads give rise to dissipative terms in the equation of motion which are calculated from first principles in the wide band limit. In contrast to earlier ab initio implementations of this formalism, the Hamiltonian is here approximated in the spirit of the density functional based tight-binding (DFTB) method. Results are presented for two prototypical molecular devices and compared to full TDDFT calculations. The temporal profile of the current traces is qualitatively well captured by the DFTB scheme. Steady state currents show considerable variations, both in comparison of approximate and full TDDFT, but also among TDDFT calculations with different basis sets.

A far-wing line shape theory which satisfies the detailed balance principle

NASA Technical Reports Server (NTRS)

Ma, Q.; Tipping, R. H.; Hartmann, J.-M.; Boulet, C.

1995-01-01

A far-wing theory in which the validity of the detailed balance principle is maintained in each step of the derivation is presented. The role of the total density matrix including the initial correlations is analyzed rigorously. By factoring out the rapidly varying terms in the complex-time development operator in the interaction representation, better approximate expressions can be obtained. As a result, the spectral density can be expressed in terms of the line-coupling functions in which two coupled lines are arranged symmetrically and whose frequency detunings are omega - 1/2(omega(sub ji) + omega (sub j'i'). Using the approximate values omega - omega(sub ji) results in expressions that do not satisfy the detailed balance principle. However, this principle remains satisfied for the symmetrized spectral density in which not only the coupled lines are arranged symmetrically, but also the initial and final states belonging to the same lines are arranged symmetrically as well.

Quantum crystallography: A perspective.

PubMed

Massa, Lou; Matta, Chérif F

2018-06-30

Extraction of the complete quantum mechanics from X-ray scattering data is the ultimate goal of quantum crystallography. This article delivers a perspective for that possibility. It is desirable to have a method for the conversion of X-ray diffraction data into an electron density that reflects the antisymmetry of an N-electron wave function. A formalism for this was developed early on for the determination of a constrained idempotent one-body density matrix. The formalism ensures pure-state N-representability in the single determinant sense. Applications to crystals show that quantum mechanical density matrices of large molecules can be extracted from X-ray scattering data by implementing a fragmentation method termed the kernel energy method (KEM). It is shown how KEM can be used within the context of quantum crystallography to derive quantum mechanical properties of biological molecules (with low data-to-parameters ratio). © 2017 Wiley Periodicals, Inc. © 2017 Wiley Periodicals, Inc.

Tuning three-dimensional collagen matrix stiffness independently of collagen concentration modulates endothelial cell behavior.

PubMed

Mason, Brooke N; Starchenko, Alina; Williams, Rebecca M; Bonassar, Lawrence J; Reinhart-King, Cynthia A

2013-01-01

Numerous studies have described the effects of matrix stiffening on cell behavior using two-dimensional synthetic surfaces; however, less is known about the effects of matrix stiffening on cells embedded in three-dimensional in vivo-like matrices. A primary limitation in investigating the effects of matrix stiffness in three dimensions is the lack of materials that can be tuned to control stiffness independently of matrix density. Here, we use collagen-based scaffolds where the mechanical properties are tuned using non-enzymatic glycation of the collagen in solution, prior to polymerization. Collagen solutions glycated prior to polymerization result in collagen gels with a threefold increase in compressive modulus without significant changes to the collagen architecture. Using these scaffolds, we show that endothelial cell spreading increases with matrix stiffness, as does the number and length of angiogenic sprouts and the overall spheroid outgrowth. Differences in sprout length are maintained even when the receptor for advanced glycation end products is inhibited. Our results demonstrate the ability to de-couple matrix stiffness from matrix density and structure in collagen gels, and that increased matrix stiffness results in increased sprouting and outgrowth. Copyright © 2012 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Dynamics and thermodynamics of linear quantum open systems.

PubMed

Martinez, Esteban A; Paz, Juan Pablo

2013-03-29

We analyze the evolution of the quantum state of networks of quantum oscillators coupled with arbitrary external environments. We show that the reduced density matrix of the network always obeys a local master equation with a simple analytical solution. We use this to study the emergence of thermodynamical laws in the long time regime demonstrating two main results: First, we show that it is impossible to build a quantum absorption refrigerator using linear networks (thus, nonlinearity is an essential resource for such refrigerators recently studied by Levy and Kosloff [Phys. Rev. Lett. 108, 070604 (2012)] and Levy et al. [Phys. Rev. B 85, 061126 (2012)]). Then, we show that the third law imposes constraints on the low frequency behavior of the environmental spectral densities.

Superfluid density of states and pseudogap phenomenon in the BCS-BEC crossover regime of a superfluid Fermi gas

DOE Office of Scientific and Technical Information (OSTI.GOV)

Watanabe, Ryota; Tsuchiya, Shunji; CREST

2010-10-15

We investigate single-particle excitations and strong-coupling effects in the BCS-BEC crossover regime of a superfluid Fermi gas. Including phase and amplitude fluctuations of the superfluid order parameter within a T-matrix theory, we calculate the superfluid density of states (DOS), as well as single-particle spectral weight, over the entire BCS-BEC crossover region below the superfluid transition temperature T{sub c}. We clarify how the pseudogap in the normal state evolves into the superfluid gap, as one passes through T{sub c}. While the pseudogap in DOS continuously evolves into the superfluid gap in the weak-coupling BCS regime, the superfluid gap in the crossovermore » region is shown to appear in DOS after the pseudogap disappears below T{sub c}. In the phase diagram with respect to the temperature and interaction strength, we determine the region where strong pairing fluctuations dominate over single-particle properties of the system. Our results would be useful for the study of strong-coupling phenomena in the BCS-BEC crossover regime of a superfluid Fermi gas.« less

Current reversals and metastable states in the infinite Bose-Hubbard chain with local particle loss

NASA Astrophysics Data System (ADS)

Kiefer-Emmanouilidis, M.; Sirker, J.

2017-12-01

We present an algorithm which combines the quantum trajectory approach to open quantum systems with a density-matrix renormalization-group scheme for infinite one-dimensional lattice systems. We apply this method to investigate the long-time dynamics in the Bose-Hubbard model with local particle loss starting from a Mott-insulating initial state with one boson per site. While the short-time dynamics can be described even quantitatively by an equation of motion (EOM) approach at the mean-field level, many-body interactions lead to unexpected effects at intermediate and long times: local particle currents far away from the dissipative site start to reverse direction ultimately leading to a metastable state with a total particle current pointing away from the lossy site. An alternative EOM approach based on an effective fermion model shows that the reversal of currents can be understood qualitatively by the creation of holon-doublon pairs at the edge of the region of reduced particle density. The doublons are then able to escape while the holes move towards the dissipative site, a process reminiscent—in a loose sense—of Hawking radiation.

Construction of CASCI-type wave functions for very large active spaces.

PubMed

Boguslawski, Katharina; Marti, Konrad H; Reiher, Markus

2011-06-14

We present a procedure to construct a configuration-interaction expansion containing arbitrary excitations from an underlying full-configuration-interaction-type wave function defined for a very large active space. Our procedure is based on the density-matrix renormalization group (DMRG) algorithm that provides the necessary information in terms of the eigenstates of the reduced density matrices to calculate the coefficient of any basis state in the many-particle Hilbert space. Since the dimension of the Hilbert space scales binomially with the size of the active space, a sophisticated Monte Carlo sampling routine is employed. This sampling algorithm can also construct such configuration-interaction-type wave functions from any other type of tensor network states. The configuration-interaction information obtained serves several purposes. It yields a qualitatively correct description of the molecule's electronic structure, it allows us to analyze DMRG wave functions converged for the same molecular system but with different parameter sets (e.g., different numbers of active-system (block) states), and it can be considered a balanced reference for the application of a subsequent standard multi-reference configuration-interaction method.

Generalized Gibbs state with modified Redfield solution: Exact agreement up to second order

DOE Office of Scientific and Technical Information (OSTI.GOV)

Thingna, Juzar; Wang, Jian-Sheng; Haenggi, Peter

A novel scheme for the steady state solution of the standard Redfield quantum master equation is developed which yields agreement with the exact result for the corresponding reduced density matrix up to second order in the system-bath coupling strength. We achieve this objective by use of an analytic continuation of the off-diagonal matrix elements of the Redfield solution towards its diagonal limit. Notably, our scheme does not require the provision of yet higher order relaxation tensors. Testing this modified method for a heat bath consisting of a collection of harmonic oscillators we assess that the system relaxes towards its correctmore » coupling-dependent, generalized quantum Gibbs state in second order. We numerically compare our formulation for a damped quantum harmonic system with the nonequilibrium Green's function formalism: we find good agreement at low temperatures for coupling strengths that are even larger than expected from the very regime of validity of the second-order Redfield quantum master equation. Yet another advantage of our method is that it markedly reduces the numerical complexity of the problem; thus, allowing to study efficiently large-sized system Hilbert spaces.« less

Effects of the U boson on the inner edge of neutron star crusts

NASA Astrophysics Data System (ADS)

Zheng, Hao; Chen, Lie-Wen

2012-02-01

We explore effects of the light vector U boson, which is weakly coupled to nucleons, on the transition density ρt and pressure Pt at the inner edge separating the liquid core from the solid crust of neutron stars. Three methods, i.e., the thermodynamical approach, the curvature matrix approach, and the Vlasov equation approach, are used to determine the transition density ρt with the Skyrme effective nucleon-nucleon interactions. We find that the ρt and Pt depend on not only the ratio of coupling strength to mass squared of the U boson g2/μ2 but also its mass μ due to the finite-range interaction from the U-boson exchange. In particular, our results indicate that the ρt and Pt are sensitive to both g2/μ2 and μ if the U-boson mass μ is larger than about 2 MeV. Furthermore, we show that both g2/μ2 and μ can have significant influence on the mass-radius relation and the crustal fraction of total moment of inertia of neutron stars. In addition, we study the exchange term contribution of the U boson based on the density matrix expansion method, and demonstrate that the exchange term effects on the nuclear matter equation of state as well as the ρt and Pt are generally negligible.

Dynamics anomaly in high-density amorphous ice between 0.7 and 1.1 GPa

NASA Astrophysics Data System (ADS)

Handle, Philip H.; Loerting, Thomas

2016-02-01

We studied high-density amorphous ices between 0.004 and 1.6 GPa by isobaric in situ volumetry and by subsequent ex situ x-ray diffraction and differential scanning calorimetry at 1 bar. Our observations indicate two processes, namely, relaxation in the amorphous matrix and crystallization, taking place at well-separated time scales. For this reason, we are able to report rate constants of crystallization kX and glass-transition temperatures Tg in an unprecedented pressure range. Tg's agree within ±3 K with earlier work in the small pressure range where there is overlap. Both Tg and kX show a pressure anomaly between 0.7 and 1.1 GPa, namely, a kX minimum and a Tg maximum. This anomalous pressure dependence suggests a continuous phase transition from high- (HDA) to very-high-density amorphous ice (VHDA) and faster hydrogen bond dynamics in VHDA. We speculate this phenomenology can be rationalized by invoking the crossing of a Widom line between 0.7 and 1.1 GPa emanating from a low-lying HDA-VHDA critical point. Furthermore, we interpret the volumetric relaxation of the amorphous matrix to be accompanied by viscosity change to explain the findings such that the liquid state can be accessed prior to the crystallization temperature TX at <0.4 GPa and >0.8 GPa.

Variational second order density matrix study of F3-: importance of subspace constraints for size-consistency.

PubMed

van Aggelen, Helen; Verstichel, Brecht; Bultinck, Patrick; Van Neck, Dimitri; Ayers, Paul W; Cooper, David L

2011-02-07

Variational second order density matrix theory under "two-positivity" constraints tends to dissociate molecules into unphysical fractionally charged products with too low energies. We aim to construct a qualitatively correct potential energy surface for F(3)(-) by applying subspace energy constraints on mono- and diatomic subspaces of the molecular basis space. Monoatomic subspace constraints do not guarantee correct dissociation: the constraints are thus geometry dependent. Furthermore, the number of subspace constraints needed for correct dissociation does not grow linearly with the number of atoms. The subspace constraints do impose correct chemical properties in the dissociation limit and size-consistency, but the structure of the resulting second order density matrix method does not exactly correspond to a system of noninteracting units.

Confinement of anomalous liquids in nanoporous matrices.

PubMed

Strekalova, Elena G; Luo, Jiayuan; Stanley, H Eugene; Franzese, Giancarlo; Buldyrev, Sergey V

2012-09-07

Using molecular dynamics simulations, we investigate the effects of different nanoconfinements on complex liquids-e.g., colloids or protein solutions-with density anomalies and a liquid-liquid phase transition (LLPT). In all the confinements, we find a strong depletion effect with a large increase in liquid density near the confining surface. If the nanoconfinement is modeled by an ordered matrix of nanoparticles, we find that the anomalies are preserved. On the contrary, if the confinement is modeled by a disordered matrix of nanoparticles, we find a drastically different phase diagram: the LLPT shifts to lower pressures and temperatures, and the anomalies become weaker, as the disorder increases. We find that the density heterogeneities induced by the disordered matrix are responsible for the weakening of the LLPT and the disappearance of the anomalies.

Quantum Effects at a Proton Relaxation at Low Temperatures

NASA Astrophysics Data System (ADS)

Kalytka, V. A.; Korovkin, M. V.

2016-11-01

Quantum effects during migratory polarization in multi-well crystals (including multi-well silicates and crystalline hydrates) are investigated in a variable electric field at low temperatures by direct quantum-mechanical calculations. Based on analytical solution of the quantum Liouville kinetic equation in the linear approximation for the polarizing field, the non-stationary density matrix is calculated for an ensemble of non-interacting protons moving in the field of one-dimensional multi-well crystal potential relief of rectangular shape. An expression for the complex dielectric constant convenient for a comparison with experiment and calculation of relaxer parameters is derived using the nonequilibrium polarization density matrix. The density matrix apparatus can be used for analytical investigation of the quantum mechanism of spontaneous polarization of a ferroelectric material (KDP and DKDP).

