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.

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.

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

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

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

Malone, Fionn D., E-mail: f.malone13@imperial.ac.uk; Lee, D. K. K.; Foulkes, W. M. C.

The recently developed density matrix quantum Monte Carlo (DMQMC) algorithm stochastically samples the N-body thermal density matrix and hence provides access to exact properties of many-particle quantum systems at arbitrary temperatures. We demonstrate that moving to the interaction picture provides substantial benefits when applying DMQMC to interacting fermions. In this first study, we focus on a system of much recent interest: the uniform electron gas in the warm dense regime. The basis set incompleteness error at finite temperature is investigated and extrapolated via a simple Monte Carlo sampling procedure. Finally, we provide benchmark calculations for a four-electron system, comparing ourmore » results to previous work where possible.« less

Exact and Optimal Quantum Mechanics/Molecular Mechanics Boundaries.

PubMed

Sun, Qiming; Chan, Garnet Kin-Lic

2014-09-09

Motivated by recent work in density matrix embedding theory, we define exact link orbitals that capture all quantum mechanical (QM) effects across arbitrary quantum mechanics/molecular mechanics (QM/MM) boundaries. Exact link orbitals are rigorously defined from the full QM solution, and their number is equal to the number of orbitals in the primary QM region. Truncating the exact set yields a smaller set of link orbitals optimal with respect to reproducing the primary region density matrix. We use the optimal link orbitals to obtain insight into the limits of QM/MM boundary treatments. We further analyze the popular general hybrid orbital (GHO) QM/MM boundary across a test suite of molecules. We find that GHOs are often good proxies for the most important optimal link orbital, although there is little detailed correlation between the detailed GHO composition and optimal link orbital valence weights. The optimal theory shows that anions and cations cannot be described by a single link orbital. However, expanding to include the second most important optimal link orbital in the boundary recovers an accurate description. The second optimal link orbital takes the chemically intuitive form of a donor or acceptor orbital for charge redistribution, suggesting that optimal link orbitals can be used as interpretative tools for electron transfer. We further find that two optimal link orbitals are also sufficient for boundaries that cut across double bonds. Finally, we suggest how to construct "approximately" optimal link orbitals for practical QM/MM calculations.

Energy conserving, linear scaling Born-Oppenheimer molecular dynamics.

PubMed

Cawkwell, M J; Niklasson, Anders M N

2012-10-07

Born-Oppenheimer molecular dynamics simulations with long-term conservation of the total energy and a computational cost that scales linearly with system size have been obtained simultaneously. Linear scaling with a low pre-factor is achieved using density matrix purification with sparse matrix algebra and a numerical threshold on matrix elements. The extended Lagrangian Born-Oppenheimer molecular dynamics formalism [A. M. N. Niklasson, Phys. Rev. Lett. 100, 123004 (2008)] yields microcanonical trajectories with the approximate forces obtained from the linear scaling method that exhibit no systematic drift over hundreds of picoseconds and which are indistinguishable from trajectories computed using exact forces.

RT DDA: A hybrid method for predicting the scattering properties by densely packed media

NASA Astrophysics Data System (ADS)

Ramezan Pour, B.; Mackowski, D.

2017-12-01

The most accurate approaches to predicting the scattering properties of particulate media are based on exact solutions of the Maxwell's equations (MEs), such as the T-matrix and discrete dipole methods. Applying these techniques for optically thick targets is challenging problem due to the large-scale computations and are usually substituted by phenomenological radiative transfer (RT) methods. On the other hand, the RT technique is of questionable validity in media with large particle packing densities. In recent works, we used numerically exact ME solvers to examine the effects of particle concentration on the polarized reflection properties of plane parallel random media. The simulations were performed for plane parallel layers of wavelength-sized spherical particles, and results were compared with RT predictions. We have shown that RTE results monotonically converge to the exact solution as the particle volume fraction becomes smaller and one can observe a nearly perfect fit for packing densities of 2%-5%. This study describes the hybrid technique composed of exact and numerical scalar RT methods. The exact methodology in this work is the plane parallel discrete dipole approximation whereas the numerical method is based on the adding and doubling method. This approach not only decreases the computational time owing to the RT method but also includes the interference and multiple scattering effects, so it may be applicable to large particle density conditions.

Radiative Transfer Theory Verified by Controlled Laboratory Experiments

NASA Technical Reports Server (NTRS)

Mishchenko, Michael I.; Goldstein, Dennis H.; Chowdhary, Jacek; Lompado, Arthur

2013-01-01

We report the results of high-accuracy controlled laboratory measurements of the Stokes reflection matrix for suspensions of submicrometer-sized latex particles in water and compare them with the results of a numerically exact computer solution of the vector radiative transfer equation (VRTE). The quantitative performance of the VRTE is monitored by increasing the volume packing density of the latex particles from 2 to 10. Our results indicate that the VRTE can be applied safely to random particulate media with packing densities up to 2. VRTE results for packing densities of the order of 5 should be taken with caution, whereas the polarized bidirectional reflectivity of suspensions with larger packing densities cannot be accurately predicted. We demonstrate that a simple modification of the phase matrix entering the VRTE based on the so-called static structure factor can be a promising remedy that deserves further examination.

Excitation energies from range-separated time-dependent density and density matrix functional theory.

PubMed

Pernal, Katarzyna

2012-05-14

Time-dependent density functional theory (TD-DFT) in the adiabatic formulation exhibits known failures when applied to predicting excitation energies. One of them is the lack of the doubly excited configurations. On the other hand, the time-dependent theory based on a one-electron reduced density matrix functional (time-dependent density matrix functional theory, TD-DMFT) has proven accurate in determining single and double excitations of H(2) molecule if the exact functional is employed in the adiabatic approximation. We propose a new approach for computing excited state energies that relies on functionals of electron density and one-electron reduced density matrix, where the latter is applied in the long-range region of electron-electron interactions. A similar approach has been recently successfully employed in predicting ground state potential energy curves of diatomic molecules even in the dissociation limit, where static correlation effects are dominating. In the paper, a time-dependent functional theory based on the range-separation of electronic interaction operator is rigorously formulated. To turn the approach into a practical scheme the adiabatic approximation is proposed for the short- and long-range components of the coupling matrix present in the linear response equations. In the end, the problem of finding excitation energies is turned into an eigenproblem for a symmetric matrix. Assignment of obtained excitations is discussed and it is shown how to identify double excitations from the analysis of approximate transition density matrix elements. The proposed method used with the short-range local density approximation (srLDA) and the long-range Buijse-Baerends density matrix functional (lrBB) is applied to H(2) molecule (at equilibrium geometry and in the dissociation limit) and to Be atom. The method accounts for double excitations in the investigated systems but, unfortunately, the accuracy of some of them is poor. The quality of the other excitations is in general much better than that offered by TD-DFT-LDA or TD-DMFT-BB approximations if the range-separation parameter is properly chosen. The latter remains an open problem.

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

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.

Site-occupation embedding theory using Bethe ansatz local density approximations

NASA Astrophysics Data System (ADS)

Senjean, Bruno; Nakatani, Naoki; Tsuchiizu, Masahisa; Fromager, Emmanuel

2018-06-01

Site-occupation embedding theory (SOET) is an alternative formulation of density functional theory (DFT) for model Hamiltonians where the fully interacting Hubbard problem is mapped, in principle exactly, onto an impurity-interacting (rather than a noninteracting) one. It provides a rigorous framework for combining wave-function (or Green function)-based methods with DFT. In this work, exact expressions for the per-site energy and double occupation of the uniform Hubbard model are derived in the context of SOET. As readily seen from these derivations, the so-called bath contribution to the per-site correlation energy is, in addition to the latter, the key density functional quantity to model in SOET. Various approximations based on Bethe ansatz and perturbative solutions to the Hubbard and single-impurity Anderson models are constructed and tested on a one-dimensional ring. The self-consistent calculation of the embedded impurity wave function has been performed with the density-matrix renormalization group method. It has been shown that promising results are obtained in specific regimes of correlation and density. Possible further developments have been proposed in order to provide reliable embedding functionals and potentials.

Symmetry Transition Preserving Chirality in QCD: A Versatile Random Matrix Model

NASA Astrophysics Data System (ADS)

Kanazawa, Takuya; Kieburg, Mario

2018-06-01

We consider a random matrix model which interpolates between the chiral Gaussian unitary ensemble and the Gaussian unitary ensemble while preserving chiral symmetry. This ensemble describes flavor symmetry breaking for staggered fermions in 3D QCD as well as in 4D QCD at high temperature or in 3D QCD at a finite isospin chemical potential. Our model is an Osborn-type two-matrix model which is equivalent to the elliptic ensemble but we consider the singular value statistics rather than the complex eigenvalue statistics. We report on exact results for the partition function and the microscopic level density of the Dirac operator in the ɛ regime of QCD. We compare these analytical results with Monte Carlo simulations of the matrix model.

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.

Continuum Level Density of a Coupled-Channel System in the Complex Scaling Method

NASA Astrophysics Data System (ADS)

Suzuki, R.; Kruppa, A. T.; Giraud, B. G.; Katō, K.

2008-06-01

We study the continuum level density (CLD) in the formalism of the complex scaling method (CSM) for coupled-channel systems. We apply the formalism to the ^{4}He = [^{3}H + p] + [^3{He} + n] coupled-channel cluster model where there are resonances at low energy. Numerical calculations of the CLD in the CSM with a finite number of L^{2} basis functions are consistent with the exact result calculated from the S-matrix by solving coupled-channel equations. We also study channel densities. In this framework, the extended completeness relation (ECR) plays an important role.

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

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."

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

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.

Measuring order in disordered systems and disorder in ordered systems: Random matrix theory for isotropic and nematic liquid crystals and its perspective on pseudo-nematic domains

NASA Astrophysics Data System (ADS)

Zhao, Yan; Stratt, Richard M.

2018-05-01

Surprisingly long-ranged intermolecular correlations begin to appear in isotropic (orientationally disordered) phases of liquid crystal forming molecules when the temperature or density starts to close in on the boundary with the nematic (ordered) phase. Indeed, the presence of slowly relaxing, strongly orientationally correlated, sets of molecules under putatively disordered conditions ("pseudo-nematic domains") has been apparent for some time from light-scattering and optical-Kerr experiments. Still, a fully microscopic characterization of these domains has been lacking. We illustrate in this paper how pseudo-nematic domains can be studied in even relatively small computer simulations by looking for order-parameter tensor fluctuations much larger than one would expect from random matrix theory. To develop this idea, we show that random matrix theory offers an exact description of how the probability distribution for liquid-crystal order parameter tensors converges to its macroscopic-system limit. We then illustrate how domain properties can be inferred from finite-size-induced deviations from these random matrix predictions. A straightforward generalization of time-independent random matrix theory also allows us to prove that the analogous random matrix predictions for the time dependence of the order-parameter tensor are similarly exact in the macroscopic limit, and that relaxation behavior of the domains can be seen in the breakdown of the finite-size scaling required by that random-matrix theory.