Quantum non-Abelian hydrodynamics: Anyonic or spin-orbital entangled liquids, nonunitarity of scattering matrix and charge fractionalization

NASA Astrophysics Data System (ADS)

Pareek, Tribhuvan Prasad

2015-09-01

In this article, we develop an exact (nonadiabatic, nonperturbative) density matrix scattering theory for a two component quantum liquid which interacts or scatters off from a generic spin-dependent quantum potential. The generic spin dependent quantum potential [Eq. (1)] is a matrix potential, hence, adiabaticity criterion is ill-defined. Therefore the full matrix potential should be treated nonadiabatically. We succeed in doing so using the notion of vectorial matrices which allows us to obtain an exact analytical expression for the scattered density matrix (SDM), ϱsc [Eq. (30)]. We find that the number or charge density in scattered fluid, Tr(ϱsc), expressions in Eqs. (32) depends on nontrivial quantum interference coefficients, Qα β 0ijk, which arises due to quantum interference between spin-independent and spin-dependent scattering amplitudes and among spin-dependent scattering amplitudes. Further it is shown that Tr(ϱsc) can be expressed in a compact form [Eq. (39)] where the effect of quantum interference coefficients can be included using a vector Qαβ, which allows us to define a vector order parameterQ. Since the number density is obtained using an exact scattered density matrix, therefore, we do not need to prove that Q is non-zero. However, for sake of completeness, we make detailed mathematical analysis for the conditions under which the vector order parameterQ would be zero or nonzero. We find that in presence of spin-dependent interaction the vector order parameterQ is necessarily nonzero and is related to the commutator and anti-commutator of scattering matrix S with its dagger S† [Eq. (78)]. It is further shown that Q≠0, implies four physically equivalent conditions,i.e., spin-orbital entanglement is nonzero, non-Abelian scattering phase, i.e., matrices, scattering matrix is nonunitary and the broken time reversal symmetry for SDM. This also implies that quasi particle excitation are anyonic in nature, hence, charge fractionalization is a natural consequence. This aspect has also been discussed from the perspective of number or charge density conservation, which implies i.e., Tr(ϱ} sc) = Tr(ϱin). On the other hand Q = 0 turns out to be a mathematically forced unphysical solution in presence of spin-dependent potential or scattering which is equivalent to Abelian hydrodynamics, unitary scattering matrix, absence of spin-space entanglement and preserved time reversal symmetry. We have formulated the theory using mesoscopic language, specifically, we have considered two terminal systems connected to spin-dependent scattering region, which is equivalent to having two potential wells separated by a generic spin-dependent potential barrier. The formulation using mesoscopic language is practically useful because it leads directly to the measured quantities such as conductance and spin-polarization density in the leads, however, the presented formulation is not limited to the mesoscopic system only, its generality has been stressed at various places in this article.

Generation of Stationary Non-Gaussian Time Histories with a Specified Cross-spectral Density

DOE PAGES

Smallwood, David O.

1997-01-01

The paper reviews several methods for the generation of stationary realizations of sampled time histories with non-Gaussian distributions and introduces a new method which can be used to control the cross-spectral density matrix and the probability density functions (pdfs) of the multiple input problem. Discussed first are two methods for the specialized case of matching the auto (power) spectrum, the skewness, and kurtosis using generalized shot noise and using polynomial functions. It is then shown that the skewness and kurtosis can also be controlled by the phase of a complex frequency domain description of the random process. The general casemore » of matching a target probability density function using a zero memory nonlinear (ZMNL) function is then covered. Next methods for generating vectors of random variables with a specified covariance matrix for a class of spherically invariant random vectors (SIRV) are discussed. Finally the general case of matching the cross-spectral density matrix of a vector of inputs with non-Gaussian marginal distributions is presented.« less

Floquet Engineering in Quantum Chains

NASA Astrophysics Data System (ADS)

Kennes, D. M.; de la Torre, A.; Ron, A.; Hsieh, D.; Millis, A. J.

2018-03-01

We consider a one-dimensional interacting spinless fermion model, which displays the well-known Luttinger liquid (LL) to charge density wave (CDW) transition as a function of the ratio between the strength of the interaction U and the hopping J . We subject this system to a spatially uniform drive which is ramped up over a finite time interval and becomes time periodic in the long-time limit. We show that by using a density matrix renormalization group approach formulated for infinite system sizes, we can access the large-time limit even when the drive induces finite heating. When both the initial and long-time states are in the gapless (LL) phase, the final state has power-law correlations for all ramp speeds. However, when the initial and final state are gapped (CDW phase), we find a pseudothermal state with an effective temperature that depends on the ramp rate, both for the Magnus regime in which the drive frequency is very large compared to other scales in the system and in the opposite limit where the drive frequency is less than the gap. Remarkably, quantum defects (instantons) appear when the drive tunes the system through the quantum critical point, in a realization of the Kibble-Zurek mechanism.

Enhanced osteoprogenitor elongated collagen fiber matrix formation by bioactive glass ionic silicon dependent on Sp7 (osterix) transcription.

PubMed

Varanasi, Venu G; Odatsu, Tetsurou; Bishop, Timothy; Chang, Joyce; Owyoung, Jeremy; Loomer, Peter M

2016-10-01

Bioactive glasses release ions, those enhance osteoblast collagen matrix synthesis and osteogenic marker expression during bone healing. Collagen matrix density and osteogenic marker expression depend on osteogenic transcription factors, (e.g., Osterix (OSX)). We hypothesize that enhanced expression and formation of collagen by Si(4+) depends on enhanced expression of OSX transcription. Experimental bioactive glass (6P53-b) and commercial Bioglass(TM) (45S5) were dissolved in basal medium to make glass conditioned medium (GCM). ICP-MS analysis was used to measure bioactive glass ion release rates. MC3T3-E1 cells were cultured for 20 days, and gene expression and extracellular matrix collagen formation was analyzed. In a separate study, siRNA was used to determine the effect of OSX knockdown on impacting the effect of Si(4+) on osteogenic markers and matrix collagen formation. Each bioactive glass exhibited similar ion release rates for all ions, except Mg(2+) released by 6P53-b. Gene expression results showed that GCM markedly enhanced many osteogenic markers, and 45S5 GCM showed higher levels of expression and collagen matrix fiber bundle density than 6P53-b GCM. Upon knockdown of OSX transcription, collagen type 5, alkaline phosphatase, and matrix density were not enhanced as compared to wild type cells. This study illustrates that the enhancement of elongated collagen fiber matrix formation by Si(±) depends on OSX transcription. © 2016 Wiley Periodicals, Inc. J Biomed Mater Res Part A: 104A: 2604-2615, 2016. © 2016 Wiley Periodicals, Inc.

Effect of flaw size and temperature on the matrix cracking behavior of a brittle ceramic matrix composite

DOE Office of Scientific and Technical Information (OSTI.GOV)

Anandakumar, U.; Webb, J.E.; Singh, R.N.

The matrix cracking behavior of a zircon matrix - uniaxial SCS 6 fiber composite was studied as a function of initial flaw size and temperature. The composites were fabricated by a tape casting and hot pressing technique. Surface flaws of controlled size were introduced using a vicker`s indenter. The composite samples were tested in three point flexure at three different temperatures to study the non steady state and steady state matrix cracking behavior. The composite samples exhibited steady state and non steady matrix cracking behavior at all temperatures. The steady state matrix cracking stress and steady state crack size increasedmore » with increasing temperature. The results of the study correlated well with the results predicted by the matrix cracking models.« less

Exchange-correlation approximations for reduced-density-matrix-functional theory at finite temperature: Capturing magnetic phase transitions in the homogeneous electron gas

DOE Office of Scientific and Technical Information (OSTI.GOV)

Baldsiefen, Tim; Cangi, Attila; Eich, F. G.

Here, we derive an intrinsically temperature-dependent approximation to the correlation grand potential for many-electron systems in thermodynamical equilibrium in the context of finite-temperature reduced-density-matrix-functional theory (FT-RDMFT). We demonstrate its accuracy by calculating the magnetic phase diagram of the homogeneous electron gas. We compare it to known limits from highly accurate quantum Monte Carlo calculations as well as to phase diagrams obtained within existing exchange-correlation approximations from density functional theory and zero-temperature RDMFT.

Exchange-correlation approximations for reduced-density-matrix-functional theory at finite temperature: Capturing magnetic phase transitions in the homogeneous electron gas

DOE PAGES

Baldsiefen, Tim; Cangi, Attila; Eich, F. G.; ...

2017-12-18

Here, we derive an intrinsically temperature-dependent approximation to the correlation grand potential for many-electron systems in thermodynamical equilibrium in the context of finite-temperature reduced-density-matrix-functional theory (FT-RDMFT). We demonstrate its accuracy by calculating the magnetic phase diagram of the homogeneous electron gas. We compare it to known limits from highly accurate quantum Monte Carlo calculations as well as to phase diagrams obtained within existing exchange-correlation approximations from density functional theory and zero-temperature RDMFT.

Spectral function from Reduced Density Matrix Functional Theory

NASA Astrophysics Data System (ADS)

Romaniello, Pina; di Sabatino, Stefano; Berger, Jan A.; Reining, Lucia

2015-03-01

In this work we focus on the calculation of the spectral function, which determines, for example, photoemission spectra, from reduced density matrix functional theory. Starting from its definition in terms of the one-body Green's function we derive an expression for the spectral function that depends on the natural occupation numbers and on an effective energy which accounts for all the charged excitations. This effective energy depends on the two-body as well as higher-order density matrices. Various approximations to this expression are explored by using the exactly solvable Hubbard chains.

Simple derivation of the Lindblad equation

NASA Astrophysics Data System (ADS)

Pearle, Philip

2012-07-01

The Lindblad equation is an evolution equation for the density matrix in quantum theory. It is the general linear, Markovian, form which ensures that the density matrix is Hermitian, trace 1, positive and completely positive. Some elementary examples of the Lindblad equation are given. The derivation of the Lindblad equation presented here is ‘simple’ in that all it uses is the expression of a Hermitian matrix in terms of its orthonormal eigenvectors and real eigenvalues. Thus, it is appropriate for students who have learned the algebra of quantum theory. Where helpful, arguments are first given in a two-dimensional Hilbert space.

Cross-linked κ-carrageenan polymer/zinc nanoporous composite matrix for expanded bed application: Fabrication and hydrodynamic characterization.

PubMed

Mohsenkhani, Sadaf; Jahanshahi, Mohsen; Rahimpour, Ahmad

2015-08-21

Expanded bed adsorption (EBA) is a reliable separation technique for the purification of bioproducts from complex feedstocks. The specifically designed adsorbent is necessary to form a stable expanded bed. In the present work, a novel custom-designed composite matrix has been prepared through the method of water-in-oil emulsification. In order to develop an adsorbent with desirable qualities and reduce the costs, κ-carrageenan and zinc powder were used as the polymeric skeleton and the densifier, respectively. The prepared composite matrix was named as KC-Zn. Optical microscope (OM) and scanning electron microscope (SEM) were applied to characterize the morphology and structure of prepared composite matrix. These analyses approved good spherical shape and porous structure with nano-scale pores in the range of about 60-180nm. The results from the particle size analyzer (PSA) revealed that all the KC-Zn beads followed logarithmic normal size distribution with the range of 50-350μm and average diameter of 160-230μm, respectively. Main physical properties of KC-Zn matrices were measured as a function of zinc powder ratio to κ-carrageenan slurry, which showed an appropriate wet density in the range of 1.39-2.27g/ml, water content of 72.67-36.41% and porosity of 98.07-80.24%, respectively. The effects of matrix density and liquid phase viscosity on hydrodynamic behavior of prepared matrix have been investigated by residence time distribution (RTD) experiments in an expanded bed. The results indicated that in a constant liquid velocity as the matrix density was increased, the expansion factor of bed decreased and the axial mixing coefficient increased. Moreover, an enhancement in the fluid viscosity led to an increase in the bed expansion and a decrease in the stability of expanded bed. Therefore using a matrix with higher density seems necessary to face viscous feedstocks. All the results demonstrated that proper physical properties and hydrodynamic characteristics of KC-Zn matrix confirm good potential for possible use in high flow rate expanded bed operations. Copyright © 2015 Elsevier B.V. All rights reserved.

Detection of density dependence requires density manipulations and calculation of lambda.

PubMed

Fowler, N L; Overath, R Deborah; Pease, Craig M

2006-03-01

To investigate density-dependent population regulation in the perennial bunchgrass Bouteloua rigidiseta, we experimentally manipulated density by removing adults or adding seeds to replicate quadrats in a natural population for three annual intervals. We monitored the adjacent control quadrats for 14 annual intervals. We constructed a population projection matrix for each quadrat in each interval, calculated lambda, and did a life table response experiment (LTRE) analysis. We tested the effects of density upon lambda by comparing experimental and control quadrats, and by an analysis of the 15-year observational data set. As measured by effects on lambda and on N(t+1/Nt in the experimental treatments, negative density dependence was strong: the population was being effectively regulated. The relative contributions of different matrix elements to treatment effect on lambda differed among years and treatments; overall the pattern was one of small contributions by many different life cycle stages. In contrast, density dependence could not be detected using only the observational (control quadrats) data, even though this data set covered a much longer time span. Nor did experimental effects on separate matrix elements reach statistical significance. These results suggest that ecologists may fail to detect density dependence when it is present if they have only descriptive, not experimental, data, do not have data for the entire life cycle, or analyze life cycle components separately.

Sufficient and necessary condition of separability for generalized Werner states

DOE Office of Scientific and Technical Information (OSTI.GOV)

Deng Dongling; Chen Jingling

2009-02-15

In a celebrated paper [Optics Communications 179, 447, 2000], A.O. Pittenger and M.H. Rubin presented for the first time a sufficient and necessary condition of separability for the generalized Werner states. Inspired by their ideas, we generalized their method to a more general case. We obtain a sufficient and necessary condition for the separability of a specific class of N d-dimensional system (qudits) states, namely special generalized Werner state (SGWS): W{sup [d{sup N}]}(v)=(1-v)(I{sup (N)})/(d{sup N}) +v|{psi}{sub d}{sup N}><{psi}{sub d}{sup N}|, where |{psi}{sub d}{sup N}>={sigma}{sub i=0}{sup d-1}{alpha}{sub i}|i...i> is an entangled pure state of N qudits system and {alpha}{sub i} satisfiesmore » two restrictions: (i) {sigma}{sub i=0}{sup d-1}{alpha}{sub i}{alpha}{sub i}*=1; (ii) Matrix 1/d (I{sup (1)}+T{sigma}{sub i{ne}}{sub j}{alpha}{sub i}|i>

Long-range correction for tight-binding TD-DFT

DOE Office of Scientific and Technical Information (OSTI.GOV)

Humeniuk, Alexander; Mitrić, Roland, E-mail: roland.mitric@uni-wuerzburg.de

2015-10-07

We present two improvements to the tight-binding approximation of time-dependent density functional theory (TD-DFTB): First, we add an exact Hartree-Fock exchange term, which is switched on at large distances, to the ground state Hamiltonian and similarly to the coupling matrix that enters the linear response equations for the calculation of excited electronic states. We show that the excitation energies of charge transfer states are improved relative to the standard approach without the long-range correction by testing the method on a set of molecules from the database in Peach et al. [J. Chem. Phys. 128, 044118 (2008)] which are known tomore » exhibit problematic charge transfer states. The degree of spatial overlap between occupied and virtual orbitals indicates where TD-DFTB and long-range corrected TD-DFTB (lc-TD-DFTB) can be expected to produce large errors. Second, we improve the calculation of oscillator strengths. The transition dipoles are obtained from Slater Koster files for the dipole matrix elements between valence orbitals. In particular, excitations localized on a single atom, which appear dark when using Mulliken transition charges, acquire a more realistic oscillator strength in this way. These extensions pave the way for using lc-TD-DFTB to describe the electronic structure of large chromophoric polymers, where uncorrected TD-DFTB fails to describe the high degree of conjugation and produces spurious low-lying charge transfer states.« less

Effects of autoionising states on the single and double ionisation yields of neon with soft X-ray fields. JMO Series: Attosecond and Strong Field Science

NASA Astrophysics Data System (ADS)

Middleton, D. P. W.; Nikolopoulos, L. A. A.

2012-11-01

In this work, single and double ionisation yields of neon under extreme ultraviolet free-electron laser (FEL) radiation tuned in the vicinity of the autoionising states (AIS) of Ne+ were studied. Density matrix equations were developed and were used to calculate the dependence of the branching ratios of singly and doubly ionised neon on the field intensity and its duration. In addition, in response to a recent experiment [M. Martins et al., Phys. Rev. A 2011, 80, 023411], a quantitative analysis was undertaken in order to reproduce the magnitude of the branching ratios by varying the FEL photon frequency in the range 41.0-42.0 eV in accordance with the experimental report. While the reported variations of the species' branching ratios as a function of the FEL field's photon energy were found, their magnitude and shape differ. In general, the branching ratios are found to be heavily dependent on the given combination of the peak intensity and the pulse duration. Furthermore, the FEL's stochastic fluctuation has been modelled by solving the average density matrix equations and it was found that stochastic effects should also affect branching ratios, mainly due to the increase in the effective bandwidth of the pulse in comparison with the AIS's decay ionisation width. Our calculations suggest that field fluctuations generally diminish the resonance features of the branching ratios.

Atomically thin layers of B-N-C-O with tunable composition.

PubMed

Ozturk, Birol; de-Luna-Bugallo, Andres; Panaitescu, Eugen; Chiaramonti, Ann N; Liu, Fangze; Vargas, Anthony; Jiang, Xueping; Kharche, Neerav; Yavuzcetin, Ozgur; Alnaji, Majed; Ford, Matthew J; Lok, Jay; Zhao, Yongyi; King, Nicholas; Dhar, Nibir K; Dubey, Madan; Nayak, Saroj K; Sridhar, Srinivas; Kar, Swastik

2015-07-01

In recent times, atomically thin alloys of boron, nitrogen, and carbon have generated significant excitement as a composition-tunable two-dimensional (2D) material that demonstrates rich physics as well as application potentials. The possibility of tunably incorporating oxygen, a group VI element, into the honeycomb sp(2)-type 2D-BNC lattice is an intriguing idea from both fundamental and applied perspectives. We present the first report on an atomically thin quaternary alloy of boron, nitrogen, carbon, and oxygen (2D-BNCO). Our experiments suggest, and density functional theory (DFT) calculations corroborate, stable configurations of a honeycomb 2D-BNCO lattice. We observe micrometer-scale 2D-BNCO domains within a graphene-rich 2D-BNC matrix, and are able to control the area coverage and relative composition of these domains by varying the oxygen content in the growth setup. Macroscopic samples comprising 2D-BNCO domains in a graphene-rich 2D-BNC matrix show graphene-like gate-modulated electronic transport with mobility exceeding 500 cm(2) V(-1) s(-1), and Arrhenius-like activated temperature dependence. Spin-polarized DFT calculations for nanoscale 2D-BNCO patches predict magnetic ground states originating from the B atoms closest to the O atoms and sizable (0.6 eV < E g < 0.8 eV) band gaps in their density of states. These results suggest that 2D-BNCO with novel electronic and magnetic properties have great potential for nanoelectronics and spintronic applications in an atomically thin platform.

Comment on "Nonuniqueness of algebraic first-order density-matrix functionals"

NASA Astrophysics Data System (ADS)

Gritsenko, O. V.

2018-02-01

Wang and Knowles (WK) [Phys. Rev. A 92, 012520 (2015), 10.1103/PhysRevA.92.012520] have given a counterexample to the conventional in reduced density-matrix functional theory representation of the second-order reduced density matrix (2RDM) Γi j ,k l in the basis of the natural orbitals as a function Γi j ,k l(n ) of the orbital occupation numbers (ONs) ni. The observed nonuniqueness of Γi j ,k l for prototype systems of different symmetry has been interpreted as the inherent inability of ON functions to reproduce the 2RDM, due to the insufficient information contained in the 1RDM spectrum. In this Comment, it is argued that, rather than totally invalidating Γi j ,k l(n ) , the WK example exposes its symmetry dependence which, as well as the previously established analogous dependence in density functional theory, is demonstrated with a general formulation based on the Levy constrained search.

Thermodynamic properties of water in confined environments: a Monte Carlo study

NASA Astrophysics Data System (ADS)

Gladovic, Martin; Bren, Urban; Urbic, Tomaž

2018-05-01

Monte Carlo simulations of Mercedes-Benz water in a crowded environment were performed. The simulated systems are representative of both composite, porous or sintered materials and living cells with typical matrix packings. We studied the influence of overall temperature as well as the density and size of matrix particles on water density, particle distributions, hydrogen bond formation and thermodynamic quantities. Interestingly, temperature and space occupancy of matrix exhibit a similar effect on water properties following the competition between the kinetic and the potential energy of the system, whereby temperature increases the kinetic and matrix packing decreases the potential contribution. A novel thermodynamic decomposition approach was applied to gain insight into individual contributions of different types of inter-particle interactions. This decomposition proved to be useful and in good agreement with the total thermodynamic quantities especially at higher temperatures and matrix packings, where higher-order potential-energy mixing terms lose their importance.

Quantifying matrix product state

NASA Astrophysics Data System (ADS)

Bhatia, Amandeep Singh; Kumar, Ajay

2018-03-01

Motivated by the concept of quantum finite-state machines, we have investigated their relation with matrix product state of quantum spin systems. Matrix product states play a crucial role in the context of quantum information processing and are considered as a valuable asset for quantum information and communication purpose. It is an effective way to represent states of entangled systems. In this paper, we have designed quantum finite-state machines of one-dimensional matrix product state representations for quantum spin systems.

Application of Semi-Definite Programming for Many-Fermion Systems

NASA Astrophysics Data System (ADS)

Zhao, Zhengji; Braams, Bastiaan; Fukuda, Mituhiro; Overton, Michael

2003-03-01

The ground state energy and other important observables of a many-fermion system with one- and two-body interactions only can all be obtained from the first order and second order Reduced Density Matrices (RDM's) of the system. Using these density matrices and a family of associated representability conditions one may obtain an approximation method for electronic structure theory that is in the mathematical form of Semi-Definite Programming (SDP): minimize a linear matrix functional over a space of positive semidefinite matrices subject to linear constraints. The representability conditions are some known necessary conditions, starting with the well-known P, Q, and G conditions [Claude Garrod and Jerome K. Percus, Reducation of the N-Particle Variational Problem, J. Math. Phys. 5 (1964) 1756-1776]. The RDM method with SDP has great potential advantages over the wave function method when the particle number N is large. The dimension of the full configuration space increases exponentially with N, but in RDM method with SDP the dimension of the objective matrix (which includes RDM's) increases only polynomially with N. We will report on the effect of adding the generalized three-index conditions proposed in [R. M. Erdahl, Representability, Int. J. Quantum Chem. 13 (1978) 697-718].

Time-dependent density-functional tight-binding method with the third-order expansion of electron density

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nishimoto, Yoshio, E-mail: nishimoto.yoshio@fukui.kyoto-u.ac.jp

2015-09-07

We develop a formalism for the calculation of excitation energies and excited state gradients for the self-consistent-charge density-functional tight-binding method with the third-order contributions of a Taylor series of the density functional theory energy with respect to the fluctuation of electron density (time-dependent density-functional tight-binding (TD-DFTB3)). The formulation of the excitation energy is based on the existing time-dependent density functional theory and the older TD-DFTB2 formulae. The analytical gradient is computed by solving Z-vector equations, and it requires one to calculate the third-order derivative of the total energy with respect to density matrix elements due to the inclusion of themore » third-order contributions. The comparison of adiabatic excitation energies for selected small and medium-size molecules using the TD-DFTB2 and TD-DFTB3 methods shows that the inclusion of the third-order contributions does not affect excitation energies significantly. A different set of parameters, which are optimized for DFTB3, slightly improves the prediction of adiabatic excitation energies statistically. The application of TD-DFTB for the prediction of absorption and fluorescence energies of cresyl violet demonstrates that TD-DFTB3 reproduced the experimental fluorescence energy quite well.« less

Time-dependent density-functional tight-binding method with the third-order expansion of electron density.

PubMed

Nishimoto, Yoshio

2015-09-07

We develop a formalism for the calculation of excitation energies and excited state gradients for the self-consistent-charge density-functional tight-binding method with the third-order contributions of a Taylor series of the density functional theory energy with respect to the fluctuation of electron density (time-dependent density-functional tight-binding (TD-DFTB3)). The formulation of the excitation energy is based on the existing time-dependent density functional theory and the older TD-DFTB2 formulae. The analytical gradient is computed by solving Z-vector equations, and it requires one to calculate the third-order derivative of the total energy with respect to density matrix elements due to the inclusion of the third-order contributions. The comparison of adiabatic excitation energies for selected small and medium-size molecules using the TD-DFTB2 and TD-DFTB3 methods shows that the inclusion of the third-order contributions does not affect excitation energies significantly. A different set of parameters, which are optimized for DFTB3, slightly improves the prediction of adiabatic excitation energies statistically. The application of TD-DFTB for the prediction of absorption and fluorescence energies of cresyl violet demonstrates that TD-DFTB3 reproduced the experimental fluorescence energy quite well.

Embedded random matrix ensembles from nuclear structure and their recent applications

NASA Astrophysics Data System (ADS)

Kota, V. K. B.; Chavda, N. D.

Embedded random matrix ensembles generated by random interactions (of low body rank and usually two-body) in the presence of a one-body mean field, introduced in nuclear structure physics, are now established to be indispensable in describing statistical properties of a large number of isolated finite quantum many-particle systems. Lie algebra symmetries of the interactions, as identified from nuclear shell model and the interacting boson model, led to the introduction of a variety of embedded ensembles (EEs). These ensembles with a mean field and chaos generating two-body interaction generate in three different stages, delocalization of wave functions in the Fock space of the mean-field basis states. The last stage corresponds to what one may call thermalization and complex nuclei, as seen from many shell model calculations, lie in this region. Besides briefly describing them, their recent applications to nuclear structure are presented and they are (i) nuclear level densities with interactions; (ii) orbit occupancies; (iii) neutrinoless double beta decay nuclear transition matrix elements as transition strengths. In addition, their applications are also presented briefly that go beyond nuclear structure and they are (i) fidelity, decoherence, entanglement and thermalization in isolated finite quantum systems with interactions; (ii) quantum transport in disordered networks connected by many-body interactions with centrosymmetry; (iii) semicircle to Gaussian transition in eigenvalue densities with k-body random interactions and its relation to the Sachdev-Ye-Kitaev (SYK) model for majorana fermions.

A traveling wave ultrasonic motor with a metal/polymer-matrix material compound stator

NASA Astrophysics Data System (ADS)

Li, Jinbang; Liu, Shuo; Zhou, Ningning; Yu, Aibing; Cui, Yuguo; Chen, Pengfei

2018-01-01

This study proposes a traveling wave ultrasonic motor with a metal/polymer-matrix material compound stator. The stator is composed of a metal ring and polymer-matrix teeth. The resonance frequency of the stator with different structural dimensions was analyzed by the finite element method. From the results, the structure parameters of the metal ring were obtained. The effects of the density and elastic modulus of the tooth material on the resonance frequency were also investigated. A viscoelastic contact model was built to explore the contact state between the compound stator and rotor. Considering the density, elastic modulus and tribological properties, the tooth material was prepared by a molding process. The load-torque and efficiency-torque characteristics of the motor with different tooth thicknesses were measured under different preloads using a preload controlled ultrasonic motor test device. The maximum no-load speed of the motor was about 85 r min-1 with a tooth thickness of 3 mm and a preload of 100 N, the maximum stall torque of the motor was about 0.5 N · m with a tooth thickness of 4 mm and a preload of 125 N, and a maximum efficiency of about 5.5% occurred with a tooth thickness of 4 mm, a preload of 100 N and a torque of 0.3 N · m. The main merits of the proposed ultrasonic motor are low cost, light weight, high processing efficiency and long life.

Matrix density effects on the mechanical properties of SiC/RBSN composites

NASA Technical Reports Server (NTRS)

Bhatt, Ramakrishna T.; Kiser, James D.

1990-01-01

The room temperature mechanical properties were measured for SiC fiber reinforced reaction-bonded silicon nitride composites (SiC/RBSN) of different densities. The composites consisted of approx. 30 vol percent uniaxially aligned 142 micron diameter SiC fibers (Textron SCS-6) in a reaction-bonded Si3N4 matrix. The composite density was varied by changing the consolidation pressure during RBSN processing and by hot isostatically pressing the SiC/RBSN composites. Results indicate that as the consolidation pressure was increased from 27 to 138 MPa, the average pore size of the nitrided composites decreased from 0.04 to 0.02 microns and the composite density increased from 2.07 to 2.45 gm/cc. Nonetheless, these improvements resulted in only small increases in the first matrix cracking stress, primary elastic modulus, and ultimate tensile strength values of the composites. In contrast, HIP consolidation of SiC/RBSN resulted in a fully dense material whose first matrix cracking stress and elastic modulus were approx. 15 and 50 percent higher, respectively, and ultimate tensile strength values were approx. 40 percent lower than those for unHIPed SiC/RBSN composites. The modulus behavior for all specimens can be explained by simple rule-of-mixture theory. Also, the loss in ultimate strength for the HIPed composites appears to be related to a degradation in fiber strength at the HIP temperature. However, the density effect on matrix fracture strength was much less than would be expected based on typical monolithic Si3N4 behavior, suggesting that composite theory is indeed operating. Possible practical implications of these observations are discussed.

Synthesis and Study of Fe-Doped Bi₂S₃ Semimagnetic Nanocrystals Embedded in a Glass Matrix.

PubMed

Silva, Ricardo S; Mikhail, Hanna D; Guimarães, Eder V; Gonçalves, Elis R; Cano, Nilo F; Dantas, Noelio O

2017-07-11

Iron-doped bismuth sulphide (Bi 2- x Fe x S₃) nanocrystals have been successfully synthesized in a glass matrix using the fusion method. Transmission electron microscopy images and energy dispersive spectroscopy data clearly show that nanocrystals are formed with an average diameter of 7-9 nm, depending on the thermic treatment time, and contain Fe in their chemical composition. Magnetic force microscopy measurements show magnetic phase contrast patterns, providing further evidence of Fe incorporation in the nanocrystal structure. The electron paramagnetic resonance spectra displayed Fe 3+ typical characteristics, with spin of 5/2 in the 3d⁵ electronic state, thereby confirming the expected trivalent state of Fe ions in the Bi₂S₃ host structure. Results from the spin polarized density functional theory simulations, for the bulk Fe-doped Bi₂S₃ counterpart, corroborate the experimental fact that the volume of the unit cell decreases with Fe substitutionally doping at Bi1 and Bi2 sites. The Bader charge analysis indicated a pseudo valency charge of 1.322| e | on Fe Bi ₁ and 1.306| e | on Fe Bi ₂ ions, and a spin contribution for the magnetic moment of 5.0 µ B per unit cell containing one Fe atom. Electronic band structures showed that the (indirect) band gap changes from 1.17 eV for Bi₂S₃ bulk to 0.71 eV (0.74 eV) for Bi₂S₃:Fe Bi1 (Bi₂S₃:Fe Bi2 ). These results are compatible with the 3d⁵ high-spin state of Fe 3+ , and are in agreement with the experimental results, within the density functional theory accuracy.