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.

Fast, exact k-space sample density compensation for trajectories composed of rotationally symmetric segments, and the SNR-optimized image reconstruction from non-Cartesian samples.

PubMed

Mitsouras, Dimitris; Mulkern, Robert V; Rybicki, Frank J

2008-08-01

A recently developed method for exact density compensation of non uniformly arranged samples relies on the analytically known cross-correlations of Fourier basis functions corresponding to the traced k-space trajectory. This method produces a linear system whose solution represents compensated samples that normalize the contribution of each independent element of information that can be expressed by the underlying trajectory. Unfortunately, linear system-based density compensation approaches quickly become computationally demanding with increasing number of samples (i.e., image resolution). Here, it is shown that when a trajectory is composed of rotationally symmetric interleaves, such as spiral and PROPELLER trajectories, this cross-correlations method leads to a highly simplified system of equations. Specifically, it is shown that the system matrix is circulant block-Toeplitz so that the linear system is easily block-diagonalized. The method is described and demonstrated for 32-way interleaved spiral trajectories designed for 256 image matrices; samples are compensated non iteratively in a few seconds by solving the small independent block-diagonalized linear systems in parallel. Because the method is exact and considers all the interactions between all acquired samples, up to a 10% reduction in reconstruction error concurrently with an up to 30% increase in signal to noise ratio are achieved compared to standard density compensation methods. (c) 2008 Wiley-Liss, Inc.

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.

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.

Generalization of the Kohn-Sham system that can represent arbitrary one-electron density matrices

DOE PAGES

Hubertus J. J. van Dam

2016-04-27

Density functional theory is currently the most widely applied method in electronic structure theory. The Kohn-Sham method, based on a fictitious system of noninteracting particles, is the workhorse of the theory. The particular form of the Kohn-Sham wave function admits only idempotent one-electron density matrices whereas wave functions of correlated electrons in post-Hartree-Fock methods invariably have fractional occupation numbers. Here we show that by generalizing the orbital concept and introducing a suitable dot product as well as a probability density, a noninteracting system can be chosen that can represent the one-electron density matrix of any system, even one with fractionalmore » occupation numbers. This fictitious system ensures that the exact electron density is accessible within density functional theory. It can also serve as the basis for reduced density matrix functional theory. Moreover, to aid the analysis of the results the orbitals may be assigned energies from a mean-field Hamiltonian. This produces energy levels that are akin to Hartree-Fock orbital energies such that conventional analyses based on Koopmans' theorem are available. Lastly, this system is convenient in formalisms that depend on creation and annihilation operators as they are trivially applied to single-determinant wave functions.« less

Entanglement dynamics in a non-Markovian environment: An exactly solvable model

NASA Astrophysics Data System (ADS)

Wilson, Justin H.; Fregoso, Benjamin M.; Galitski, Victor M.

2012-05-01

We study the non-Markovian effects on the dynamics of entanglement in an exactly solvable model that involves two independent oscillators, each coupled to its own stochastic noise source. First, we develop Lie algebraic and functional integral methods to find an exact solution to the single-oscillator problem which includes an analytic expression for the density matrix and the complete statistics, i.e., the probability distribution functions for observables. For long bath time correlations, we see nonmonotonic evolution of the uncertainties in observables. Further, we extend this exact solution to the two-particle problem and find the dynamics of entanglement in a subspace. We find the phenomena of “sudden death” and “rebirth” of entanglement. Interestingly, all memory effects enter via the functional form of the energy and hence the time of death and rebirth is controlled by the amount of noisy energy added into each oscillator. If this energy increases above (decreases below) a threshold, we obtain sudden death (rebirth) of entanglement.

Exact formulas for multipole moments using Slater-type molecular orbitals

NASA Technical Reports Server (NTRS)

Jones, H. W.

1986-01-01

A triple infinite sum of formulas expressed as an expansion in Legendre polynomials is generated by use of computer algebra to represent the potential from the midpoint of two Slater-type orbitals; the charge density that determines the potential is given as the product of the two orbitals. An example using 1s orbitals shows that only a few terms are needed to obtain four-figure accuracy. Exact formulas are obtained for multipole moments by means of a careful study of expanded formulas, allowing an 'extrapolation to infinity'. This Loewdin alpha-function approach augmented by using a C matrix to characterize Slater-type orbitals can be readily generalized to all cases.

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.

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

Exact stochastic unraveling of an optical coherence dynamics by cumulant expansion

NASA Astrophysics Data System (ADS)

Olšina, Jan; Kramer, Tobias; Kreisbeck, Christoph; Mančal, Tomáš

2014-10-01

A numerically exact Monte Carlo scheme for calculation of open quantum system dynamics is proposed and implemented. The method consists of a Monte Carlo summation of a perturbation expansion in terms of trajectories in Liouville phase-space with respect to the coupling between the excited states of the molecule. The trajectories are weighted by a complex decoherence factor based on the second-order cumulant expansion of the environmental evolution. The method can be used with an arbitrary environment characterized by a general correlation function and arbitrary coupling strength. It is formally exact for harmonic environments, and it can be used with arbitrary temperature. Time evolution of an optically excited Frenkel exciton dimer representing a molecular exciton interacting with a charge transfer state is calculated by the proposed method. We calculate the evolution of the optical coherence elements of the density matrix and linear absorption spectrum, and compare them with the predictions of standard simulation methods.

Theory of time-resolved photoelectron imaging. Comparison of a density functional with a time-dependent density functional approach

NASA Astrophysics Data System (ADS)

Suzuki, Yoshi-ichi; Seideman, Tamar; Stener, Mauro

2004-01-01

Time-resolved photoelectron differential cross sections are computed within a quantum dynamical theory that combines a formally exact solution of the nuclear dynamics with density functional theory (DFT)-based approximations of the electronic dynamics. Various observables of time-resolved photoelectron imaging techniques are computed at the Kohn-Sham and at the time-dependent DFT levels. Comparison of the results serves to assess the reliability of the former method and hence its usefulness as an economic approach for time-domain photoelectron cross section calculations, that is applicable to complex polyatomic systems. Analysis of the matrix elements that contain the electronic dynamics provides insight into a previously unexplored aspect of femtosecond-resolved photoelectron imaging.

Optical Control of Intersubband Absorption in a Multiple Quantum Well-Embedded Semiconductor Microcravity

NASA Technical Reports Server (NTRS)

Liu, Ansheng; Ning, Cun-Zheng

2000-01-01

Optical intersubband response of a multiple quantum well (MQW)-embedded microcavity driven by a coherent pump field is studied theoretically. The n-type doped MQW structure with three subbands in the conduction band is sandwiched between a semi-infinite medium and a distributed Bragg reflector (DBR). A strong pump field couples the two upper subbands and a weak field probes the two lower subbands. To describe the optical response of the MQW-embedded microcavity, we adopt a semi-classical nonlocal response theory. Taking into account the pump-probe interaction, we derive the probe-induced current density associated with intersubband transitions from the single-particle density-matrix formalism. By incorporating the current density into the Maxwell equation, we solve the probe local field exactly by means of Green's function technique and the transfer-matrix method. We obtain an exact expression for the probe absorption coefficient of the microcavity. For a GaAs/Al(sub x)Ga(sub 1-x)As MQW structure sandwiched between a GaAs/AlAs DBR and vacuum, we performed numerical calculations of the probe absorption spectra for different parameters such as pump intensity, pump detuning, and cavity length. We find that the probe spectrum is strongly dependent on these parameters. In particular, we find that the combination of the cavity effect and the Autler-Townes effect results in a triplet in the optical spectrum of the MQW system. The optical absorption peak value and its location can be feasibly controlled by varying the pump intensity and detuning.

Electronic coupling matrix elements from charge constrained density functional theory calculations using a plane wave basis set

NASA Astrophysics Data System (ADS)

Oberhofer, Harald; Blumberger, Jochen

2010-12-01

We present a plane wave basis set implementation for the calculation of electronic coupling matrix elements of electron transfer reactions within the framework of constrained density functional theory (CDFT). Following the work of Wu and Van Voorhis [J. Chem. Phys. 125, 164105 (2006)], the diabatic wavefunctions are approximated by the Kohn-Sham determinants obtained from CDFT calculations, and the coupling matrix element calculated by an efficient integration scheme. Our results for intermolecular electron transfer in small systems agree very well with high-level ab initio calculations based on generalized Mulliken-Hush theory, and with previous local basis set CDFT calculations. The effect of thermal fluctuations on the coupling matrix element is demonstrated for intramolecular electron transfer in the tetrathiafulvalene-diquinone (Q-TTF-Q-) anion. Sampling the electronic coupling along density functional based molecular dynamics trajectories, we find that thermal fluctuations, in particular the slow bending motion of the molecule, can lead to changes in the instantaneous electron transfer rate by more than an order of magnitude. The thermal average, ( {< {| {H_ab } |^2 } > } )^{1/2} = 6.7 {mH}, is significantly higher than the value obtained for the minimum energy structure, | {H_ab } | = 3.8 {mH}. While CDFT in combination with generalized gradient approximation (GGA) functionals describes the intermolecular electron transfer in the studied systems well, exact exchange is required for Q-TTF-Q- in order to obtain coupling matrix elements in agreement with experiment (3.9 mH). The implementation presented opens up the possibility to compute electronic coupling matrix elements for extended systems where donor, acceptor, and the environment are treated at the quantum mechanical (QM) level.