Darkness without dark matter and energy - generalized unimodular gravity

NASA Astrophysics Data System (ADS)

Barvinsky, A. O.; Kamenshchik, A. Yu.

2017-11-01

We suggest a Lorentz non-invariant generalization of the unimodular gravity theory, which is classically equivalent to general relativity with a locally inert (devoid of local degrees of freedom) perfect fluid having an equation of state with a constant parameter w. For the range of w near -1 this dark fluid can play the role of dark energy, while for w = 0 this dark dust admits spatial inhomogeneities and can be interpreted as dark matter. We discuss possible implications of this model in the cosmological initial conditions problem. In particular, this is the extension of known microcanonical density matrix predictions for the initial quantum state of the closed cosmology to the case of spatially open Universe, based on the imitation of the spatial curvature by the dark fluid density. We also briefly discuss quantization of this model necessarily involving the method of gauge systems with reducible constraints and the effect of this method on the treatment of recently! suggested mechanism of vacuum energy sequestering.

Crosslinked Polymer Ionic Liquid/Ionic Liquid Blends Prepared by Photopolymerization as Solid-State Electrolytes in Supercapacitors.

PubMed

Wang, Po-Hsin; Wang, Tzong-Liu; Lin, Wen-Churng; Lin, Hung-Yin; Lee, Mei-Hwa; Yang, Chien-Hsin

2018-04-07

A photopolymerization method is used to prepare a mixture of polymer ionic liquid (PIL) and ionic liquid (IL). This mixture is used as a solid-state electrolyte in carbon nanoparticle (CNP)-based symmetric supercapacitors. The solid electrolyte is a binary mixture of a PIL and its corresponding IL. The PIL matrix is a cross-linked polyelectrolyte with an imidazole salt cation coupled with two anions of Br - in PIL-M-(Br) and TFSI - in PIL-M-(TFSI), respectively. The corresponding ionic liquids have imidazolium salt cation coupled with two anions of Br - and TFSI - , respectively. This study investigates the electrochemical characteristics of PILs and their corresponding IL mixtures used as a solid electrolyte in supercapacitors. Results show that a specific capacitance, maximum power density and energy density of 87 and 58 F·g - ¹, 40 and 48 kW·kg - ¹, and 107 and 59.9 Wh·kg - ¹ were achieved in supercapacitors based on (PIL-M-(Br)) and (PIL-M-(TFSI)) solid electrolytes, respectively.

Some effects of electron channeling on electron energy loss spectroscopy.

PubMed

Kirkland, Earl J

2005-02-01

As an electron beam (of order 100 keV) travels through a crystalline solid it can be channeled down a zone axis of the crystal to form a channeling peak centered on the atomic columns. The channeling peak can be similar in size to the outer atomic orbitals. Electron energy loss spectroscopy (EELS) measures the losses that the electron experiences as it passes through the solid yielding information about the unoccupied density of states in the solid. The interaction matrix element for this process typically produces dipole selection rules for small angle scattering. In this paper, a theoretical calculation of the EELS cross section in the presence of strong channeling is performed for the silicon L23 edge. The presence of channeling is found to alter both the intensity and selection rules for this EELS signal as a function of depth in the solid. At some depths in the specimen small but significant non-dipole transition components can be produced, which may influence measurements of the density of states in solids.

Ab initio optimization principle for the ground states of translationally invariant strongly correlated quantum lattice models.

PubMed

Ran, Shi-Ju

2016-05-01

In this work, a simple and fundamental numeric scheme dubbed as ab initio optimization principle (AOP) is proposed for the ground states of translational invariant strongly correlated quantum lattice models. The idea is to transform a nondeterministic-polynomial-hard ground-state simulation with infinite degrees of freedom into a single optimization problem of a local function with finite number of physical and ancillary degrees of freedom. This work contributes mainly in the following aspects: (1) AOP provides a simple and efficient scheme to simulate the ground state by solving a local optimization problem. Its solution contains two kinds of boundary states, one of which play the role of the entanglement bath that mimics the interactions between a supercell and the infinite environment, and the other gives the ground state in a tensor network (TN) form. (2) In the sense of TN, a novel decomposition named as tensor ring decomposition (TRD) is proposed to implement AOP. Instead of following the contraction-truncation scheme used by many existing TN-based algorithms, TRD solves the contraction of a uniform TN in an opposite way by encoding the contraction in a set of self-consistent equations that automatically reconstruct the whole TN, making the simulation simple and unified; (3) AOP inherits and develops the ideas of different well-established methods, including the density matrix renormalization group (DMRG), infinite time-evolving block decimation (iTEBD), network contractor dynamics, density matrix embedding theory, etc., providing a unified perspective that is previously missing in this fields. (4) AOP as well as TRD give novel implications to existing TN-based algorithms: A modified iTEBD is suggested and the two-dimensional (2D) AOP is argued to be an intrinsic 2D extension of DMRG that is based on infinite projected entangled pair state. This paper is focused on one-dimensional quantum models to present AOP. The benchmark is given on a transverse Ising chain and 2D classical Ising model, showing the remarkable efficiency and accuracy of the AOP.

Efficient Suppression of Defects and Charge Trapping in High Density In-Sn-Zn-O Thin Film Transistor Prepared using Microwave-Assisted Sputter.

PubMed

Goh, Youngin; Ahn, Jaehan; Lee, Jeong Rak; Park, Wan Woo; Ko Park, Sang-Hee; Jeon, Sanghun

2017-10-25

Amorphous oxide semiconductor-based thin film transistors (TFTs) have been considered as excellent switching elements for driving active-matrix organic light-emitting diodes (AMOLED) owing to their high mobility and process compatibility. However, oxide semiconductors have inherent defects, causing fast transient charge trapping and device instability. For the next-generation displays such as flexible, wearable, or transparent displays, an active semiconductor layer with ultrahigh mobility and high reliability at low deposition temperature is required. Therefore, we introduced high density plasma microwave-assisted (MWA) sputtering method as a promising deposition tool for the formation of high density and high-performance oxide semiconductor films. In this paper, we present the effect of the MWA sputtering method on the defects and fast charge trapping in In-Sn-Zn-O (ITZO) TFTs using various AC device characterization methodologies including fast I-V, pulsed I-V, transient current, low frequency noise, and discharge current analysis. Using these methods, we were able to analyze the charge trapping mechanism and intrinsic electrical characteristics, and extract the subgap density of the states of oxide TFTs quantitatively. In comparison to conventional sputtered ITZO, high density plasma MWA-sputtered ITZO exhibits outstanding electrical performance, negligible charge trapping characteristics and low subgap density of states. High-density plasma MWA sputtering method has high deposition rate even at low working pressure and control the ion bombardment energy, resulting in forming low defect generation in ITZO and presenting high performance ITZO TFT. We expect the proposed high density plasma sputtering method to be applicable to a wide range of oxide semiconductor device applications.

Optimization of metabolite detection by quantum mechanics simulations in magnetic resonance spectroscopy.

PubMed

Gambarota, Giulio

2017-07-15

Magnetic resonance spectroscopy (MRS) is a well established modality for investigating tissue metabolism in vivo. In recent years, many efforts by the scientific community have been directed towards the improvement of metabolite detection and quantitation. Quantum mechanics simulations allow for investigations of the MR signal behaviour of metabolites; thus, they provide an essential tool in the optimization of metabolite detection. In this review, we will examine quantum mechanics simulations based on the density matrix formalism. The density matrix was introduced by von Neumann in 1927 to take into account statistical effects within the theory of quantum mechanics. We will discuss the main steps of the density matrix simulation of an arbitrary spin system and show some examples for the strongly coupled two spin system. Copyright © 2016 Elsevier Inc. All rights reserved.

Carrier-Envelope Phase Effect on Atomic Excitation by Few-Cycle rf Pulses

DOE Office of Scientific and Technical Information (OSTI.GOV)

Li Hebin; Welch, George R.; Sautenkov, Vladimir A.

2010-03-12

We present an experimental and theoretical study of the carrier-envelope phase effects on population transfer between two bound atomic states interacting with intense ultrashort pulses. Radio frequency pulses are used to transfer population among the ground state hyperfine levels in rubidium atoms. These pulses are only a few cycles in duration and have Rabi frequencies of the order of the carrier frequency. The phase difference between the carrier and the envelope of the pulses has a significant effect on the excitation of atomic coherence and population transfer. We provide a theoretical description of this phenomenon using density matrix equations. Wemore » discuss the implications and possible applications of our results.« less

Electronic and optical properties of GaN/AlN quantum dots with adjacent threading dislocations

NASA Astrophysics Data System (ADS)

Ye, Han; Lu, Peng-Fei; Yu, Zhong-Yuan; Yao, Wen-Jie; Chen, Zhi-Hui; Jia, Bo-Yong; Liu, Yu-Min

2010-04-01

We present a theory to simulate a coherent GaN QD with an adjacent pure edge threading dislocation by using a finite element method. The piezoelectric effects and the strain modified band edges are investigated in the framework of multi-band k · p theory to calculate the electron and the heavy hole energy levels. The linear optical absorption coefficients corresponding to the interband ground state transition are obtained via the density matrix approach and perturbation expansion method. The results indicate that the strain distribution of the threading dislocation affects the electronic structure. Moreover, the ground state transition behaviour is also influenced by the position of the adjacent threading dislocation.

Evolution equation of population genetics: Relation to the density-matrix theory of quasiparticles with general dispersion laws

NASA Astrophysics Data System (ADS)

Bezák, V.

2003-02-01

The Waxman-Peck theory of population genetics is discussed in regard of soil bacteria. Each bacterium is understood as a carrier of a phenotypic parameter p. The central objective is the calculation of the probability density with respect to p, Φ(p,t;p0), of the carriers living at time t>0, provided that initially at t0=0, all bacteria carried the phenotypic parameter p0=0. The theory involves two small parameters: the mutation probability μ and a parameter γ involved in a function w(p) defining the fitness of the bacteria to survive the generation time τ and give birth to an offspring. The mutation from a state p to a state q is defined by a Gaussian with a dispersion σ2m. The author focuses our attention on a function φ(p,t) which determines uniquely the function Φ(p,t;p0) and satisfies a linear equation (Waxman’s equation). The Green function of this equation is mathematically identical with the one-particle Bloch density matrix, where μ characterizes the order of magnitude of the potential energy. (In the x representation, the potential energy is proportional to the inverted Gaussian with the dispersion σ2m). The author solves Waxman’s equation in the standard style of a perturbation theory and discusses how the solution depends on the choice of the fitness function w(p). In a sense, the function c(p)=1-w(p)/w(0) is analogous to the dispersion function E(p) of fictitious quasiparticles. In contrast to Waxman’s approximation, where c(p) was taken as a quadratic function, c(p)≈γp2, the author exemplifies the problem with another function, c(p)=γ[1-exp(-ap2)], where γ is small but a may be large. The author shows that the use of this function in the theory of the population genetics is the same as the use of a nonparabolic dispersion law E=E(p) in the density-matrix theory. With a general function c(p), the distribution function Φ(p,t;0) is composed of a δ-function component, N(t)δ(p), and a blurred component. When discussing the limiting transition for t→∞, the author shows that his function c(p) implies that N(t)→N(∞)≠0 in contrast with the asymptotics N(t)→0 resulting from the use of Waxman’s function c(p)˜p2.

Effective representation of amide III, II, I, and A modes on local vibrational modes: Analysis of ab initio quantum calculation results.

PubMed

Hahn, Seungsoo

2016-10-28

The Hamiltonian matrix for the first excited vibrational states of a protein can be effectively represented by local vibrational modes constituting amide III, II, I, and A modes to simulate various vibrational spectra. Methods for obtaining the Hamiltonian matrix from ab initio quantum calculation results are discussed, where the methods consist of three steps: selection of local vibrational mode coordinates, calculation of a reduced Hessian matrix, and extraction of the Hamiltonian matrix from the Hessian matrix. We introduce several methods for each step. The methods were assessed based on the density functional theory calculation results of 24 oligopeptides with four different peptide lengths and six different secondary structures. The completeness of a Hamiltonian matrix represented in the reduced local mode space is improved by adopting a specific atom group for each amide mode and reducing the effect of ignored local modes. The calculation results are also compared to previous models using C=O stretching vibration and transition dipole couplings. We found that local electric transition dipole moments of the amide modes are mainly bound on the local peptide planes. Their direction and magnitude are well conserved except amide A modes, which show large variation. Contrary to amide I modes, the vibrational coupling constants of amide III, II, and A modes obtained by analysis of a dipeptide are not transferable to oligopeptides with the same secondary conformation because coupling constants are affected by the surrounding atomic environment.

Extended Lagrangian Excited State Molecular Dynamics

DOE PAGES

Bjorgaard, Josiah August; Sheppard, Daniel Glen; Tretiak, Sergei; ...

2018-01-09

In this work, an extended Lagrangian framework for excited state molecular dynamics (XL-ESMD) using time-dependent self-consistent field theory is proposed. The formulation is a generalization of the extended Lagrangian formulations for ground state Born–Oppenheimer molecular dynamics [Phys. Rev. Lett. 2008 100, 123004]. The theory is implemented, demonstrated, and evaluated using a time-dependent semiempirical model, though it should be generally applicable to ab initio theory. The simulations show enhanced energy stability and a significantly reduced computational cost associated with the iterative solutions of both the ground state and the electronically excited states. Relaxed convergence criteria can therefore be used both formore » the self-consistent ground state optimization and for the iterative subspace diagonalization of the random phase approximation matrix used to calculate the excited state transitions. In conclusion, the XL-ESMD approach is expected to enable numerically efficient excited state molecular dynamics for such methods as time-dependent Hartree–Fock (TD-HF), Configuration Interactions Singles (CIS), and time-dependent density functional theory (TD-DFT).« less

Extended Lagrangian Excited State Molecular Dynamics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bjorgaard, Josiah August; Sheppard, Daniel Glen; Tretiak, Sergei

In this work, an extended Lagrangian framework for excited state molecular dynamics (XL-ESMD) using time-dependent self-consistent field theory is proposed. The formulation is a generalization of the extended Lagrangian formulations for ground state Born–Oppenheimer molecular dynamics [Phys. Rev. Lett. 2008 100, 123004]. The theory is implemented, demonstrated, and evaluated using a time-dependent semiempirical model, though it should be generally applicable to ab initio theory. The simulations show enhanced energy stability and a significantly reduced computational cost associated with the iterative solutions of both the ground state and the electronically excited states. Relaxed convergence criteria can therefore be used both formore » the self-consistent ground state optimization and for the iterative subspace diagonalization of the random phase approximation matrix used to calculate the excited state transitions. In conclusion, the XL-ESMD approach is expected to enable numerically efficient excited state molecular dynamics for such methods as time-dependent Hartree–Fock (TD-HF), Configuration Interactions Singles (CIS), and time-dependent density functional theory (TD-DFT).« less

Extended Lagrangian Excited State Molecular Dynamics.