A second-order unconstrained optimization method for canonical-ensemble density-functional methods

NASA Astrophysics Data System (ADS)

Nygaard, Cecilie R.; Olsen, Jeppe

2013-03-01

A second order converging method of ensemble optimization (SOEO) in the framework of Kohn-Sham Density-Functional Theory is presented, where the energy is minimized with respect to an ensemble density matrix. It is general in the sense that the number of fractionally occupied orbitals is not predefined, but rather it is optimized by the algorithm. SOEO is a second order Newton-Raphson method of optimization, where both the form of the orbitals and the occupation numbers are optimized simultaneously. To keep the occupation numbers between zero and two, a set of occupation angles is defined, from which the occupation numbers are expressed as trigonometric functions. The total number of electrons is controlled by a built-in second order restriction of the Newton-Raphson equations, which can be deactivated in the case of a grand-canonical ensemble (where the total number of electrons is allowed to change). To test the optimization method, dissociation curves for diatomic carbon are produced using different functionals for the exchange-correlation energy. These curves show that SOEO favors symmetry broken pure-state solutions when using functionals with exact exchange such as Hartree-Fock and Becke three-parameter Lee-Yang-Parr. This is explained by an unphysical contribution to the exact exchange energy from interactions between fractional occupations. For functionals without exact exchange, such as local density approximation or Becke Lee-Yang-Parr, ensemble solutions are favored at interatomic distances larger than the equilibrium distance. Calculations on the chromium dimer are also discussed. They show that SOEO is able to converge to ensemble solutions for systems that are more complicated than diatomic carbon.

Exact zeros of entanglement for arbitrary rank-two mixtures derived from a geometric view of the zero polytope

NASA Astrophysics Data System (ADS)

Osterloh, Andreas

2016-12-01

Here I present a method for how intersections of a certain density matrix of rank 2 with the zero polytope can be calculated exactly. This is a purely geometrical procedure which thereby is applicable to obtaining the zeros of SL- and SU-invariant entanglement measures of arbitrary polynomial degree. I explain this method in detail for a recently unsolved problem. In particular, I show how a three-dimensional view, namely, in terms of the Bloch-sphere analogy, solves this problem immediately. To this end, I determine the zero polytope of the three-tangle, which is an exact result up to computer accuracy, and calculate upper bounds to its convex roof which are below the linearized upper bound. The zeros of the three-tangle (in this case) induced by the zero polytope (zero simplex) are exact values. I apply this procedure to a superposition of the four-qubit Greenberger-Horne-Zeilinger and W state. It can, however, be applied to every case one has under consideration, including an arbitrary polynomial convex-roof measure of entanglement and for arbitrary local dimension.

A new model for impregnation mechanisms in different GF/PP commingled yarns

NASA Astrophysics Data System (ADS)

Klinkmüller, V.; Um, M.-K.; Steffens, M.; Friedrich, K.; Kim, B.-S.

1994-09-01

Impregnation mechanisms of different kinds of GF/PP commingled yarns have been studied. As the reinforcing fibres were always the same, a global description has been worked out. Two different mathematical approaches for fibre bed permeability (Kozeny-Carman and Gutowski) were compared. The constants of the applied mathematical models have to stay the same if the fibre reeinforcement and the fibre arrangement is the same. Neither the kind of matrix, nor the fibre volume content may change these constants. Differences in the degree of impregnation after the same process conditions can be only due to different sizes of fibre agglomerations, thus the initial distribution of reinforcing fibres and matrix. For an exact determination of impregnation times and conditions the exact distribution of fibres in the intermediate material and after processing has to be known. This distribution is determined by SEM microscopy and data given from the material supplier. The importance of different process parameters, such as temperature, pressure, processing time is weighted by determining the density and mechanical properties of the specimens.

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.

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.

Nature of Continuous Phase Transitions in Interacting Topological Insulators

DOE PAGES

Zeng, Tian-sheng; Zhu, Wei; Zhu, Jianxin; ...

2017-11-08

Here, we revisit the effects of the Hubbard repulsion on quantum spin Hall effects (QSHE) in two-dimensional quantum lattice models. We present both unbiased exact diagonalization and density-matrix renormalization group simulations with numerical evidence for a continuous quantum phase transition (CQPT) separating QSHE from the topologically trivial antiferromagnetic phase. Our numerical results suggest that the nature of CQPT exhibits distinct finite-size scaling behaviors, which may be consistent with either Ising or XY universality classes for different time-reversal symmetric QSHE systems.

Nature of Continuous Phase Transitions in Interacting Topological Insulators

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

Zeng, Tian-sheng; Zhu, Wei; Zhu, Jianxin

Here, we revisit the effects of the Hubbard repulsion on quantum spin Hall effects (QSHE) in two-dimensional quantum lattice models. We present both unbiased exact diagonalization and density-matrix renormalization group simulations with numerical evidence for a continuous quantum phase transition (CQPT) separating QSHE from the topologically trivial antiferromagnetic phase. Our numerical results suggest that the nature of CQPT exhibits distinct finite-size scaling behaviors, which may be consistent with either Ising or XY universality classes for different time-reversal symmetric QSHE systems.

Path integral Monte Carlo and the electron gas

NASA Astrophysics Data System (ADS)

Brown, Ethan W.

Path integral Monte Carlo is a proven method for accurately simulating quantum mechanical systems at finite-temperature. By stochastically sampling Feynman's path integral representation of the quantum many-body density matrix, path integral Monte Carlo includes non-perturbative effects like thermal fluctuations and particle correlations in a natural way. Over the past 30 years, path integral Monte Carlo has been successfully employed to study the low density electron gas, high-pressure hydrogen, and superfluid helium. For systems where the role of Fermi statistics is important, however, traditional path integral Monte Carlo simulations have an exponentially decreasing efficiency with decreased temperature and increased system size. In this thesis, we work towards improving this efficiency, both through approximate and exact methods, as specifically applied to the homogeneous electron gas. We begin with a brief overview of the current state of atomic simulations at finite-temperature before we delve into a pedagogical review of the path integral Monte Carlo method. We then spend some time discussing the one major issue preventing exact simulation of Fermi systems, the sign problem. Afterwards, we introduce a way to circumvent the sign problem in PIMC simulations through a fixed-node constraint. We then apply this method to the homogeneous electron gas at a large swatch of densities and temperatures in order to map out the warm-dense matter regime. The electron gas can be a representative model for a host of real systems, from simple medals to stellar interiors. However, its most common use is as input into density functional theory. To this end, we aim to build an accurate representation of the electron gas from the ground state to the classical limit and examine its use in finite-temperature density functional formulations. The latter half of this thesis focuses on possible routes beyond the fixed-node approximation. As a first step, we utilize the variational principle inherent in the path integral Monte Carlo method to optimize the nodal surface. By using a ansatz resembling a free particle density matrix, we make a unique connection between a nodal effective mass and the traditional effective mass of many-body quantum theory. We then propose and test several alternate nodal ansatzes and apply them to single atomic systems. Finally, we propose a method to tackle the sign problem head on, by leveraging the relatively simple structure of permutation space. Using this method, we find we can perform exact simulations this of the electron gas and 3He that were previously impossible.

Ultrastable light sources in the crossover from superradiance to lasing

NASA Astrophysics Data System (ADS)

Xu, Minghui; Tieri, David; Holland, Murray

2013-05-01

We theoretically investigate the crossover from steady-state superradiance to optical lasing. An exact solution of the quantum master equation is difficult to obtain due to the exponential scaling of the Hilbert space dimension with system size. However, since Lindblad operators in the master equation are invariant under SU(4) transformations, we are able to reduce the exponential scaling of the problem to cubic by expanding the density matrix in terms of an SU(4) basis. In this way, we obtain exact quantum solutions of the superradiance-laser crossover. We use this theory to investigate the potential for ultrastable lasers in the millihertz linewidth regime, and find the behavior of important observables, such as intensity, linewidth, spin-correlation, and entanglement. This work was supported by the DARPA QUASAR program and NSF.

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.

Exact mapping between system-reservoir quantum models and semi-infinite discrete chains using orthogonal polynomials

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

Chin, Alex W.; Rivas, Angel; Huelga, Susana F.

2010-09-15

By using the properties of orthogonal polynomials, we present an exact unitary transformation that maps the Hamiltonian of a quantum system coupled linearly to a continuum of bosonic or fermionic modes to a Hamiltonian that describes a one-dimensional chain with only nearest-neighbor interactions. This analytical transformation predicts a simple set of relations between the parameters of the chain and the recurrence coefficients of the orthogonal polynomials used in the transformation and allows the chain parameters to be computed using numerically stable algorithms that have been developed to compute recurrence coefficients. We then prove some general properties of this chain systemmore » for a wide range of spectral functions and give examples drawn from physical systems where exact analytic expressions for the chain properties can be obtained. Crucially, the short-range interactions of the effective chain system permit these open-quantum systems to be efficiently simulated by the density matrix renormalization group methods.« less

Unifying model for random matrix theory in arbitrary space dimensions

NASA Astrophysics Data System (ADS)

Cicuta, Giovanni M.; Krausser, Johannes; Milkus, Rico; Zaccone, Alessio

2018-03-01

A sparse random block matrix model suggested by the Hessian matrix used in the study of elastic vibrational modes of amorphous solids is presented and analyzed. By evaluating some moments, benchmarked against numerics, differences in the eigenvalue spectrum of this model in different limits of space dimension d , and for arbitrary values of the lattice coordination number Z , are shown and discussed. As a function of these two parameters (and their ratio Z /d ), the most studied models in random matrix theory (Erdos-Renyi graphs, effective medium, and replicas) can be reproduced in the various limits of block dimensionality d . Remarkably, the Marchenko-Pastur spectral density (which is recovered by replica calculations for the Laplacian matrix) is reproduced exactly in the limit of infinite size of the blocks, or d →∞ , which clarifies the physical meaning of space dimension in these models. We feel that the approximate results for d =3 provided by our method may have many potential applications in the future, from the vibrational spectrum of glasses and elastic networks to wave localization, disordered conductors, random resistor networks, and random walks.

Connection between the regular approximation and the normalized elimination of the small component in relativistic quantum theory

NASA Astrophysics Data System (ADS)

Filatov, Michael; Cremer, Dieter

2005-02-01

The regular approximation to the normalized elimination of the small component (NESC) in the modified Dirac equation has been developed and presented in matrix form. The matrix form of the infinite-order regular approximation (IORA) expressions, obtained in [Filatov and Cremer, J. Chem. Phys. 118, 6741 (2003)] using the resolution of the identity, is the exact matrix representation and corresponds to the zeroth-order regular approximation to NESC (NESC-ZORA). Because IORA (=NESC-ZORA) is a variationally stable method, it was used as a suitable starting point for the development of the second-order regular approximation to NESC (NESC-SORA). As shown for hydrogenlike ions, NESC-SORA energies are closer to the exact Dirac energies than the energies from the fifth-order Douglas-Kroll approximation, which is much more computationally demanding than NESC-SORA. For the application of IORA (=NESC-ZORA) and NESC-SORA to many-electron systems, the number of the two-electron integrals that need to be evaluated (identical to the number of the two-electron integrals of a full Dirac-Hartree-Fock calculation) was drastically reduced by using the resolution of the identity technique. An approximation was derived, which requires only the two-electron integrals of a nonrelativistic calculation. The accuracy of this approach was demonstrated for heliumlike ions. The total energy based on the approximate integrals deviates from the energy calculated with the exact integrals by less than 5×10-9hartree units. NESC-ZORA and NESC-SORA can easily be implemented in any nonrelativistic quantum chemical program. Their application is comparable in cost with that of nonrelativistic methods. The methods can be run with density functional theory and any wave function method. NESC-SORA has the advantage that it does not imply a picture change.

Accurate Semilocal Density Functional for Condensed-Matter Physics and Quantum Chemistry.

PubMed

Tao, Jianmin; Mo, Yuxiang

2016-08-12

Most density functionals have been developed by imposing the known exact constraints on the exchange-correlation energy, or by a fit to a set of properties of selected systems, or by both. However, accurate modeling of the conventional exchange hole presents a great challenge, due to the delocalization of the hole. Making use of the property that the hole can be made localized under a general coordinate transformation, here we derive an exchange hole from the density matrix expansion, while the correlation part is obtained by imposing the low-density limit constraint. From the hole, a semilocal exchange-correlation functional is calculated. Our comprehensive test shows that this functional can achieve remarkable accuracy for diverse properties of molecules, solids, and solid surfaces, substantially improving upon the nonempirical functionals proposed in recent years. Accurate semilocal functionals based on their associated holes are physically appealing and practically useful for developing nonlocal functionals.

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

Filinov, A.V.; Golubnychiy, V.O.; Bonitz, M.

Extending our previous work [A.V. Filinov et al., J. Phys. A 36, 5957 (2003)], we present a detailed discussion of accuracy and practical applications of finite-temperature pseudopotentials for two-component Coulomb systems. Different pseudopotentials are discussed: (i) the diagonal Kelbg potential, (ii) the off-diagonal Kelbg potential, (iii) the improved diagonal Kelbg potential, (iv) an effective potential obtained with the Feynman-Kleinert variational principle, and (v) the 'exact' quantum pair potential derived from the two-particle density matrix. For the improved diagonal Kelbg potential, a simple temperature-dependent fit is derived which accurately reproduces the 'exact' pair potential in the whole temperature range. The derivedmore » pseudopotentials are then used in path integral Monte Carlo and molecular-dynamics (MD) simulations to obtain thermodynamical properties of strongly coupled hydrogen. It is demonstrated that classical MD simulations with spin-dependent interaction potentials for the electrons allow for an accurate description of the internal energy of hydrogen in the difficult regime of partial ionization down to the temperatures of about 60 000 K. Finally, we point out an interesting relationship between the quantum potentials and the effective potentials used in density-functional theory.« less

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

Density functional with full exact exchange, balanced nonlocality of correlations, and constraint satisfaction

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

Tao, Jianmin; Perdew, John P; Staroverov, Viktor N

2008-01-01

We construct a nonlocal density functional approximation with full exact exchange, while preserving the constraint-satisfaction approach and justified error cancellations of simpler semilocal functionals. This is achieved by interpolating between different approximations suitable for two extreme regions of the electron density. In a 'normal' region, the exact exchange-correlation hole density around an electron is semilocal because its spatial range is reduced by correlation and because it integrates over a narrow range to -1. These regions are well described by popular semilocal approximations (many of which have been constructed nonempirically), because of proper accuracy for a slowly-varying density or because ofmore » error cancellation between exchange and correlation. 'Abnormal' regions, where non locality is unveiled, include those in which exchange can dominate correlation (one-electron, nonuniform high-density, and rapidly-varying limits), and those open subsystems of fluctuating electron number over which the exact exchange-correlation hole integrates to a value greater than -1. Regions between these extremes are described by a hybrid functional mixing exact and semi local exchange energy densities locally (i.e., with a mixing fraction that is a function of position r and a functional of the density). Because our mixing fraction tends to 1 in the high-density limit, we employ full exact exchange according to the rigorous definition of the exchange component of any exchange-correlation energy functional. Use of full exact exchange permits the satisfaction of many exact constraints, but the nonlocality of exchange also requires balanced nonlocality of correlation. We find that this nonlocality can demand at least five empirical parameters (corresponding roughly to the four kinds of abnormal regions). Our local hybrid functional is perhaps the first accurate size-consistent density functional with full exact exchange. It satisfies other known exact constraints, including exactness for all one-electron densities, and provides an excellent, fit 1.0 the 223 molecular enthalpies of formation of the G3/99 set and the 42 reaction barrier heights of the BH42/03 set, improving both (but especially the latter) over most semilocal functionals and global hybrids. Exact constraints, physical insights, and paradigm examples hopefully suppress 'overfitting'.« less

Does a Single Eigenstate Encode the Full Hamiltonian?

NASA Astrophysics Data System (ADS)

Garrison, James R.; Grover, Tarun

2018-04-01

The eigenstate thermalization hypothesis (ETH) posits that the reduced density matrix for a subsystem corresponding to an excited eigenstate is "thermal." Here we expound on this hypothesis by asking: For which class of operators, local or nonlocal, is ETH satisfied? We show that this question is directly related to a seemingly unrelated question: Is the Hamiltonian of a system encoded within a single eigenstate? We formulate a strong form of ETH where, in the thermodynamic limit, the reduced density matrix of a subsystem corresponding to a pure, finite energy density eigenstate asymptotically becomes equal to the thermal reduced density matrix, as long as the subsystem size is much less than the total system size, irrespective of how large the subsystem is compared to any intrinsic length scale of the system. This allows one to access the properties of the underlying Hamiltonian at arbitrary energy densities (or temperatures) using just a single eigenstate. We provide support for our conjecture by performing an exact diagonalization study of a nonintegrable 1D quantum lattice model with only energy conservation. In addition, we examine the case in which the subsystem size is a finite fraction of the total system size, and we find that, even in this case, many operators continue to match their canonical expectation values, at least approximately. In particular, the von Neumann entanglement entropy equals the thermal entropy as long as the subsystem is less than half the total system. Our results are consistent with the possibility that a single eigenstate correctly predicts the expectation values of all operators with support on less than half the total system, as long as one uses a microcanonical ensemble with vanishing energy width for comparison. We also study, both analytically and numerically, a particle-number conserving model at infinite temperature that substantiates our conjectures.

Approximations and Implementations of Nonlinear Filtering Schemes.

DTIC Science & Technology

1988-02-01

17) 0 0 3) P(fn) - (pf)n 4) Pf v0 - (Po <-> dp - (p0 dm is invariant under f (i.e. for all measurable A: (f’l(A)) - p(A) Remark: The Perron - Frobenius ...invariant density of the map f is then nothing else than the fixed point of the Perron - Frobenius operator. The following theorem by Lasota and Yorke [8...transition matrix R is defined. With this construct, the Perron - Frobenius operator is effectively 39 A A . w7 approximated (exact for Markov Maps)by

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.

Fractional charge and emergent mass hierarchy in diagonal two-leg t – J cylinders

DOE PAGES

Jiang, Yi-Fan; Jiang, Hong-Chen; Yao, Hong; ...

2017-06-06

Here, we define a class of “diagonal” tmore » $-$ J ladders rotated by π / 4 relative to the canonical lattice directions of the square lattice, and study it using density matrix renormalization group. Here, we focus on the two-leg cylinder with a doped hole concentration near x = $$\\frac{1}{4}$$ . At exactly x = $$\\frac{1}{4}$$, the system forms a period 4 charge density wave and exhibits spin-charge separation. Slightly away from $$\\frac{1}{4}$$ doping, we observe several topologically distinct types of solitons with well-defined fractionalized quantum numbers. Remarkably, given the absence of any obvious small parameter, the effective masses of the emergent solitons differ by several orders of magnitude.« less

Exact solution for four-order acousto-optic Bragg diffraction with arbitrary initial conditions.

PubMed

Pieper, Ron; Koslover, Deborah; Poon, Ting-Chung

2009-03-01

An exact solution to the four-order acousto-optic (AO) Bragg diffraction problem with arbitrary initial conditions compatible with exact Bragg angle incident light is developed. The solution, obtained by solving a 4th-order differential equation, is formalized into a transition matrix operator predicting diffracted light orders at the exit of the AO cell in terms of the same diffracted light orders at the entrance. It is shown that the transition matrix is unitary and that this unitary matrix condition is sufficient to guarantee energy conservation. A comparison of analytical solutions with numerical predictions validates the formalism. Although not directly related to the approach used to obtain the solution, it was discovered that all four generated eigenvalues from the four-order AO differential matrix operator are expressed simply in terms of Euclid's Divine Proportion.

Class of cooperative stochastic models: Exact and approximate solutions, simulations, and experiments using ionic self-assembly of nanoparticles.

PubMed

Mazilu, I; Mazilu, D A; Melkerson, R E; Hall-Mejia, E; Beck, G J; Nshimyumukiza, S; da Fonseca, Carlos M

2016-03-01

We present exact and approximate results for a class of cooperative sequential adsorption models using matrix theory, mean-field theory, and computer simulations. We validate our models with two customized experiments using ionically self-assembled nanoparticles on glass slides. We also address the limitations of our models and their range of applicability. The exact results obtained using matrix theory can be applied to a variety of two-state systems with cooperative effects.

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.

Role of protein fluctuation correlations in electron transfer in photosynthetic complexes.

PubMed

Nesterov, Alexander I; Berman, Gennady P

2015-04-01

We consider the dependence of the electron transfer in photosynthetic complexes on correlation properties of random fluctuations of the protein environment. The electron subsystem is modeled by a finite network of connected electron (exciton) sites. The fluctuations of the protein environment are modeled by random telegraph processes, which act either collectively (correlated) or independently (uncorrelated) on the electron sites. We derived an exact closed system of first-order linear differential equations with constant coefficients, for the average density matrix elements and for their first moments. Under some conditions, we obtained analytic expressions for the electron transfer rates and found the range of parameters for their applicability by comparing with the exact numerical simulations. We also compared the correlated and uncorrelated regimes and demonstrated numerically that the uncorrelated fluctuations of the protein environment can, under some conditions, either increase or decrease the electron transfer rates.

Modeling of Electromagnetic Scattering by Discrete and Discretely Heterogeneous Random Media by Using Numerically Exact Solutions of the Maxwell Equations

NASA Technical Reports Server (NTRS)

Dlugach, Janna M.; Mishchenko, Michael I.