PubMed

Bjorgaard, J A; Sheppard, D; Tretiak, S; Niklasson, A M N

2018-02-13

An extended Lagrangian framework for excited state molecular dynamics (XL-ESMD) using time-dependent self-consistent field theory is proposed. The formulation is a generalization of the extended Lagrangian formulations for ground state Born-Oppenheimer molecular dynamics [Phys. Rev. Lett. 2008 100, 123004]. The theory is implemented, demonstrated, and evaluated using a time-dependent semiempirical model, though it should be generally applicable to ab initio theory. The simulations show enhanced energy stability and a significantly reduced computational cost associated with the iterative solutions of both the ground state and the electronically excited states. Relaxed convergence criteria can therefore be used both for the self-consistent ground state optimization and for the iterative subspace diagonalization of the random phase approximation matrix used to calculate the excited state transitions. The XL-ESMD approach is expected to enable numerically efficient excited state molecular dynamics for such methods as time-dependent Hartree-Fock (TD-HF), Configuration Interactions Singles (CIS), and time-dependent density functional theory (TD-DFT).

Exact and quasi-classical density matrix and Wigner functions for a particle in the box and half space

NASA Technical Reports Server (NTRS)

Akhundova, E. A.; Dodonov, V. V.; Manko, V. I.

1993-01-01

The exact expressions for density matrix and Wigner functions of quantum systems are known only in special cases. Corresponding Hamiltonians are quadratic forms of Euclidean coordinates and momenta. In this paper we consider the problem of one-dimensional free particle movement in the bounded region 0 is less than x is less than a (including the case a = infinity).

Time-dependent transition density matrix for visualizing charge-transfer excitations in photoexcited organic donor-acceptor systems

NASA Astrophysics Data System (ADS)

Li, Yonghui; Ullrich, Carsten

2013-03-01

The time-dependent transition density matrix (TDM) is a useful tool to visualize and interpret the induced charges and electron-hole coherences of excitonic processes in large molecules. Combined with time-dependent density functional theory on a real-space grid (as implemented in the octopus code), the TDM is a computationally viable visualization tool for optical excitation processes in molecules. It provides real-time maps of particles and holes which gives information on excitations, in particular those that have charge-transfer character, that cannot be obtained from the density alone. Some illustration of the TDM and comparison with standard density difference plots will be shown for photoexcited organic donor-acceptor molecules. This work is supported by NSF Grant DMR-1005651

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yanai, Takeshi; Fann, George I.; Beylkin, Gregory

Using the fully numerical method for time-dependent Hartree–Fock and density functional theory (TD-HF/DFT) with the Tamm–Dancoff (TD) approximation we use a multiresolution analysis (MRA) approach to present our findings. From a reformulation with effective use of the density matrix operator, we obtain a general form of the HF/DFT linear response equation in the first quantization formalism. It can be readily rewritten as an integral equation with the bound-state Helmholtz (BSH) kernel for the Green's function. The MRA implementation of the resultant equation permits excited state calculations without virtual orbitals. Moreover, the integral equation is efficiently and adaptively solved using amore » numerical multiresolution solver with multiwavelet bases. Our implementation of the TD-HF/DFT methods is applied for calculating the excitation energies of H 2, Be, N 2, H 2O, and C 2H 4 molecules. The numerical errors of the calculated excitation energies converge in proportion to the residuals of the equation in the molecular orbitals and response functions. The energies of the excited states at a variety of length scales ranging from short-range valence excitations to long-range Rydberg-type ones are consistently accurate. It is shown that the multiresolution calculations yield the correct exponential asymptotic tails for the response functions, whereas those computed with Gaussian basis functions are too diffuse or decay too rapidly. Finally, we introduce a simple asymptotic correction to the local spin-density approximation (LSDA) so that in the TDDFT calculations, the excited states are correctly bound.« less

Use of density functional theory orbitals in the GVVPT2 variant of second-order multistate multireference perturbation theory.

PubMed

Hoffmann, Mark R; Helgaker, Trygve

2015-03-05

A new variation of the second-order generalized van Vleck perturbation theory (GVVPT2) for molecular electronic structure is suggested. In contrast to the established procedure, in which CASSCF or MCSCF orbitals are first obtained and subsequently used to define a many-electron model (or reference) space, the use of an orbital space obtained from the local density approximation (LDA) variant of density functional theory is considered. Through a final, noniterative diagonalization of an average Fock matrix within orbital subspaces, quasicanonical orbitals that are otherwise indistinguishable from quasicanonical orbitals obtained from a CASSCF or MCSCF calculation are obtained. Consequently, all advantages of the GVVPT2 method are retained, including use of macroconfigurations to define incomplete active spaces and rigorous avoidance of intruder states. The suggested variant is vetted on three well-known model problems: the symmetric stretching of the O-H bonds in water, the dissociation of N2, and the stretching of ground and excited states C2 to more than twice the equilibrium bond length of the ground state. It is observed that the LDA-based GVVPT2 calculations yield good results, of comparable quality to conventional CASSCF-based calculations. This is true even for the C2 model problem, in which the orbital space for each state was defined by the LDA orbitals. These results suggest that GVVPT2 can be applied to much larger problems than previously accessible.

Comparison of collagen matrix treatment impregnated with platelet rich plasma vs bone marrow.

PubMed

Minamimura, Ai; Ichioka, Shigeru; Sano, Hitomi; Sekiya, Naomi

2014-02-01

This study has reported the efficacy of an autologous bone marrow-impregnated collagen matrix experimentally and clinically. Then, it reflected that platelet rich plasma (PRP) was as good a source of growth factors as bone marrow and available in a less invasive procedure. This study aimed to compare the efficacy of a PRP-impregnated collagen matrix with that of a bone marrow-impregnated collagen matrix by quantifying wound size and capillary density using genetically diabetic db/db mice. Bone marrow cells were obtained from femurs of ddy mice. Then, a small amount of collagen matrix was immersed in bone marrow suspension. This is called a bone marrow-impregnated collagen matrix. PRP was obtained from healthy human blood and a small amount of collagen matrix was immersed in PRP. This is called a PRP-impregnated collagen matrix. A bone marrow-impregnated collagen matrix and PRP-impregnated collagen matrix were applied to excisional skin wounds on a genetically healing-impaired mouse (n = 6) and wounds were evaluated 6 days after the procedure. Wounds were divided into two groups: PRP (n = 6), in which a PRP-impregnated collagen matrix was applied; and bone marrow (n = 6), in which collagen immersed in a bone marrow suspension was applied. There was no significant difference between the PRP and bone-marrow groups in the rate of vascular density increase or wound size decrease. The present study suggested that the PRP-impregnated collagen matrix promotes repair processes at least as strongly as the bone marrow-impregnated collagen matrix. Given lower invasiveness, the PRP-impregnated collagen matrix would have advantages in clinical use.

A robust variant of block Jacobi-Davidson for extracting a large number of eigenpairs: Application to grid-based real-space density functional theory

NASA Astrophysics Data System (ADS)

Lee, M.; Leiter, K.; Eisner, C.; Breuer, A.; Wang, X.

2017-09-01

In this work, we investigate a block Jacobi-Davidson (J-D) variant suitable for sparse symmetric eigenproblems where a substantial number of extremal eigenvalues are desired (e.g., ground-state real-space quantum chemistry). Most J-D algorithm variations tend to slow down as the number of desired eigenpairs increases due to frequent orthogonalization against a growing list of solved eigenvectors. In our specification of block J-D, all of the steps of the algorithm are performed in clusters, including the linear solves, which allows us to greatly reduce computational effort with blocked matrix-vector multiplies. In addition, we move orthogonalization against locked eigenvectors and working eigenvectors outside of the inner loop but retain the single Ritz vector projection corresponding to the index of the correction vector. Furthermore, we minimize the computational effort by constraining the working subspace to the current vectors being updated and the latest set of corresponding correction vectors. Finally, we incorporate accuracy thresholds based on the precision required by the Fermi-Dirac distribution. The net result is a significant reduction in the computational effort against most previous block J-D implementations, especially as the number of wanted eigenpairs grows. We compare our approach with another robust implementation of block J-D (JDQMR) and the state-of-the-art Chebyshev filter subspace (CheFSI) method for various real-space density functional theory systems. Versus CheFSI, for first-row elements, our method yields competitive timings for valence-only systems and 4-6× speedups for all-electron systems with up to 10× reduced matrix-vector multiplies. For all-electron calculations on larger elements (e.g., gold) where the wanted spectrum is quite narrow compared to the full spectrum, we observe 60× speedup with 200× fewer matrix-vector multiples vs. CheFSI.

A robust variant of block Jacobi-Davidson for extracting a large number of eigenpairs: Application to grid-based real-space density functional theory.

PubMed

Lee, M; Leiter, K; Eisner, C; Breuer, A; Wang, X

2017-09-21

In this work, we investigate a block Jacobi-Davidson (J-D) variant suitable for sparse symmetric eigenproblems where a substantial number of extremal eigenvalues are desired (e.g., ground-state real-space quantum chemistry). Most J-D algorithm variations tend to slow down as the number of desired eigenpairs increases due to frequent orthogonalization against a growing list of solved eigenvectors. In our specification of block J-D, all of the steps of the algorithm are performed in clusters, including the linear solves, which allows us to greatly reduce computational effort with blocked matrix-vector multiplies. In addition, we move orthogonalization against locked eigenvectors and working eigenvectors outside of the inner loop but retain the single Ritz vector projection corresponding to the index of the correction vector. Furthermore, we minimize the computational effort by constraining the working subspace to the current vectors being updated and the latest set of corresponding correction vectors. Finally, we incorporate accuracy thresholds based on the precision required by the Fermi-Dirac distribution. The net result is a significant reduction in the computational effort against most previous block J-D implementations, especially as the number of wanted eigenpairs grows. We compare our approach with another robust implementation of block J-D (JDQMR) and the state-of-the-art Chebyshev filter subspace (CheFSI) method for various real-space density functional theory systems. Versus CheFSI, for first-row elements, our method yields competitive timings for valence-only systems and 4-6× speedups for all-electron systems with up to 10× reduced matrix-vector multiplies. For all-electron calculations on larger elements (e.g., gold) where the wanted spectrum is quite narrow compared to the full spectrum, we observe 60× speedup with 200× fewer matrix-vector multiples vs. CheFSI.

Stimulated emission and optical properties of pyranyliden fragment containing compounds in PVK matrix

NASA Astrophysics Data System (ADS)

Vembris, Aivars; Zarins, Elmars; Kokars, Valdis

2017-10-01

Organic solid state lasers are thoughtfully investigated due to their potential applications in communication, sensors, biomedicine, etc. Low amplified spontaneous emission (ASE) excitation threshold value is essential for further use of the material in devices. Intramolecular interaction limits high molecule density load in the matrix. It is the case of the well-known red light emitting laser dye - 4-(dicyanomethylene)-2-methyl-6-(4-dimethylaminostyryl)-4H-pyran (DCM). The lowest ASE threshold value of the mentioned laser dye could be obtained within the concentration range between 2 and 4 wt%. At higher concentration threshold energy drastically increases. In this work optical and ASE properties of three original DCM derivatives in poly(N-vinylcarbazole) (PVK) at various concentrations will be discussed. One of the derivatives is modified DCM dye in which the methyl substituents in the electron donor part have been replaced with bulky trityloxyethyl groups (DWK-1). These sterically significant functional groups do not influence electron transitions in the dye but prevent aggregation of the molecules. The chemical structure of the second investigated compound is similar to DWK-1 where the methyl group is replaced with the tert-butyl substituent (DWK-1TB). The third derivative (DWK-2) consists of two N,N-di(trityloxyethyl)amino electron donor groups. All results were compared with DCM:PVK system. Photoluminescence quantum yield (PLQY) is up to ten times larger for DWK-1TB with respect to DCM systems. Bulky trityloxyethyl groups prevent aggregation of the molecules thus decreasing interaction between dyes and amount of non-radiative decays. The red shift of the photoluminescence and amplified spontaneous emission at higher concentrations were observed due to the solid state solvation effect. The increase of the investigated dye density in the matrix with a smaller reduction in PLQY resulted in low ASE threshold energy. The lowest threshold value was obtained around 21 μJ/cm2 (2.1 kW/cm2) in DWK-1TB:PVK films.

Electrical Resistance of SiC/SiC Ceramic Matrix Composites for Damage Detection and Life-Prediction

NASA Technical Reports Server (NTRS)

Smith, Craig; Morscher, Gregory; Xia, Zhenhai

2009-01-01

Ceramic matrix composites (CMC) are suitable for high temperature structural applications such as turbine airfoils and hypersonic thermal protection systems due to their low density high thermal conductivity. The employment of these materials in such applications is limited by the ability to accurately monitor and predict damage evolution. Current nondestructive methods such as ultrasound, x-ray, and thermal imaging are limited in their ability to quantify small scale, transverse, in-plane, matrix cracks developed over long-time creep and fatigue conditions. CMC is a multifunctional material in which the damage is coupled with the material s electrical resistance, providing the possibility of real-time information about the damage state through monitoring of resistance. Here, resistance measurement of SiC/SiC composites under mechanical load at both room temperature monotonic and high temperature creep conditions, coupled with a modal acoustic emission technique, can relate the effects of temperature, strain, matrix cracks, fiber breaks, and oxidation to the change in electrical resistance. A multiscale model can in turn be developed for life prediction of in-service composites, based on electrical resistance methods. Results of tensile mechanical testing of SiC/SiC composites at room and high temperatures will be discussed. Data relating electrical resistivity to composite constituent content, fiber architecture, temperature, matrix crack formation, and oxidation will be explained, along with progress in modeling such properties.

Effect of process parameters on the density and porosity of laser melted AlSi10Mg/SiC metal matrix composite

NASA Astrophysics Data System (ADS)

Famodimu, Omotoyosi H.; Stanford, Mark; Oduoza, Chike F.; Zhang, Lijuan

2018-06-01

Laser melting of aluminium alloy—AlSi10Mg has increasingly been used to create specialised products in various industrial applications, however, research on utilising laser melting of aluminium matrix composites in replacing specialised parts have been slow on the uptake. This has been attributed to the complexity of the laser melting process, metal/ceramic feedstock for the process and the reaction of the feedstock material to the laser. Thus, an understanding of the process, material microstructure and mechanical properties is important for its adoption as a manufacturing route of aluminium metal matrix composites. The effects of several parameters of the laser melting process on the mechanical blended composite were thus investigated in this research. This included single track formations of the matrix alloy and the composite alloyed with 5% and 10% respectively for their reaction to laser melting and the fabrication of density blocks to investigate the relative density and porosity over different scan speeds. The results from these experiments were utilised in determining a process window in fabricating near-fully dense parts.

Collective neutrino oscillations and neutrino wave packets

DOE Office of Scientific and Technical Information (OSTI.GOV)

Akhmedov, Evgeny; Lindner, Manfred; Kopp, Joachim, E-mail: akhmedov@mpi-hd.mpg.de, E-mail: jkopp@uni-mainz.de, E-mail: lindner@mpi-hd.mpg.de

Effects of decoherence by wave packet separation on collective neutrino oscillations in dense neutrino gases are considered. We estimate the length of the wave packets of neutrinos produced in core collapse supernovae and the expected neutrino coherence length, and then proceed to consider the decoherence effects within the density matrix formalism of neutrino flavour transitions. First, we demonstrate that for neutrino oscillations in vacuum the decoherence effects are described by a damping term in the equation of motion of the density matrix of a neutrino as a whole (as contrasted to that of the fixed-momentum components of the neutrino densitymore » matrix). Next, we consider neutrino oscillations in ordinary matter and dense neutrino backgrounds, both in the adiabatic and non-adiabatic regimes. In the latter case we study two specific models of adiabaticity violation—one with short-term and another with extended non-adiabaticity. It is demonstrated that, while in the adiabatic case a damping term is present in the equation of motion of the neutrino density matrix (just like in the vacuum oscillation case), no such term in general appears in the non-adiabatic regime.« less

Variational Optimization of the Second-Order Density Matrix Corresponding to a Seniority-Zero Configuration Interaction Wave Function.