2017-01-01

In this paper, we discuss some aspects of numerical modeling of electromagnetic scattering by discrete random medium by using numerically exact solutions of the macroscopic Maxwell equations. Typical examples of such media are clouds of interstellar dust, clouds of interplanetary dust in the Solar system, dusty atmospheres of comets, particulate planetary rings, clouds in planetary atmospheres, aerosol particles with numerous inclusions and so on. Our study is based on the results of extensive computations of different characteristics of electromagnetic scattering obtained by using the superposition T-matrix method which represents a direct computer solver of the macroscopic Maxwell equations for an arbitrary multisphere configuration. As a result, in particular, we clarify the range of applicability of the low-density theories of radiative transfer and coherent backscattering as well as of widely used effective-medium approximations.

Phase space explorations in time dependent density functional theory

NASA Astrophysics Data System (ADS)

Rajam, Aruna K.

Time dependent density functional theory (TDDFT) is one of the useful tools for the study of the dynamic behavior of correlated electronic systems under the influence of external potentials. The success of this formally exact theory practically relies on approximations for the exchange-correlation potential which is a complicated functional of the co-ordinate density, non-local in space and time. Adiabatic approximations (such as ALDA), which are local in time, are most commonly used in the increasing applications of the field. Going beyond ALDA, has been proved difficult leading to mathematical inconsistencies. We explore the regions where the theory faces challenges, and try to answer some of them via the insights from two electron model systems. In this thesis work we propose a phase-space extension of the TDDFT. We want to answer the challenges the theory is facing currently by exploring the one-body phase-space. We give a general introduction to this theory and its mathematical background in the first chapter. In second chapter, we carryout a detailed study of instantaneous phase-space densities and argue that the functionals of distributions can be a better alternative to the nonlocality issue of the exchange-correlation potentials. For this we study in detail the interacting and the non-interacting phase-space distributions for Hookes atom model. The applicability of ALDA-based TDDFT for the dynamics in strongfields can become severely problematic due to the failure of single-Slater determinant picture.. In the third chapter, we analyze how the phase-space distributions can shine some light into this problem. We do a comparative study of Kohn-Sham and interacting phase-space and momentum distributions for single ionization and double ionization systems. Using a simple model of two-electron systems, we have showed that the momentum distribution computed directly from the exact KS system contains spurious oscillations: a non-classical description of the essentially classical two-electron dynamics. In Time dependent density matrix functional theory (TDDMFT), the evolution scheme of the 1RDM (first order reduced density matrix) contains second-order reduced density matrix (2RDM), which has to be expressed in terms of 1RDMs. Any non-correlated approximations (Hartree-Fock) for 2RDM would fail to capture the natural occupations of the system. In our fourth chapter, we show that by applying the quasi-classical and semi-classical approximations one can capture the natural occupations of the excited systems. We study a time-dependent Moshinsky atom model for this. The fifth chapter contains a comparative work on the existing non-local exchange-correlation kernels that are based on current density response frame work and the co-moving frame work. We show that the two approaches though coinciding with each other in linear response regime, actually turn out to be different in non-linear regime.

Analytical results for the time-dependent current density distribution of expanding ultracold gases after a sudden change of the confining potential

NASA Astrophysics Data System (ADS)

Boumaza, R.; Bencheikh, K.

2017-12-01

Using the so-called operator product expansion to lowest order, we extend the work in Campbell et al (2015 Phys. Rev. Lett 114 125302) by deriving a simple analytical expression for the long-time asymptotic one-body reduced density matrix during free expansion for a one-dimensional system of bosons with large atom number interacting through a repulsive delta potential initially confined by a potential well. This density matrix allows direct access to the momentum distribution and also to the mass current density. For initially confining power-law potentials we give explicit expressions, in the limits of very weak and very strong interaction, for the current density distributions during the free expansion. In the second part of the work we consider the expansion of ultracold gas from a confining harmonic trap to another harmonic trap with a different frequency. For the case of a quantum impenetrable gas of bosons (a Tonks-Girardeau gas) with a given atom number, we present an exact analytical expression for the mass current distribution (mass transport) after release from one harmonic trap to another harmonic trap. It is shown that, for a harmonically quenched Tonks-Girardeau gas, the current distribution is a suitable collective observable and under the weak quench regime, it exhibits oscillations at the same frequencies as those recently predicted for the peak momentum distribution in the breathing mode. The analysis is extended to other possible quenched systems.

A first-principles study of the influence of helium atoms on the optical response of small silver clusters.

PubMed

Pereiro, M; Baldomir, D; Arias, J E

2011-02-28

Optical excitation spectra of Ag(n) and Ag(n)@He(60) (n = 2, 8) clusters are investigated in the framework of the time-dependent density functional theory (TDDFT) within the linear response regime. We have performed the ab initio calculations for two different exact exchange functionals (GGA-exact and LDA-exact). The computed spectra of Ag(n)@He(60) clusters with the GGA-exact functional accounting for exchange-correlation effects are found to be generally in a relatively good agreement with the experiment. A strategy is proposed to obtain the ground-state structures of the Ag(n)@He(60) clusters and in the initial process of the geometry optimization, the He environment is simulated with buckyballs. A redshift of the silver clusters spectra is observed in the He environment with respect to the ones of bare silver clusters. This observation is discussed and explained in terms of a contraction of the Ag-He bonding length and a consequent confinement of the s valence electrons in silver clusters. Likewise, the Mie-Gans predictions combined with our TDDFT calculations also show that the dielectric effect produced by the He matrix is considerably less important in explaining the redshifting observed in the optical spectra of Ag(n)@He(60) clusters.

Negative refraction using Raman transitions and chirality

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

Sikes, D. E.; Yavuz, D. D.

2011-11-15

We present a scheme that achieves negative refraction with low absorption in far-off resonant atomic systems. The scheme utilizes Raman resonances and does not require the simultaneous presence of an electric-dipole transition and a magnetic-dipole transition near the same wavelength. We show that two interfering Raman tran-sitions coupled to a magnetic-dipole transition can achieve a negative index of refraction with low absorption through magnetoelectric cross-coupling. We confirm the validity of the analytical results with exact numerical simulations of the density matrix. We also discuss possible experimental implementations of the scheme in rare-earth metal atomic systems.

Investigating decoherence in a simple system

NASA Technical Reports Server (NTRS)

Albrecht, Andreas

1991-01-01

The results of some simple calculations designed to study quantum decoherence are presented. The physics of quantum decoherence are briefly reviewed, and a very simple 'toy' model is analyzed. Exact solutions are found using numerical techniques. The type of incoherence exhibited by the model can be changed by varying a coupling strength. The author explains why the conventional approach to studying decoherence by checking the diagonality of the density matrix is not always adequate. Two other approaches, the decoherence functional and the Schmidt paths approach, are applied to the toy model and contrasted to each other. Possible problems with each are discussed.

Thermal Pairing in Nuclei

NASA Astrophysics Data System (ADS)

Dang, Nguyen Dinh

2008-04-01

The modified Hartree-Fock-Bogoliubov (MHFB) theory at finite temperature is derived for finite nuclei.1 In the limit of constant pairing parameter, the MHFB theory yields the modified BCS (MBCS) theory.2 These are the microscopic theories that can describe the crossover region at temperature T around the critical value Tc of the BCS superfluid-normal (SN) phase transition. By requiring the unitarity conservation of the particle-density matrix, the derivation of these theories 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. The calculations of the thermal pairing gap, total energy, heat capacity, quasiparticle and pairing correlation functions were carried out within MBCS theory for the Richardson model3 as well as realistic single-particle spectra. The Richardson model under consideration has varying Ω equidistant levels and N particles with a level distant equal to 1 MeV. It is shown that the limitation of the configuration space sets a limiting temperature TM up to which the MBCS theory can be applied. Enlarging the space in the half-filled case (Ω = N) by one valence level (Ω = N + 1) extends TM to a much higher temperature so that the predictions by the MBCS theory can be compared directly with the exact results up to T ~ 4 - 5 MeV even for small N. The MBCS gap does not collapse, but decreases monotonously with increasing T. The total energy and heat capacity predicted by the MBCS theory are closer to the exact results than those predicted by the BCS theory, especially in the region of the SN phase transition predicted within the BCS theory. The discontinuity in the BCS heat capacity at the critical temperature Tc is smoothed out within the MBCS theory, especially for small N, showing the disappearance of SN phase transition in very light systems. With increasing N the peak at Tc in the heat capacity becomes more pronounced, showing a phase-transition-like behavior in heavy systems. The effect of approximated particle-number projection using the Lipkin-Nogami method is also discussed. An application of the MBCS theory to the description of the damping of giant dipole resonances (GDR) in hot nuclei shows that, because of the existence of the pseudo gap, the GDR width remains nearly constant at temperatures up to around 1 MeV in tin isotopes in good agreement with the recent experimental systematic.4

Computation of the asymptotic states of modulated open quantum systems with a numerically exact realization of the quantum trajectory method

NASA Astrophysics Data System (ADS)

Volokitin, V.; Liniov, A.; Meyerov, I.; Hartmann, M.; Ivanchenko, M.; Hänggi, P.; Denisov, S.

2017-11-01

Quantum systems out of equilibrium are presently a subject of active research, both in theoretical and experimental domains. In this work, we consider time-periodically modulated quantum systems that are in contact with a stationary environment. Within the framework of a quantum master equation, the asymptotic states of such systems are described by time-periodic density operators. Resolution of these operators constitutes a nontrivial computational task. Approaches based on spectral and iterative methods are restricted to systems with the dimension of the hosting Hilbert space dim H =N ≲300 , while the direct long-time numerical integration of the master equation becomes increasingly problematic for N ≳400 , especially when the coupling to the environment is weak. To go beyond this limit, we use the quantum trajectory method, which unravels the master equation for the density operator into a set of stochastic processes for wave functions. The asymptotic density matrix is calculated by performing a statistical sampling over the ensemble of quantum trajectories, preceded by a long transient propagation. We follow the ideology of event-driven programming and construct a new algorithmic realization of the method. The algorithm is computationally efficient, allowing for long "leaps" forward in time. It is also numerically exact, in the sense that, being given the list of uniformly distributed (on the unit interval) random numbers, {η1,η2,...,ηn} , one could propagate a quantum trajectory (with ηi's as norm thresholds) in a numerically exact way. By using a scalable N -particle quantum model, we demonstrate that the algorithm allows us to resolve the asymptotic density operator of the model system with N =2000 states on a regular-size computer cluster, thus reaching the scale on which numerical studies of modulated Hamiltonian systems are currently performed.