PubMed

Poelmans, Ward; Van Raemdonck, Mario; Verstichel, Brecht; De Baerdemacker, Stijn; Torre, Alicia; Lain, Luis; Massaccesi, Gustavo E; Alcoba, Diego R; Bultinck, Patrick; Van Neck, Dimitri

2015-09-08

We perform a direct variational determination of the second-order (two-particle) density matrix corresponding to a many-electron system, under a restricted set of the two-index N-representability P-, Q-, and G-conditions. In addition, we impose a set of necessary constraints that the two-particle density matrix must be derivable from a doubly occupied many-electron wave function, i.e., a singlet wave function for which the Slater determinant decomposition only contains determinants in which spatial orbitals are doubly occupied. We rederive the two-index N-representability conditions first found by Weinhold and Wilson and apply them to various benchmark systems (linear hydrogen chains, He, N2, and CN(-)). This work is motivated by the fact that a doubly occupied many-electron wave function captures in many cases the bulk of the static correlation. Compared to the general case, the structure of doubly occupied two-particle density matrices causes the associate semidefinite program to have a very favorable scaling as L(3), where L is the number of spatial orbitals. Since the doubly occupied Hilbert space depends on the choice of the orbitals, variational calculation steps of the two-particle density matrix are interspersed with orbital-optimization steps (based on Jacobi rotations in the space of the spatial orbitals). We also point to the importance of symmetry breaking of the orbitals when performing calculations in a doubly occupied framework.

Fractal heterogeneity in minimal matrix models of scars modulates stiff-niche stem-cell responses via nuclear exit of a mechanorepressor

NASA Astrophysics Data System (ADS)

Dingal, P. C. Dave P.; Bradshaw, Andrew M.; Cho, Sangkyun; Raab, Matthew; Buxboim, Amnon; Swift, Joe; Discher, Dennis E.

2015-09-01

Scarring is a long-lasting problem in higher animals, and reductionist approaches could aid in developing treatments. Here, we show that copolymerization of collagen I with polyacrylamide produces minimal matrix models of scars (MMMS), in which fractal-fibre bundles segregate heterogeneously to the hydrogel subsurface. Matrix stiffens locally--as in scars--while allowing separate control over adhesive-ligand density. The MMMS elicits scar-like phenotypes from mesenchymal stem cells (MSCs): cells spread and polarize quickly, increasing nucleoskeletal lamin-A yet expressing the `scar marker' smooth muscle actin (SMA) more slowly. Surprisingly, expression responses to MMMS exhibit less cell-to-cell noise than homogeneously stiff gels. Such differences from bulk-average responses arise because a strong SMA repressor, NKX2.5, slowly exits the nucleus on rigid matrices. NKX2.5 overexpression overrides rigid phenotypes, inhibiting SMA and cell spreading, whereas cytoplasm-localized NKX2.5 mutants degrade in well-spread cells. MSCs thus form a `mechanical memory' of rigidity by progressively suppressing NKX2.5, thereby elevating SMA in a scar-like state.

Preparation and surface characteristics of Re3W matrix scandate cathode: An experimental and theoretical study

NASA Astrophysics Data System (ADS)

Lai, Chen; Wang, Jinshu; Zhou, Fan; Liu, Wei; Hu, Peng; Wang, Changhao; Wang, Ruzhi; Miao, Naihua

2018-05-01

The Scandia doped thermionic cathodes have received great attention owing to their high electron emission density in past two decades. Here, Scandia doped Re3W matrix scandate (RS) cathodes are fabricated by using Sc2O3 doped Re3W powders that prepared by spray drying method. The micromorphology, surface composition and chemical states of RS cathode are investigated with various modern technologies. It reveals that the reduction temperature of RS powders is dramatically increased by Sc2O3. On the surface of RS cathode, a certain amount of Sc2O3 nanoparticles and barium salt submicron particles are observed. According to the in situ Auger electron spectroscopy analysis, the concentration ratio of Ba:Sc:O is determined to be 2.9:1.1:2.7. The X-ray photoelectron spectroscopy data indicates that low oxidation state of Sc is clearly observed in scandate cathodes. The high atomic ratio of Ba on RS cathode surface is suggested due to the high adsorption of Re3W to Ba. Moreover, RS cathode shows better adsorption to Sc by comparison with conventional tungsten matrix scandate cathode. For RS cathode, the main depletion of Sc is suggested to -OSc desorbing from RS cathode surface. RS cathode is expected to be an impressive thermionic cathode with good emission properties and ion anti-bombarding insensitivity.

A Gleason-Type Theorem for Any Dimension Based on a Gambling Formulation of Quantum Mechanics

NASA Astrophysics Data System (ADS)

Benavoli, Alessio; Facchini, Alessandro; Zaffalon, Marco

2017-07-01

Based on a gambling formulation of quantum mechanics, we derive a Gleason-type theorem that holds for any dimension n of a quantum system, and in particular for n=2. The theorem states that the only logically consistent probability assignments are exactly the ones that are definable as the trace of the product of a projector and a density matrix operator. In addition, we detail the reason why dispersion-free probabilities are actually not valid, or rational, probabilities for quantum mechanics, and hence should be excluded from consideration.

Effect of distribution, interface property and density of hydrogel-embedded vertically aligned carbon nanotube arrays on the properties of a flexible solid state supercapacitor

NASA Astrophysics Data System (ADS)

Zhu, Qi; Yuan, Xietao; Zhu, Yihao; Ni, Jiangfeng; Zhang, Xiaohua; Yang, Zhaohui

2018-05-01

In this paper we fabricate a robust flexible solid-state supercapacitor (FSC) device by embedding a conductive poly(vinyl alcohol) hydrogel into aligned carbon nanotube (CNT) arrays. We carefully investigate the effect of distribution, interface properties and densification of CNTs in the gel matrix on the electrochemical properties of an FSC. The total electrochemical capacitance of the device is measured to be 227 mF cm‑3 with a maximum energy density of 0.02 mWh cm‑3, which is dramatically enhanced compared with a similar device composed of non-parallel CNTs. Additionally, controllable in situ electrochemical oxidation greatly improved the compatibility between the hydrophobic CNTs and the hydrophilic hydrogel, which decreased the resistance of the device and introduced extra pseudocapacitance. After such oxidation treatment the energy storage ability further doubled to 430 mF cm‑3 with a maximum energy density of 0.04 mWh cm‑3 . The FSCs based on densified CNT arrays exhibited a much higher volumetric capacitance of 1140 mF cm‑3 and a larger energy density of 0.1 mWh cm‑3, with a large power density of 14 mW cm‑3. All devices show excellent stability of capacitance after at least 10 000 charge–discharge cycles with a loss of less than 2%. These easy-to-assemble hybrid arrays thus potentially provide a new method for manufacturing wearable devices and implantable medical devices.

Effect of distribution, interface property and density of hydrogel-embedded vertically aligned carbon nanotube arrays on the properties of a flexible solid state supercapacitor.

PubMed

Zhu, Qi; Yuan, Xietao; Zhu, Yihao; Ni, Jiangfeng; Zhang, Xiaohua; Yang, Zhaohui

2018-05-11

In this paper we fabricate a robust flexible solid-state supercapacitor (FSC) device by embedding a conductive poly(vinyl alcohol) hydrogel into aligned carbon nanotube (CNT) arrays. We carefully investigate the effect of distribution, interface properties and densification of CNTs in the gel matrix on the electrochemical properties of an FSC. The total electrochemical capacitance of the device is measured to be 227 mF cm -3 with a maximum energy density of 0.02 mWh cm -3 , which is dramatically enhanced compared with a similar device composed of non-parallel CNTs. Additionally, controllable in situ electrochemical oxidation greatly improved the compatibility between the hydrophobic CNTs and the hydrophilic hydrogel, which decreased the resistance of the device and introduced extra pseudocapacitance. After such oxidation treatment the energy storage ability further doubled to 430 mF cm -3 with a maximum energy density of 0.04 mWh cm -3 . The FSCs based on densified CNT arrays exhibited a much higher volumetric capacitance of 1140 mF cm -3 and a larger energy density of 0.1 mWh cm -3 , with a large power density of 14 mW cm -3 . All devices show excellent stability of capacitance after at least 10 000 charge-discharge cycles with a loss of less than 2%. These easy-to-assemble hybrid arrays thus potentially provide a new method for manufacturing wearable devices and implantable medical devices.

Reconstructing high-dimensional two-photon entangled states via compressive sensing

PubMed Central

Tonolini, Francesco; Chan, Susan; Agnew, Megan; Lindsay, Alan; Leach, Jonathan

2014-01-01

Accurately establishing the state of large-scale quantum systems is an important tool in quantum information science; however, the large number of unknown parameters hinders the rapid characterisation of such states, and reconstruction procedures can become prohibitively time-consuming. Compressive sensing, a procedure for solving inverse problems by incorporating prior knowledge about the form of the solution, provides an attractive alternative to the problem of high-dimensional quantum state characterisation. Using a modified version of compressive sensing that incorporates the principles of singular value thresholding, we reconstruct the density matrix of a high-dimensional two-photon entangled system. The dimension of each photon is equal to d = 17, corresponding to a system of 83521 unknown real parameters. Accurate reconstruction is achieved with approximately 2500 measurements, only 3% of the total number of unknown parameters in the state. The algorithm we develop is fast, computationally inexpensive, and applicable to a wide range of quantum states, thus demonstrating compressive sensing as an effective technique for measuring the state of large-scale quantum systems. PMID:25306850

Analytical and numerical studies of Bose-Fermi mixtures in a one-dimensional harmonic trap

NASA Astrophysics Data System (ADS)

Dehkharghani, A. S.; Bellotti, F. F.; Zinner, N. T.

2017-07-01

In this paper we study a mixed system of bosons and fermions with up to six particles in total. All particles are assumed to have the same mass. The two-body interactions are repulsive and are assumed to have equal strength in both the Bose-Bose and the Fermi-Boson channels. The particles are confined externally by a harmonic oscillator one-body potential. For the case of four particles, two identical fermions and two identical bosons, we focus on the strongly interacting regime and analyze the system using both an analytical approach and density matrix renormalization group calculations using a discrete version of the underlying continuum Hamiltonian. This provides us with insight into both the ground state and the manifold of excited states that are almost degenerate for large interaction strength. Our results show great variation in the density profiles for bosons and fermions in different states for strongly interacting mixtures. By moving to slightly larger systems, we find that the ground state of balanced mixtures of four to six particles tends to separate bosons and fermions for strong (repulsive) interactions. On the other hand, in imbalanced Bose-Fermi mixtures we find pronounced odd-even effects in systems of five particles. These few-body results suggest that question of phase separation in one-dimensional confined mixtures are very sensitive to system composition, both for the ground state and the excited states.

Classification of matrix-product ground states corresponding to one-dimensional chains of two-state sites of nearest neighbor interactions

NASA Astrophysics Data System (ADS)

Fatollahi, Amir H.; Khorrami, Mohammad; Shariati, Ahmad; Aghamohammadi, Amir

2011-04-01

A complete classification is given for one-dimensional chains with nearest-neighbor interactions having two states in each site, for which a matrix product ground state exists. The Hamiltonians and their corresponding matrix product ground states are explicitly obtained.

Energy Dissipation of Rayleigh Waves due to Absorption Along the Path by the Use of Finite Element Method

DTIC Science & Technology

1979-07-31

3 x 3 t Strain vector a ij,j Space derivative of the stress tensor Fi Force vector per unit volume o Density x CHAPTER III F Total force K Stiffness...matrix 6Vector displacements M Mass matrix B Space operating matrix DO Matrix moduli 2 x 3 DZ Operating matrix in Z direction N Matrix of shape...dissipating medium the deformation of a solid is a function of time, temperature and space . Creep phenomenon is a deformation process in which there is

Coherent nonlinear optical studies of elementary processes in biological complexes: diagrammatic techniques based on the wave function versus the density matrix

PubMed Central

Biggs, Jason D.; Voll, Judith A.; Mukamel, Shaul

2012-01-01

Two types of diagrammatic approaches for the design and simulation of nonlinear optical experiments (closed-time path loops based on the wave function and double-sided Feynman diagrams for the density matrix) are presented and compared. We give guidelines for the assignment of relevant pathways and provide rules for the interpretation of existing nonlinear experiments in carotenoids. PMID:22753822

DOE Office of Scientific and Technical Information (OSTI.GOV)

Parrish, Robert M.; Liu, Fang; Martínez, Todd J., E-mail: toddjmartinez@gmail.com

We formulate self-consistent field (SCF) theory in terms of an interaction picture where the working variable is the difference density matrix between the true system and a corresponding superposition of atomic densities. As the difference density matrix directly represents the electronic deformations inherent in chemical bonding, this “difference self-consistent field (dSCF)” picture provides a number of significant conceptual and computational advantages. We show that this allows for a stable and efficient dSCF iterative procedure with wholly single-precision Coulomb and exchange matrix builds. We also show that the dSCF iterative procedure can be performed with aggressive screening of the pair space.more » These approximations are tested and found to be accurate for systems with up to 1860 atoms and >10 000 basis functions, providing for immediate overall speedups of up to 70% in the heavily optimized TERACHEM SCF implementation.« less

Multireference quantum chemistry through a joint density matrix renormalization group and canonical transformation theory.

PubMed

Yanai, Takeshi; Kurashige, Yuki; Neuscamman, Eric; Chan, Garnet Kin-Lic

2010-01-14

We describe the joint application of the density matrix renormalization group and canonical transformation theory to multireference quantum chemistry. The density matrix renormalization group provides the ability to describe static correlation in large active spaces, while the canonical transformation theory provides a high-order description of the dynamic correlation effects. We demonstrate the joint theory in two benchmark systems designed to test the dynamic and static correlation capabilities of the methods, namely, (i) total correlation energies in long polyenes and (ii) the isomerization curve of the [Cu(2)O(2)](2+) core. The largest complete active spaces and atomic orbital basis sets treated by the joint DMRG-CT theory in these systems correspond to a (24e,24o) active space and 268 atomic orbitals in the polyenes and a (28e,32o) active space and 278 atomic orbitals in [Cu(2)O(2)](2+).

GeV-scale hot sterile neutrino oscillations: a numerical solution

NASA Astrophysics Data System (ADS)

Ghiglieri, J.; Laine, M.

2018-02-01

The scenario of baryogenesis through GeV-scale sterile neutrino oscillations is governed by non-linear differential equations for the time evolution of a sterile neutrino density matrix and Standard Model lepton and baryon asymmetries. By employing up-to-date rate coefficients and a non-perturbatively estimated Chern-Simons diffusion rate, we present a numerical solution of this system, incorporating the full momentum and helicity dependences of the density matrix. The density matrix deviates significantly from kinetic equilibrium, with the IR modes equilibrating much faster than the UV modes. For equivalent input parameters, our final results differ moderately (˜50%) from recent benchmarks in the literature. The possibility of producing an observable baryon asymmetry is nevertheless confirmed. We illustrate the dependence of the baryon asymmetry on the sterile neutrino mass splitting and on the CP-violating phase measurable in active neutrino oscillation experiments.

A general non-Abelian density matrix renormalization group algorithm with application to the C2 dimer.

PubMed

Sharma, Sandeep

2015-01-14

We extend our previous work [S. Sharma and G. K.-L. Chan, J. Chem. Phys. 136, 124121 (2012)], which described a spin-adapted (SU(2) symmetry) density matrix renormalization group algorithm, to additionally utilize general non-Abelian point group symmetries. A key strength of the present formulation is that the requisite tensor operators are not hard-coded for each symmetry group, but are instead generated on the fly using the appropriate Clebsch-Gordan coefficients. This allows our single implementation to easily enable (or disable) any non-Abelian point group symmetry (including SU(2) spin symmetry). We use our implementation to compute the ground state potential energy curve of the C2 dimer in the cc-pVQZ basis set (with a frozen-core), corresponding to a Hilbert space dimension of 10(12) many-body states. While our calculated energy lies within the 0.3 mEh error bound of previous initiator full configuration interaction quantum Monte Carlo and correlation energy extrapolation by intrinsic scaling calculations, our estimated residual error is only 0.01 mEh, much more accurate than these previous estimates. Due to the additional efficiency afforded by the algorithm, the excitation energies (Te) of eight lowest lying excited states: a(3)Πu, b(3)Σg (-), A(1)Πu, c(3)Σu (+), B(1)Δg, B(') (1)Σg (+), d(3)Πg, and C(1)Πg are calculated, which agree with experimentally derived values to better than 0.06 eV. In addition, we also compute the potential energy curves of twelve states: the three lowest levels for each of the irreducible representations (1)Σg (+), (1)Σu (+), (1)Σg (-), and (1)Σu (-), to an estimated accuracy of 0.1 mEh of the exact result in this basis.

A general non-Abelian density matrix renormalization group algorithm with application to the C2 dimer

NASA Astrophysics Data System (ADS)

Sharma, Sandeep

2015-01-01

We extend our previous work [S. Sharma and G. K.-L. Chan, J. Chem. Phys. 136, 124121 (2012)], which described a spin-adapted (SU(2) symmetry) density matrix renormalization group algorithm, to additionally utilize general non-Abelian point group symmetries. A key strength of the present formulation is that the requisite tensor operators are not hard-coded for each symmetry group, but are instead generated on the fly using the appropriate Clebsch-Gordan coefficients. This allows our single implementation to easily enable (or disable) any non-Abelian point group symmetry (including SU(2) spin symmetry). We use our implementation to compute the ground state potential energy curve of the C2 dimer in the cc-pVQZ basis set (with a frozen-core), corresponding to a Hilbert space dimension of 1012 many-body states. While our calculated energy lies within the 0.3 mEh error bound of previous initiator full configuration interaction quantum Monte Carlo and correlation energy extrapolation by intrinsic scaling calculations, our estimated residual error is only 0.01 mEh, much more accurate than these previous estimates. Due to the additional efficiency afforded by the algorithm, the excitation energies (Te) of eight lowest lying excited states: a3Πu, b 3 Σg - , A1Πu, c 3 Σu + , B1Δg, B ' 1 Σg + , d3Πg, and C1Πg are calculated, which agree with experimentally derived values to better than 0.06 eV. In addition, we also compute the potential energy curves of twelve states: the three lowest levels for each of the irreducible representations 1 Σg + , 1 Σu + , 1 Σg - , and 1 Σu - , to an estimated accuracy of 0.1 mEh of the exact result in this basis.

Low-dimensional Representation of Error Covariance

NASA Technical Reports Server (NTRS)

Tippett, Michael K.; Cohn, Stephen E.; Todling, Ricardo; Marchesin, Dan

2000-01-01

Ensemble and reduced-rank approaches to prediction and assimilation rely on low-dimensional approximations of the estimation error covariances. Here stability properties of the forecast/analysis cycle for linear, time-independent systems are used to identify factors that cause the steady-state analysis error covariance to admit a low-dimensional representation. A useful measure of forecast/analysis cycle stability is the bound matrix, a function of the dynamics, observation operator and assimilation method. Upper and lower estimates for the steady-state analysis error covariance matrix eigenvalues are derived from the bound matrix. The estimates generalize to time-dependent systems. If much of the steady-state analysis error variance is due to a few dominant modes, the leading eigenvectors of the bound matrix approximate those of the steady-state analysis error covariance matrix. The analytical results are illustrated in two numerical examples where the Kalman filter is carried to steady state. The first example uses the dynamics of a generalized advection equation exhibiting nonmodal transient growth. Failure to observe growing modes leads to increased steady-state analysis error variances. Leading eigenvectors of the steady-state analysis error covariance matrix are well approximated by leading eigenvectors of the bound matrix. The second example uses the dynamics of a damped baroclinic wave model. The leading eigenvectors of a lowest-order approximation of the bound matrix are shown to approximate well the leading eigenvectors of the steady-state analysis error covariance matrix.

Liquid-gas phase transitions and C K symmetry in quantum field theories

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nishimura, Hiromichi; Ogilvie, Michael C.; Pangeni, Kamal

A general field-theoretic framework for the treatment of liquid-gas phase transitions is developed. Starting from a fundamental four-dimensional field theory at nonzero temperature and density, an effective three-dimensional field theory is derived. The effective field theory has a sign problem at finite density. Although finite density explicitly breaks charge conjugation C , there remains a symmetry under C K , where K is complex conjugation. Here, we consider four models: relativistic fermions, nonrelativistic fermions, static fermions and classical particles. The interactions are via an attractive potential due to scalar field exchange and a repulsive potential due to massive vector exchange.more » The field-theoretic representation of the partition function is closely related to the equivalence of the sine-Gordon field theory with a classical gas. The thermodynamic behavior is extracted from C K -symmetric complex saddle points of the effective field theory at tree level. In the cases of nonrelativistic fermions and classical particles, we find complex saddle point solutions but no first-order transitions, and neither model has a ground state at tree level. The relativistic and static fermions show a liquid-gas transition at tree level in the effective field theory. The liquid-gas transition, when it occurs, manifests as a first-order line at low temperature and high density, terminated by a critical end point. The mass matrix controlling the behavior of correlation functions is obtained from fluctuations around the saddle points. Due to the C K symmetry of the models, the eigenvalues of the mass matrix are not always real but can be complex. This then leads to the existence of disorder lines, which mark the boundaries where the eigenvalues go from purely real to complex. The regions where the mass matrix eigenvalues are complex are associated with the critical line. In the case of static fermions, a powerful duality between particles and holes allows for the analytic determination of both the critical line and the disorder lines. Depending on the values of the parameters, either zero, one, or two disorder lines are found. Our numerical results for relativistic fermions give a very similar picture.« less

Liquid-gas phase transitions and C K symmetry in quantum field theories

DOE PAGES

Nishimura, Hiromichi; Ogilvie, Michael C.; Pangeni, Kamal

2017-04-04

A general field-theoretic framework for the treatment of liquid-gas phase transitions is developed. Starting from a fundamental four-dimensional field theory at nonzero temperature and density, an effective three-dimensional field theory is derived. The effective field theory has a sign problem at finite density. Although finite density explicitly breaks charge conjugation C , there remains a symmetry under C K , where K is complex conjugation. Here, we consider four models: relativistic fermions, nonrelativistic fermions, static fermions and classical particles. The interactions are via an attractive potential due to scalar field exchange and a repulsive potential due to massive vector exchange.more » The field-theoretic representation of the partition function is closely related to the equivalence of the sine-Gordon field theory with a classical gas. The thermodynamic behavior is extracted from C K -symmetric complex saddle points of the effective field theory at tree level. In the cases of nonrelativistic fermions and classical particles, we find complex saddle point solutions but no first-order transitions, and neither model has a ground state at tree level. The relativistic and static fermions show a liquid-gas transition at tree level in the effective field theory. The liquid-gas transition, when it occurs, manifests as a first-order line at low temperature and high density, terminated by a critical end point. The mass matrix controlling the behavior of correlation functions is obtained from fluctuations around the saddle points. Due to the C K symmetry of the models, the eigenvalues of the mass matrix are not always real but can be complex. This then leads to the existence of disorder lines, which mark the boundaries where the eigenvalues go from purely real to complex. The regions where the mass matrix eigenvalues are complex are associated with the critical line. In the case of static fermions, a powerful duality between particles and holes allows for the analytic determination of both the critical line and the disorder lines. Depending on the values of the parameters, either zero, one, or two disorder lines are found. Our numerical results for relativistic fermions give a very similar picture.« less

The degree and nature of radiation damage in zircon observed by 29Si nuclear magnetic resonance

NASA Astrophysics Data System (ADS)

Farnan, I.; Salje, E. K. H.

2001-02-01

A quantitative analysis of 29Si nuclear magnetic resonance spectra of radiation damaged, natural zircons showed that the local structure in crystalline and amorphous regions depend explicitly on radiation dose. Nonpercolating amorphous islands of high density "glass" within the crystalline matrix show a low interconnectivity of SiO4 tetrahedra. This structural state is quite different from that of the high dose, percolating regions of low density glass with more polymerised tetrahedra. A continuous nonlinear dose dependence between the high and low density glass states is reported. A continuous evolution of the local structure of the crystalline phase up to the percolation point is also reported. No phase separation into binary oxides was observed. The total number of permanently displaced atoms per α-recoil event is ˜3800 atoms for low radiation doses and decreases to ˜2000 atoms for 10×1018 α events/g. No indication of partitioning of paramagnetic impurities between crystalline and amorphous regions was found for these natural zircons. The amorphous fractions of the metamict zircons were determined as a function of their accumulated radiation dose. These values coincide closely with those recently determined by x-ray diffraction studies. They are much greater than previously assumed based on density measurements. The dose dependence is consistent with the concept of direct impact amorphization in the atomic cascade following an α-recoil event.

Microfluidic engineered high cell density three-dimensional neural cultures

NASA Astrophysics Data System (ADS)

Cullen, D. Kacy; Vukasinovic, Jelena; Glezer, Ari; La Placa, Michelle C.

2007-06-01

Three-dimensional (3D) neural cultures with cells distributed throughout a thick, bioactive protein scaffold may better represent neurobiological phenomena than planar correlates lacking matrix support. Neural cells in vivo interact within a complex, multicellular environment with tightly coupled 3D cell-cell/cell-matrix interactions; however, thick 3D neural cultures at cell densities approaching that of brain rapidly decay, presumably due to diffusion limited interstitial mass transport. To address this issue, we have developed a novel perfusion platform that utilizes forced intercellular convection to enhance mass transport. First, we demonstrated that in thick (>500 µm) 3D neural cultures supported by passive diffusion, cell densities <=5.0 × 103 cells mm-3 were required for survival. In 3D neuronal and neuronal-astrocytic co-cultures with increased cell density (>=104 cells mm-3), continuous medium perfusion at 2.0-11.0 µL min-1 improved viability compared to non-perfused cultures (p < 0.01), which exhibited widespread cell death and matrix degradation. In perfused cultures, survival was dependent on proximity to the perfusion source at 2.00-6.25 µL min-1 (p < 0.05); however, at perfusion rates of 10.0-11.0 µL min-1 survival did not depend on the distance from the perfusion source, and resulted in a preservation of cell density with >90% viability in both neuronal cultures and neuronal-astrocytic co-cultures. This work demonstrates the utility of forced interstitial convection in improving the survival of high cell density 3D engineered neural constructs and may aid in the development of novel tissue-engineered systems reconstituting 3D cell-cell/cell-matrix interactions.

Spin-memory loss due to spin-orbit coupling at ferromagnet/heavy-metal interfaces: Ab initio spin-density matrix approach

NASA Astrophysics Data System (ADS)

Dolui, Kapildeb; Nikolić, Branislav K.

2017-12-01

Spin-memory loss (SML) of electrons traversing ferromagnetic-metal/heavy-metal (FM/HM), FM/normal-metal (FM/NM), and HM/NM interfaces is a fundamental phenomenon that must be invoked to explain consistently large numbers of spintronic experiments. However, its strength extracted by fitting experimental data to phenomenological semiclassical theory, which replaces each interface by a fictitious bulk diffusive layer, is poorly understood from a microscopic quantum framework and/or materials properties. Here we describe an ensemble of flowing spin quantum states using spin-density matrix, so that SML is measured like any decoherence process by the decay of its off-diagonal elements or, equivalently, by the reduction of the magnitude of polarization vector. By combining this framework with density functional theory, we examine how all three components of the polarization vector change at Co/Ta, Co/Pt, Co/Cu, Pt/Cu, and Pt/Au interfaces embedded within Cu/FM/HM/Cu vertical heterostructures. In addition, we use ab initio Green's functions to compute spectral functions and spin textures over FM, HM, and NM monolayers around these interfaces which quantify interfacial spin-orbit coupling and explain the microscopic origin of SML in long-standing puzzles, such as why it is nonzero at the Co/Cu interface; why it is very large at the Pt/Cu interface; and why it occurs even in the absence of disorder, intermixing and magnons at the interface.

Development of 10×10 Matrix-anode MCP-PMT

NASA Astrophysics Data System (ADS)

Yang, Jie; Li, Yongbin; Xu, Pengxiao; Zhao, Wenjin

2018-02-01

10×10 matrix-anode is developed by high-temperature co-fired ceramics (HTCC) technology. Based on the new matrix-anode, a new kind of photon counting imaging detector - 10×10 matrix-anode MCP-PMT is developed, and its performance parameters are tested. HTCC technology is suitable for the MCP-PMT's air impermeability and its baking process. Its response uniformity is better than the metal-ceramic or metal-glass sealing anode, and it is also a promising method to realize a higher density matrix-anode.

Oil-free hyaluronic acid matrix for serial femtosecond crystallography

NASA Astrophysics Data System (ADS)

Sugahara, Michihiro; Song, Changyong; Suzuki, Mamoru; Masuda, Tetsuya; Inoue, Shigeyuki; Nakane, Takanori; Yumoto, Fumiaki; Nango, Eriko; Tanaka, Rie; Tono, Kensuke; Joti, Yasumasa; Kameshima, Takashi; Hatsui, Takaki; Yabashi, Makina; Nureki, Osamu; Numata, Keiji; Iwata, So

2016-04-01

The grease matrix was originally introduced as a microcrystal-carrier for serial femtosecond crystallography and has been expanded to applications for various types of proteins, including membrane proteins. However, the grease-based matrix has limited application for oil-sensitive proteins. Here we introduce a grease-free, water-based hyaluronic acid matrix. Applications for proteinase K and lysozyme proteins were able to produce electron density maps at 2.3-Å resolution.