Computation of the asymptotic states of modulated open quantum systems with a numerically exact realization of the quantum trajectory method.

PubMed

Volokitin, V; Liniov, A; Meyerov, I; Hartmann, M; Ivanchenko, M; Hänggi, P; Denisov, S

2017-11-01

Quantum systems out of equilibrium are presently a subject of active research, both in theoretical and experimental domains. In this work, we consider time-periodically modulated quantum systems that are in contact with a stationary environment. Within the framework of a quantum master equation, the asymptotic states of such systems are described by time-periodic density operators. Resolution of these operators constitutes a nontrivial computational task. Approaches based on spectral and iterative methods are restricted to systems with the dimension of the hosting Hilbert space dimH=N≲300, while the direct long-time numerical integration of the master equation becomes increasingly problematic for N≳400, especially when the coupling to the environment is weak. To go beyond this limit, we use the quantum trajectory method, which unravels the master equation for the density operator into a set of stochastic processes for wave functions. The asymptotic density matrix is calculated by performing a statistical sampling over the ensemble of quantum trajectories, preceded by a long transient propagation. We follow the ideology of event-driven programming and construct a new algorithmic realization of the method. The algorithm is computationally efficient, allowing for long "leaps" forward in time. It is also numerically exact, in the sense that, being given the list of uniformly distributed (on the unit interval) random numbers, {η_{1},η_{2},...,η_{n}}, one could propagate a quantum trajectory (with η_{i}'s as norm thresholds) in a numerically exact way. By using a scalable N-particle quantum model, we demonstrate that the algorithm allows us to resolve the asymptotic density operator of the model system with N=2000 states on a regular-size computer cluster, thus reaching the scale on which numerical studies of modulated Hamiltonian systems are currently performed.

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.

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.

Measures for the Dynamics in a Few-Body Quantum System with Harmonic Interactions

NASA Astrophysics Data System (ADS)

Nagy, I.; Pipek, J.; Glasser, M. L.

2018-01-01

We determine the exact time-dependent non-idempotent one-particle reduced density matrix and its spectral decomposition for a harmonically confined two-particle correlated one-dimensional system when the interaction terms in the Schrödinger Hamiltonian are changed abruptly. Based on this matrix in coordinate space we derive a precise condition for the equivalence of the purity and the overlap-square of the correlated and non-correlated wave functions as the model system with harmonic interactions evolves in time. This equivalence holds only if the interparticle interactions are affected, while the confinement terms are unaffected within the stability range of the system. Under this condition we analyze various time-dependent measures of entanglement and demonstrate that, depending on the magnitude of the changes made in the Hamiltonian, periodic, logarithmically increasing or constant value behavior of the von Neumann entropy can occur.

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.

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.

A Numerical Scheme for Ordinary Differential Equations Having Time Varying and Nonlinear Coefficients Based on the State Transition Matrix

NASA Technical Reports Server (NTRS)

Bartels, Robert E.

2002-01-01

A variable order method of integrating initial value ordinary differential equations that is based on the state transition matrix has been developed. The method has been evaluated for linear time variant and nonlinear systems of equations. While it is more complex than most other methods, it produces exact solutions at arbitrary time step size when the time variation of the system can be modeled exactly by a polynomial. Solutions to several nonlinear problems exhibiting chaotic behavior have been computed. Accuracy of the method has been demonstrated by comparison with an exact solution and with solutions obtained by established methods.

Quantum critical spin-2 chain with emergent SU(3) symmetry.

PubMed

Chen, Pochung; Xue, Zhi-Long; McCulloch, I P; Chung, Ming-Chiang; Huang, Chao-Chun; Yip, S-K

2015-04-10

We study the quantum critical phase of an SU(2) symmetric spin-2 chain obtained from spin-2 bosons in a one-dimensional lattice. We obtain the scaling of the finite-size energies and entanglement entropy by exact diagonalization and density-matrix renormalization group methods. From the numerical results of the energy spectra, central charge, and scaling dimension we identify the conformal field theory describing the whole critical phase to be the SU(3)_{1} Wess-Zumino-Witten model. We find that, while the Hamiltonian is only SU(2) invariant, in this critical phase there is an emergent SU(3) symmetry in the thermodynamic limit.

Experimental observation of the 1/3 magnetization plateau in the diamond-chain compound Cu3(CO3)2(OH)2.

PubMed

Kikuchi, H; Fujii, Y; Chiba, M; Mitsudo, S; Idehara, T; Tonegawa, T; Okamoto, K; Sakai, T; Kuwai, T; Ohta, H

2005-06-10

The magnetic susceptibility, high field magnetization, and specific heat measurements of Cu3(CO3)2(OH)2, which is a model substance for the frustrating diamond spin chain model, have been performed using single crystals. Two broad peaks are observed at around 20 and 5 K in both magnetic susceptibility and specific heat results. The magnetization curve has a clear plateau at one third of the saturation magnetization. The experimental results are examined in terms of theoretical expectations based on exact diagonalization and density matrix renormalization group methods. An origin of magnetic anisotropy is also discussed.

Interband excitations in the 1D limit of two-band fractional Chern insulators

NASA Astrophysics Data System (ADS)

Jaworowski, Błażej; Kaczmarkiewicz, Piotr; Potasz, Paweł; Wójs, Arkadiusz

2018-05-01

We investigate the stability of the one-dimensional limit of ν = 1 / 3 Laughlin-like fractional Chern insulator with respect to the interband interaction. We propose a construction for the excitations in the infinite-interaction case and show that the energy gap remains finite in the thermodynamic limit. Next, by means of exact diagonalization and Density Matrix Renormalization Group approaches, we consider deviations from ideal dimerization and show that they reduce the stability of the FCI-like states. Finally, to show that our approach is not restricted to one model, we identify the dimer structure behind the thin-torus limit of other system - the checkerboard lattice.

Microscopic nonlinear relativistic quantum theory of absorption of powerful x-ray radiation in plasma.

PubMed

Avetissian, H K; Ghazaryan, A G; Matevosyan, H H; Mkrtchian, G F

2015-10-01

The microscopic quantum theory of plasma nonlinear interaction with the coherent shortwave electromagnetic radiation of arbitrary intensity is developed. The Liouville-von Neumann equation for the density matrix is solved analytically considering a wave field exactly and a scattering potential of plasma ions as a perturbation. With the help of this solution we calculate the nonlinear inverse-bremsstrahlung absorption rate for a grand canonical ensemble of electrons. The latter is studied in Maxwellian, as well as in degenerate quantum plasma for x-ray lasers at superhigh intensities and it is shown that one can achieve the efficient absorption coefficient in these cases.

The exponential parameterization of the neutrino mixing matrix as an SU(3) group element and an account for new experimental data

NASA Astrophysics Data System (ADS)

Zhukovsky, K. V.

2017-09-01

The exponential form of the Pontecorvo-Maki-Nakagawa-Sakata mixing matrix for neutrinos is considered in the context of the fundamental representation of the SU(3) group. The logarithm of the mixing matrix is obtained. Based on the most recent experimental data on neutrino mixing, the exact values of the entries of the exponential matrix are calculated. The exact values for its real and imaginary parts are determined, respectively, in charge of the mixing without CP violation and of the pure CP violation effect. The hypothesis of complementarity for quarks and neutrinos is confirmed. The factorization of the exponential mixing matrix, which allows the separation of the mixing and of the CP violation itself in the form of the product of rotations around the real and imaginary axes, is demonstrated.

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.

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

Towards the stabilization of the low density elements in topology optimization with large deformation

NASA Astrophysics Data System (ADS)

Lahuerta, Ricardo Doll; Simões, Eduardo T.; Campello, Eduardo M. B.; Pimenta, Paulo M.; Silva, Emilio C. N.

2013-10-01

This work addresses the treatment of lower density regions of structures undergoing large deformations during the design process by the topology optimization method (TOM) based on the finite element method. During the design process the nonlinear elastic behavior of the structure is based on exact kinematics. The material model applied in the TOM is based on the solid isotropic microstructure with penalization approach. No void elements are deleted and all internal forces of the nodes surrounding the void elements are considered during the nonlinear equilibrium solution. The distribution of design variables is solved through the method of moving asymptotes, in which the sensitivity of the objective function is obtained directly. In addition, a continuation function and a nonlinear projection function are invoked to obtain a checkerboard free and mesh independent design. 2D examples with both plane strain and plane stress conditions hypothesis are presented and compared. The problem of instability is overcome by adopting a polyconvex constitutive model in conjunction with a suggested relaxation function to stabilize the excessive distorted elements. The exact tangent stiffness matrix is used. The optimal topology results are compared to the results obtained by using the classical Saint Venant-Kirchhoff constitutive law, and strong differences are found.

Exact thermal density functional theory for a model system: Correlation components and accuracy of the zero-temperature exchange-correlation approximation

DOE PAGES

Smith, J. C.; Pribram-Jones, A.; Burke, K.

2016-06-14

Thermal density functional theory calculations often use the Mermin-Kohn-Sham scheme, but employ ground-state approximations to the exchange-correlation (XC) free energy. In the simplest solvable nontrivial model, an asymmetric Hubbard dimer, we calculate the exact many-body energies and the exact Mermin-Kohn-Sham functionals for this system and extract the exact XC free energy. For moderate temperatures and weak correlation, we find this approximation to be excellent. Here we extract various exact free-energy correlation components and the exact adiabatic connection formula.

Exact thermal density functional theory for a model system: Correlation components and accuracy of the zero-temperature exchange-correlation approximation

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

Smith, J. C.; Pribram-Jones, A.; Burke, K.

Thermal density functional theory calculations often use the Mermin-Kohn-Sham scheme, but employ ground-state approximations to the exchange-correlation (XC) free energy. In the simplest solvable nontrivial model, an asymmetric Hubbard dimer, we calculate the exact many-body energies and the exact Mermin-Kohn-Sham functionals for this system and extract the exact XC free energy. For moderate temperatures and weak correlation, we find this approximation to be excellent. Here we extract various exact free-energy correlation components and the exact adiabatic connection formula.

Calculating Relativistic Transition Matrix Elements for Hydrogenic Atoms Using Monte Carlo Methods

NASA Astrophysics Data System (ADS)

Alexander, Steven; Coldwell, R. L.