Optical properties of an inhomogeneously broadened ΛV-system with multiple excited states

NASA Astrophysics Data System (ADS)

Kaur, Paramjit; Bharti, Vineet; Wasan, Ajay

2014-09-01

We present a theoretical model using a density matrix approach to show the influence of multiple excited states on the optical properties of an inhomogeneously broadened ?V-system of the ?Rb D2 line. These closely spaced multiple excited states cause asymmetry in absorption and dispersion profiles. We observe the reduced absorption profiles, due to dressed state interactions of the applied electromagnetic fields, which results the Mollow sideband-like transparency windows. In a room temperature vapor, we obtain a narrow enhanced absorption and steep positive dispersion at the line center when the strengths of control and pump fields are equal. Here, we show how the probe transmittance varies when it passes through the atomic medium. We also discuss the transient behavior of our system which agrees well with the corresponding absorption and dispersion profiles. This study has potential applications in controllability of group velocity, and for optical and quantum information processing.

Realistic Covariance Prediction for the Earth Science Constellation

NASA Technical Reports Server (NTRS)

Duncan, Matthew; Long, Anne

2006-01-01

Routine satellite operations for the Earth Science Constellation (ESC) include collision risk assessment between members of the constellation and other orbiting space objects. One component of the risk assessment process is computing the collision probability between two space objects. The collision probability is computed using Monte Carlo techniques as well as by numerically integrating relative state probability density functions. Each algorithm takes as inputs state vector and state vector uncertainty information for both objects. The state vector uncertainty information is expressed in terms of a covariance matrix. The collision probability computation is only as good as the inputs. Therefore, to obtain a collision calculation that is a useful decision-making metric, realistic covariance matrices must be used as inputs to the calculation. This paper describes the process used by the NASA/Goddard Space Flight Center's Earth Science Mission Operations Project to generate realistic covariance predictions for three of the Earth Science Constellation satellites: Aqua, Aura and Terra.

Maximal coherence and the resource theory of purity

NASA Astrophysics Data System (ADS)

Streltsov, Alexander; Kampermann, Hermann; Wölk, Sabine; Gessner, Manuel; Bruß, Dagmar

2018-05-01

The resource theory of quantum coherence studies the off-diagonal elements of a density matrix in a distinguished basis, whereas the resource theory of purity studies all deviations from the maximally mixed state. We establish a direct connection between the two resource theories, by identifying purity as the maximal coherence which is achievable by unitary operations. The states that saturate this maximum identify a universal family of maximally coherent mixed states. These states are optimal resources under maximally incoherent operations, and thus independent of the way coherence is quantified. For all distance-based coherence quantifiers the maximal coherence can be evaluated exactly, and is shown to coincide with the corresponding distance-based purity quantifier. We further show that purity bounds the maximal amount of entanglement and discord that can be generated by unitary operations, thus demonstrating that purity is the most elementary resource for quantum information processing.

Constructing 1/omegaalpha noise from reversible Markov chains.

PubMed

Erland, Sveinung; Greenwood, Priscilla E

2007-09-01

This paper gives sufficient conditions for the output of 1/omegaalpha noise from reversible Markov chains on finite state spaces. We construct several examples exhibiting this behavior in a specified range of frequencies. We apply simple representations of the covariance function and the spectral density in terms of the eigendecomposition of the probability transition matrix. The results extend to hidden Markov chains. We generalize the results for aggregations of AR1-processes of C. W. J. Granger [J. Econometrics 14, 227 (1980)]. Given the eigenvalue function, there is a variety of ways to assign values to the states such that the 1/omegaalpha condition is satisfied. We show that a random walk on a certain state space is complementary to the point process model of 1/omega noise of B. Kaulakys and T. Meskauskas [Phys. Rev. E 58, 7013 (1998)]. Passing to a continuous state space, we construct 1/omegaalpha noise which also has a long memory.

Effects of a hyperonic many-body force on BΛ values of hypernuclei

NASA Astrophysics Data System (ADS)

Isaka, M.; Yamamoto, Y.; Rijken, Th. A.

2017-04-01

The stiff equation of state (EoS) giving the neutron-star mass of 2 M⊙ suggests the existence of strongly repulsive many-body effects (MBE) not only in nucleon channels but also in hyperonic ones. As a specific model for MBE, the repulsive multi-Pomeron exchange potential (MPP) is added to the two-body interaction together with the phenomenological three-body attraction. For various versions of the Nijmegen interaction models, the MBE parts are determined so as to reproduce the observed data of BΛ. The mass dependence of BΛ values is shown to be reproduced well by adding MBE to the strong MPP repulsion, assuring the stiff EoS of hyperon-mixed neutron-star matter, in which P -state components of the adopted interaction model lead to almost vanishing contributions. The nuclear matter Λ N G -matrix interactions are derived and used in Λ hypernuclei on the basis of the averaged-density approximation (ADA). The BΛ values of hypernuclei with 9 ≤A ≤59 are analyzed in the framework of antisymmetrized molecular dynamics with use of the two types of Λ N G -matrix interactions including strong and weak MPP repulsions. The calculated values of BΛ reproduce the experimental data well within a few hundred keV. The values of BΛ in p states also can be reproduced well, when the ADA is modified to be suitable also for weakly bound Λ states.

Performance of the density matrix functional theory in the quantum theory of atoms in molecules.

PubMed

García-Revilla, Marco; Francisco, E; Costales, A; Martín Pendás, A

2012-02-02

The generalization to arbitrary molecular geometries of the energetic partitioning provided by the atomic virial theorem of the quantum theory of atoms in molecules (QTAIM) leads to an exact and chemically intuitive energy partitioning scheme, the interacting quantum atoms (IQA) approach, that depends on the availability of second-order reduced density matrices (2-RDMs). This work explores the performance of this approach in particular and of the QTAIM in general with approximate 2-RDMs obtained from the density matrix functional theory (DMFT), which rests on the natural expansion (natural orbitals and their corresponding occupation numbers) of the first-order reduced density matrix (1-RDM). A number of these functionals have been implemented in the promolden code and used to perform QTAIM and IQA analyses on several representative molecules and model chemical reactions. Total energies, covalent intra- and interbasin exchange-correlation interactions, as well as localization and delocalization indices have been determined with these functionals from 1-RDMs obtained at different levels of theory. Results are compared to the values computed from the exact 2-RDMs, whenever possible.

Raney Distributions and Random Matrix Theory

NASA Astrophysics Data System (ADS)

Forrester, Peter J.; Liu, Dang-Zheng

2015-03-01

Recent works have shown that the family of probability distributions with moments given by the Fuss-Catalan numbers permit a simple parameterized form for their density. We extend this result to the Raney distribution which by definition has its moments given by a generalization of the Fuss-Catalan numbers. Such computations begin with an algebraic equation satisfied by the Stieltjes transform, which we show can be derived from the linear differential equation satisfied by the characteristic polynomial of random matrix realizations of the Raney distribution. For the Fuss-Catalan distribution, an equilibrium problem characterizing the density is identified. The Stieltjes transform for the limiting spectral density of the singular values squared of the matrix product formed from inverse standard Gaussian matrices, and standard Gaussian matrices, is shown to satisfy a variant of the algebraic equation relating to the Raney distribution. Supported on , we show that it too permits a simple functional form upon the introduction of an appropriate choice of parameterization. As an application, the leading asymptotic form of the density as the endpoints of the support are approached is computed, and is shown to have some universal features.

GPU acceleration of the Locally Selfconsistent Multiple Scattering code for first principles calculation of the ground state and statistical physics of materials

NASA Astrophysics Data System (ADS)

Eisenbach, Markus; Larkin, Jeff; Lutjens, Justin; Rennich, Steven; Rogers, James H.

2017-02-01

The Locally Self-consistent Multiple Scattering (LSMS) code solves the first principles Density Functional theory Kohn-Sham equation for a wide range of materials with a special focus on metals, alloys and metallic nano-structures. It has traditionally exhibited near perfect scalability on massively parallel high performance computer architectures. We present our efforts to exploit GPUs to accelerate the LSMS code to enable first principles calculations of O(100,000) atoms and statistical physics sampling of finite temperature properties. We reimplement the scattering matrix calculation for GPUs with a block matrix inversion algorithm that only uses accelerator memory. Using the Cray XK7 system Titan at the Oak Ridge Leadership Computing Facility we achieve a sustained performance of 14.5PFlop/s and a speedup of 8.6 compared to the CPU only code.

An Interview with Matthew P. Greving, PhD. Interview by Vicki Glaser.

PubMed

Greving, Matthew P

2011-10-01

Matthew P. Greving is Chief Scientific Officer at Nextval Inc., a company founded in early 2010 that has developed a discovery platform called MassInsight™.. He received his PhD in Biochemistry from Arizona State University, and prior to that he spent nearly 7 years working as a software engineer. This experience in solving complex computational problems fueled his interest in developing technologies and algorithms related to acquisition and analysis of high-dimensional biochemical data. To address the existing problems associated with label-based microarray readouts, he beganwork on a technique for label-free mass spectrometry (MS) microarray readout compatible with both matrix-assisted laser/desorption ionization (MALDI) and matrix-free nanostructure initiator mass spectrometry (NIMS). This is the core of Nextval’s MassInsight technology, which utilizes picoliter noncontact deposition of high-density arrays on mass-readout substrates along with computational algorithms for high-dimensional data processingand reduction.

Molecular Detection of Avian Influenza Virus from Sediment Samples in Waterfowl Habitats on the Delmarva Peninsula, United States.

PubMed

Densmore, C L; Iwanowicz, D D; Ottinger, C A; Hindman, L J; Bessler, A M; Iwanowicz, L R; Prosser, D J; Whitbeck, M; Driscoll, C P

2017-12-01

Avian influenza viruses (AIV) affect many species of birds including waterfowl and may persist in sediment in aquatic habitats. Sediment samples were collected from two areas representative of prime migration and overwintering waterfowl habitat in Dorchester County, Maryland in the fall and winter of 2013-2014. Samples were screened for the presence of AIV via reverse transcriptase-quantitative PCR targeting the matrix gene. Although 13.6% of sediment samples were positive for the AIV matrix gene across all collection dates and locations, differences in detection were noted with location and collection season. Percentage of AIV-positive sediment samples recovered corresponded to trends in waterfowl abundance at collection sites both temporally and spatially. These findings provide further support for the assertion that the presence of AIV in the aquatic environment is likely affected by the total number, site-specific density, and array of waterfowl species.

Structural Polymer-Based Carbon Nanotube Composite Fibers: Understanding the Processing–Structure–Performance Relationship

PubMed Central

Song, Kenan; Zhang, Yiying; Meng, Jiangsha; Green, Emily C.; Tajaddod, Navid; Li, Heng; Minus, Marilyn L.

2013-01-01

Among the many potential applications of carbon nanotubes (CNT), its usage to strengthen polymers has been paid considerable attention due to the exceptional stiffness, excellent strength, and the low density of CNT. This has provided numerous opportunities for the invention of new material systems for applications requiring high strength and high modulus. Precise control over processing factors, including preserving intact CNT structure, uniform dispersion of CNT within the polymer matrix, effective filler–matrix interfacial interactions, and alignment/orientation of polymer chains/CNT, contribute to the composite fibers’ superior properties. For this reason, fabrication methods play an important role in determining the composite fibers’ microstructure and ultimate mechanical behavior. The current state-of-the-art polymer/CNT high-performance composite fibers, especially in regards to processing–structure–performance, are reviewed in this contribution. Future needs for material by design approaches for processing these nano-composite systems are also discussed. PMID:28809290

Bivariate- distribution for transition matrix elements in Breit-Wigner to Gaussian domains of interacting particle systems.

PubMed

Kota, V K B; Chavda, N D; Sahu, R

2006-04-01

Interacting many-particle systems with a mean-field one-body part plus a chaos generating random two-body interaction having strength lambda exhibit Poisson to Gaussian orthogonal ensemble and Breit-Wigner (BW) to Gaussian transitions in level fluctuations and strength functions with transition points marked by lambda = lambda c and lambda = lambda F, respectively; lambda F > lambda c. For these systems a theory for the matrix elements of one-body transition operators is available, as valid in the Gaussian domain, with lambda > lambda F, in terms of orbital occupation numbers, level densities, and an integral involving a bivariate Gaussian in the initial and final energies. Here we show that, using a bivariate-t distribution, the theory extends below from the Gaussian regime to the BW regime up to lambda = lambda c. This is well tested in numerical calculations for 6 spinless fermions in 12 single-particle states.

Properties of quantum systems via diagonalization of transition amplitudes. II. Systematic improvements of short-time propagation

NASA Astrophysics Data System (ADS)

Vidanović, Ivana; Bogojević, Aleksandar; Balaž, Antun; Belić, Aleksandar

2009-12-01

In this paper, building on a previous analysis [I. Vidanović, A. Bogojević, and A. Belić, preceding paper, Phys. Rev. E 80, 066705 (2009)] of exact diagonalization of the space-discretized evolution operator for the study of properties of nonrelativistic quantum systems, we present a substantial improvement to this method. We apply recently introduced effective action approach for obtaining short-time expansion of the propagator up to very high orders to calculate matrix elements of space-discretized evolution operator. This improves by many orders of magnitude previously used approximations for discretized matrix elements and allows us to numerically obtain large numbers of accurate energy eigenvalues and eigenstates using numerical diagonalization. We illustrate this approach on several one- and two-dimensional models. The quality of numerically calculated higher-order eigenstates is assessed by comparison with semiclassical cumulative density of states.

GPU acceleration of the Locally Selfconsistent Multiple Scattering code for first principles calculation of the ground state and statistical physics of materials

DOE PAGES

Eisenbach, Markus; Larkin, Jeff; Lutjens, Justin; ...

2016-07-12

The Locally Self-consistent Multiple Scattering (LSMS) code solves the first principles Density Functional theory Kohn–Sham equation for a wide range of materials with a special focus on metals, alloys and metallic nano-structures. It has traditionally exhibited near perfect scalability on massively parallel high performance computer architectures. In this paper, we present our efforts to exploit GPUs to accelerate the LSMS code to enable first principles calculations of O(100,000) atoms and statistical physics sampling of finite temperature properties. We reimplement the scattering matrix calculation for GPUs with a block matrix inversion algorithm that only uses accelerator memory. Finally, using the Craymore » XK7 system Titan at the Oak Ridge Leadership Computing Facility we achieve a sustained performance of 14.5PFlop/s and a speedup of 8.6 compared to the CPU only code.« less

Robust validation of approximate 1-matrix functionals with few-electron harmonium atoms

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cioslowski, Jerzy, E-mail: jerzy@wmf.univ.szczecin.pl; Piris, Mario; Matito, Eduard

2015-12-07

A simple comparison between the exact and approximate correlation components U of the electron-electron repulsion energy of several states of few-electron harmonium atoms with varying confinement strengths provides a stringent validation tool for 1-matrix functionals. The robustness of this tool is clearly demonstrated in a survey of 14 known functionals, which reveals their substandard performance within different electron correlation regimes. Unlike spot-testing that employs dissociation curves of diatomic molecules or more extensive benchmarking against experimental atomization energies of molecules comprising some standard set, the present approach not only uncovers the flaws and patent failures of the functionals but, even moremore » importantly, also allows for pinpointing their root causes. Since the approximate values of U are computed at exact 1-densities, the testing requires minimal programming and thus is particularly suitable for rapid screening of new functionals.« less