2015-03-01

The nonrelativistic transition matrix elements for hydrogen atoms can be computed exactly and these expressions are given in a number of classic textbooks. The relativistic counterparts of these equations can also be computed exactly but these expressions have been described in only a few places in the literature. In part, this is because the relativistic equations lack the elegant simplicity of the nonrelativistic equations. In this poster I will describe how variational Monte Carlo methods can be used to calculate the energy and properties of relativistic hydrogen atoms and how the wavefunctions for these systems can be used to calculate transition matrix elements.

The bilinear complexity and practical algorithms for matrix multiplication

NASA Astrophysics Data System (ADS)

Smirnov, A. V.

2013-12-01

A method for deriving bilinear algorithms for matrix multiplication is proposed. New estimates for the bilinear complexity of a number of problems of the exact and approximate multiplication of rectangular matrices are obtained. In particular, the estimate for the boundary rank of multiplying 3 × 3 matrices is improved and a practical algorithm for the exact multiplication of square n × n matrices is proposed. The asymptotic arithmetic complexity of this algorithm is O( n 2.7743).

A Parameter-Free Semilocal Exchange Energy Functional for Two-Dimensional Quantum Systems.

PubMed

Patra, Abhilash; Jana, Subrata; Samal, Prasanjit

2018-04-05

The method of constructing semilocal density functional for exchange in two dimensions using one of the premier approaches, i.e., density matrix expansion, is revisited, and an accurate functional is constructed. The form of the functional is quite simple and includes no adjustable semiempirical parameters. In it, the kinetic energy dependent momentum is used to compensate nonlocal effects of the system. The functional is then examined by considering the very well-known semiconductor quantum dot systems. And despite its very simple form, the results obtained for quantum dots containing a higher number of electrons agrees pretty well with that of the standard exact exchange theory. Some of the desired properties relevant for the two-dimensional exchange functional and the lower bound associated with it are also discussed. It is observed that the above parameter-free semilocal exchange functional satisfies most of the discussed conditions.

Coarse-grained forms for equations describing the microscopic motion of particles in a fluid.

PubMed

Das, Shankar P; Yoshimori, Akira

2013-10-01

Exact equations of motion for the microscopically defined collective density ρ(x,t) and the momentum density ĝ(x,t) of a fluid have been obtained in the past starting from the corresponding Langevin equations representing the dynamics of the fluid particles. In the present work we average these exact equations of microscopic dynamics over the local equilibrium distribution to obtain stochastic partial differential equations for the coarse-grained densities with smooth spatial and temporal dependence. In particular, we consider Dean's exact balance equation for the microscopic density of a system of interacting Brownian particles to obtain the basic equation of the dynamic density functional theory with noise. Our analysis demonstrates that on thermal averaging the dependence of the exact equations on the bare interaction potential is converted to dependence on the corresponding thermodynamic direct correlation functions in the coarse-grained equations.

Monte Carlo study of exact {ital S}-matrix duality in nonsimply laced affine Toda theories

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

Beccaria, M.

The ({ital g}{sub 2}{sup (1)},{ital d}{sub 4}{sup (3)}) pair of nonsimply laced affine Toda theories is studied from the point of view of nonperturbative duality. The classical spectrum of each member is composed of two massive scalar particles. The exact {ital S}-matrix prediction for the dual behavior of the coupling-dependent mass ratio is found to be in strong agreement with Monte Carlo data. {copyright} {ital 1996 The American Physical Society.}

Exact first order scattering correction for vector radiative transfer in coupled atmosphere and ocean systems

NASA Astrophysics Data System (ADS)

Zhai, Peng-Wang; Hu, Yongxiang; Josset, Damien B.; Trepte, Charles R.; Lucker, Patricia L.; Lin, Bing

2012-06-01

We have developed a Vector Radiative Transfer (VRT) code for coupled atmosphere and ocean systems based on the successive order of scattering (SOS) method. In order to achieve efficiency and maintain accuracy, the scattering matrix is expanded in terms of the Wigner d functions and the delta fit or delta-M technique is used to truncate the commonly-present large forward scattering peak. To further improve the accuracy of the SOS code, we have implemented the analytical first order scattering treatment using the exact scattering matrix of the medium in the SOS code. The expansion and truncation techniques are kept for higher order scattering. The exact first order scattering correction was originally published by Nakajima and Takana.1 A new contribution of this work is to account for the exact secondary light scattering caused by the light reflected by and transmitted through the rough air-sea interface.

Exact and Approximate Statistical Inference for Nonlinear Regression and the Estimating Equation Approach.

PubMed

Demidenko, Eugene

2017-09-01

The exact density distribution of the nonlinear least squares estimator in the one-parameter regression model is derived in closed form and expressed through the cumulative distribution function of the standard normal variable. Several proposals to generalize this result are discussed. The exact density is extended to the estimating equation (EE) approach and the nonlinear regression with an arbitrary number of linear parameters and one intrinsically nonlinear parameter. For a very special nonlinear regression model, the derived density coincides with the distribution of the ratio of two normally distributed random variables previously obtained by Fieller (1932), unlike other approximations previously suggested by other authors. Approximations to the density of the EE estimators are discussed in the multivariate case. Numerical complications associated with the nonlinear least squares are illustrated, such as nonexistence and/or multiple solutions, as major factors contributing to poor density approximation. The nonlinear Markov-Gauss theorem is formulated based on the near exact EE density approximation.

Asymptotic behavior of exact exchange potential of slabs

NASA Astrophysics Data System (ADS)

Engel, E.

2014-06-01

In this contribution the exact exchange potential vx of density functional theory is examined for slabs such as graphene, for which one has a Bravais lattice in the x-y directions, while the electrons are confined to the finite region -L≤z≤L in the z direction. It is demonstrated analytically that the exact vx behaves as -e2/z for z ≫L. This result extends the corresponding statement of Horowitz, Proetto, and Rigamonti [Phys. Rev. Lett. 97, 026802 (2006), 10.1103/PhysRevLett.97.026802] for jellium slabs to slabs with arbitrary periodic density distributions. Application of the exact exchange to a Si(111) slab (within the Krieger-Li-Iafrate approximation) indicates that the corrugation of the exact vx is more pronounced than that of the local density approximation for vx.

EXACT DISTRIBUTIONS OF INTRACLASS CORRELATION AND CRONBACH'S ALPHA WITH GAUSSIAN DATA AND GENERAL COVARIANCE.

PubMed

Kistner, Emily O; Muller, Keith E

2004-09-01

Intraclass correlation and Cronbach's alpha are widely used to describe reliability of tests and measurements. Even with Gaussian data, exact distributions are known only for compound symmetric covariance (equal variances and equal correlations). Recently, large sample Gaussian approximations were derived for the distribution functions. New exact results allow calculating the exact distribution function and other properties of intraclass correlation and Cronbach's alpha, for Gaussian data with any covariance pattern, not just compound symmetry. Probabilities are computed in terms of the distribution function of a weighted sum of independent chi-square random variables. New F approximations for the distribution functions of intraclass correlation and Cronbach's alpha are much simpler and faster to compute than the exact forms. Assuming the covariance matrix is known, the approximations typically provide sufficient accuracy, even with as few as ten observations. Either the exact or approximate distributions may be used to create confidence intervals around an estimate of reliability. Monte Carlo simulations led to a number of conclusions. Correctly assuming that the covariance matrix is compound symmetric leads to accurate confidence intervals, as was expected from previously known results. However, assuming and estimating a general covariance matrix produces somewhat optimistically narrow confidence intervals with 10 observations. Increasing sample size to 100 gives essentially unbiased coverage. Incorrectly assuming compound symmetry leads to pessimistically large confidence intervals, with pessimism increasing with sample size. In contrast, incorrectly assuming general covariance introduces only a modest optimistic bias in small samples. Hence the new methods seem preferable for creating confidence intervals, except when compound symmetry definitely holds.

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

Universality of quantum information in chaotic CFTs

NASA Astrophysics Data System (ADS)

Lashkari, Nima; Dymarsky, Anatoly; Liu, Hong

2018-03-01

We study the Eigenstate Thermalization Hypothesis (ETH) in chaotic conformal field theories (CFTs) of arbitrary dimensions. Assuming local ETH, we compute the reduced density matrix of a ball-shaped subsystem of finite size in the infinite volume limit when the full system is an energy eigenstate. This reduced density matrix is close in trace distance to a density matrix, to which we refer as the ETH density matrix, that is independent of all the details of an eigenstate except its energy and charges under global symmetries. In two dimensions, the ETH density matrix is universal for all theories with the same value of central charge. We argue that the ETH density matrix is close in trace distance to the reduced density matrix of the (micro)canonical ensemble. We support the argument in higher dimensions by comparing the Von Neumann entropy of the ETH density matrix with the entropy of a black hole in holographic systems in the low temperature limit. Finally, we generalize our analysis to the coherent states with energy density that varies slowly in space, and show that locally such states are well described by the ETH density matrix.

Entanglement classification in the noninteracting Fermi gas

NASA Astrophysics Data System (ADS)

Jafarizadeh, M. A.; Eghbalifam, F.; Nami, S.; Yahyavi, M.

In this paper, entanglement classification shared among the spins of localized fermions in the noninteracting Fermi gas is studied. It is proven that the Fermi gas density matrix is block diagonal on the basis of the projection operators to the irreducible representations of symmetric group Sn. Every block of density matrix is in the form of the direct product of a matrix and identity matrix. Then it is useful to study entanglement in every block of density matrix separately. The basis of corresponding Hilbert space are identified from the Schur-Weyl duality theorem. Also, it can be shown that the symmetric part of the density matrix is fully separable. Then it has been shown that the entanglement measure which is introduced in Eltschka et al. [New J. Phys. 10, 043104 (2008)] and Guhne et al. [New J. Phys. 7, 229 (2005)], is zero for the even n qubit Fermi gas density matrix. Then by focusing on three spin reduced density matrix, the entanglement classes have been investigated. In three qubit states there is an entanglement measure which is called 3-tangle. It can be shown that 3-tangle is zero for three qubit density matrix, but the density matrix is not biseparable for all possible values of its parameters and its eigenvectors are in the form of W-states. Then an entanglement witness for detecting non-separable state and an entanglement witness for detecting nonbiseparable states, have been introduced for three qubit density matrix by using convex optimization problem. Finally, the four spin reduced density matrix has been investigated by restricting the density matrix to the irreducible representations of Sn. The restricted density matrix to the subspaces of the irreducible representations: Ssym, S3,1 and S2,2 are denoted by ρsym, ρ3,1 and ρ2,2, respectively. It has been shown that some highly entangled classes (by using the results of Miyake [Phys. Rev. A 67, 012108 (2003)] for entanglement classification) do not exist in the blocks of density matrix ρ3,1 and ρ2,2, so these classes do not exist in the total Fermi gas density matrix.

Optimizations for the EcoPod field identification tool

PubMed Central

Manoharan, Aswath; Stamberger, Jeannie; Yu, YuanYuan; Paepcke, Andreas

2008-01-01

Background We sketch our species identification tool for palm sized computers that helps knowledgeable observers with census activities. An algorithm turns an identification matrix into a minimal length series of questions that guide the operator towards identification. Historic observation data from the census geographic area helps minimize question volume. We explore how much historic data is required to boost performance, and whether the use of history negatively impacts identification of rare species. We also explore how characteristics of the matrix interact with the algorithm, and how best to predict the probability of observing a previously unseen species. Results Point counts of birds taken at Stanford University's Jasper Ridge Biological Preserve between 2000 and 2005 were used to examine the algorithm. A computer identified species by correctly answering, and counting the algorithm's questions. We also explored how the character density of the key matrix and the theoretical minimum number of questions for each bird in the matrix influenced the algorithm. Our investigation of the required probability smoothing determined whether Laplace smoothing of observation probabilities was sufficient, or whether the more complex Good-Turing technique is required. Conclusion Historic data improved identification speed, but only impacted the top 25% most frequently observed birds. For rare birds the history based algorithms did not impose a noticeable penalty in the number of questions required for identification. For our dataset neither age of the historic data, nor the number of observation years impacted the algorithm. Density of characters for different taxa in the identification matrix did not impact the algorithms. Intrinsic differences in identifying different birds did affect the algorithm, but the differences affected the baseline method of not using historic data to exactly the same degree. We found that Laplace smoothing performed better for rare species than Simple Good-Turing, and that, contrary to expectation, the technique did not then adversely affect identification performance for frequently observed birds. PMID:18366649

Wave function continuity and the diagonal Born-Oppenheimer correction at conical intersections

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

Meek, Garrett A.; Levine, Benjamin G., E-mail: levine@chemistry.msu.edu

2016-05-14

We demonstrate that though exact in principle, the expansion of the total molecular wave function as a sum over adiabatic Born-Oppenheimer (BO) vibronic states makes inclusion of the second-derivative nonadiabatic energy term near conical intersections practically problematic. In order to construct a well-behaved molecular wave function that has density at a conical intersection, the individual BO vibronic states in the summation must be discontinuous. When the second-derivative nonadiabatic terms are added to the Hamiltonian, singularities in the diagonal BO corrections (DBOCs) of the individual BO states arise from these discontinuities. In contrast to the well-known singularities in the first-derivative couplingsmore » at conical intersections, these singularities are non-integrable, resulting in undefined DBOC matrix elements. Though these singularities suggest that the exact molecular wave function may not have density at the conical intersection point, there is no physical basis for this constraint. Instead, the singularities are artifacts of the chosen basis of discontinuous functions. We also demonstrate that continuity of the total molecular wave function does not require continuity of the individual adiabatic nuclear wave functions. We classify nonadiabatic molecular dynamics methods according to the constraints placed on wave function continuity and analyze their formal properties. Based on our analysis, it is recommended that the DBOC be neglected when employing mixed quantum-classical methods and certain approximate quantum dynamical methods in the adiabatic representation.« less

Wave function continuity and the diagonal Born-Oppenheimer correction at conical intersections

NASA Astrophysics Data System (ADS)

Meek, Garrett A.; Levine, Benjamin G.

2016-05-01

We demonstrate that though exact in principle, the expansion of the total molecular wave function as a sum over adiabatic Born-Oppenheimer (BO) vibronic states makes inclusion of the second-derivative nonadiabatic energy term near conical intersections practically problematic. In order to construct a well-behaved molecular wave function that has density at a conical intersection, the individual BO vibronic states in the summation must be discontinuous. When the second-derivative nonadiabatic terms are added to the Hamiltonian, singularities in the diagonal BO corrections (DBOCs) of the individual BO states arise from these discontinuities. In contrast to the well-known singularities in the first-derivative couplings at conical intersections, these singularities are non-integrable, resulting in undefined DBOC matrix elements. Though these singularities suggest that the exact molecular wave function may not have density at the conical intersection point, there is no physical basis for this constraint. Instead, the singularities are artifacts of the chosen basis of discontinuous functions. We also demonstrate that continuity of the total molecular wave function does not require continuity of the individual adiabatic nuclear wave functions. We classify nonadiabatic molecular dynamics methods according to the constraints placed on wave function continuity and analyze their formal properties. Based on our analysis, it is recommended that the DBOC be neglected when employing mixed quantum-classical methods and certain approximate quantum dynamical methods in the adiabatic representation.

Wave function continuity and the diagonal Born-Oppenheimer correction at conical intersections.

PubMed

Meek, Garrett A; Levine, Benjamin G

2016-05-14

We demonstrate that though exact in principle, the expansion of the total molecular wave function as a sum over adiabatic Born-Oppenheimer (BO) vibronic states makes inclusion of the second-derivative nonadiabatic energy term near conical intersections practically problematic. In order to construct a well-behaved molecular wave function that has density at a conical intersection, the individual BO vibronic states in the summation must be discontinuous. When the second-derivative nonadiabatic terms are added to the Hamiltonian, singularities in the diagonal BO corrections (DBOCs) of the individual BO states arise from these discontinuities. In contrast to the well-known singularities in the first-derivative couplings at conical intersections, these singularities are non-integrable, resulting in undefined DBOC matrix elements. Though these singularities suggest that the exact molecular wave function may not have density at the conical intersection point, there is no physical basis for this constraint. Instead, the singularities are artifacts of the chosen basis of discontinuous functions. We also demonstrate that continuity of the total molecular wave function does not require continuity of the individual adiabatic nuclear wave functions. We classify nonadiabatic molecular dynamics methods according to the constraints placed on wave function continuity and analyze their formal properties. Based on our analysis, it is recommended that the DBOC be neglected when employing mixed quantum-classical methods and certain approximate quantum dynamical methods in the adiabatic representation.

Interior radiances in optically deep absorbing media. I - Exact solutions for one-dimensional model.

NASA Technical Reports Server (NTRS)

Kattawar, G. W.; Plass, G. N.

1973-01-01

An exact analytic solution to the one-dimensional scattering problem with arbitrary single scattering albedo and arbitrary surface albedo is presented. Expressions are given for the emergent flux from a homogeneous layer, the internal flux within the layer, and the radiative heating. A comparison of these results with the values calculated from the matrix operator theory indicates an exceedingly high accuracy. A detailed study is made of the error in the matrix operator results and its dependence on the accuracy of the starting value.

Towards an exact theory of linear absorbance and circular dichroism of pigment-protein complexes: Importance of non-secular contributions

NASA Astrophysics Data System (ADS)

Dinh, Thanh-Chung; Renger, Thomas

2015-01-01

A challenge for the theory of optical spectra of pigment-protein complexes is the equal strength of the pigment-pigment and the pigment-protein couplings. Treating both on an equal footing so far can only be managed by numerically costly approaches. Here, we exploit recent results on a normal mode analysis derived spectral density that revealed the dominance of the diagonal matrix elements of the exciton-vibrational coupling in the exciton state representation. We use a cumulant expansion technique that treats the diagonal parts exactly, includes an infinite summation of the off-diagonal parts in secular and Markov approximations, and provides a systematic perturbative way to include non-secular and non-Markov corrections. The theory is applied to a model dimer and to chlorophyll (Chl) a and Chl b homodimers of the reconstituted water-soluble chlorophyll-binding protein (WSCP) from cauliflower. The model calculations reveal that the non-secular/non-Markov effects redistribute oscillator strength from the strong to the weak exciton transition in absorbance and they diminish the rotational strength of the exciton transitions in circular dichroism. The magnitude of these corrections is in a few percent range of the overall signal, providing a quantitative explanation of the success of time-local convolution-less density matrix theory applied earlier. A close examination of the optical spectra of Chl a and Chl b homodimers in WSCP suggests that the opening angle between Qy transition dipole moments in Chl b homodimers is larger by about 9∘ than for Chl a homodimers for which a crystal structure of a related WSCP complex exists. It remains to be investigated whether this change is due to a different mutual geometry of the pigments or due to the different electronic structures of Chl a and Chl b.

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

Bezák, Viktor, E-mail: bezak@fmph.uniba.sk

Quantum theory of the non-harmonic oscillator defined by the energy operator proposed by Yurke and Buks (2006) is presented. Although these authors considered a specific problem related to a model of transmission lines in a Kerr medium, our ambition is not to discuss the physical substantiation of their model. Instead, we consider the problem from an abstract, logically deductive, viewpoint. Using the Yurke–Buks energy operator, we focus attention on the imaginary-time propagator. We derive it as a functional of the Mehler kernel and, alternatively, as an exact series involving Hermite polynomials. For a statistical ensemble of identical oscillators defined bymore » the Yurke–Buks energy operator, we calculate the partition function, average energy, free energy and entropy. Using the diagonal element of the canonical density matrix of this ensemble in the coordinate representation, we define a probability density, which appears to be a deformed Gaussian distribution. A peculiarity of this probability density is that it may reveal, when plotted as a function of the position variable, a shape with two peaks located symmetrically with respect to the central point.« less

Penetrable square-well fluids: exact results in one dimension.

PubMed

Santos, Andrés; Fantoni, Riccardo; Giacometti, Achille

2008-05-01

We introduce a model of attractive penetrable spheres by adding a short-range attractive square well outside a penetrable core, and we provide a detailed analysis of structural and thermodynamical properties in one dimension using the exact impenetrable counterpart as a starting point. The model is expected to describe star polymers in regimes of good and moderate solvent under dilute conditions. We derive the exact coefficients of a low-density expansion up to second order for the radial distribution function and up to fourth order in the virial expansion. These exact results are used as a benchmark to test the reliability of approximate theories (Percus-Yevick and hypernetted chain). Notwithstanding the lack of an exact solution for arbitrary densities, our results are expected to be rather precise within a wide range of temperatures and densities. A detailed analysis of some limiting cases is carried out. In particular, we provide a complete solution of the sticky penetrable-sphere model in one dimension up to the same order in density. The issue of Ruelle's thermodynamics stability is analyzed and the region of a well-defined thermodynamic limit is identified.

Exact results for Schrödinger cats in driven-dissipative systems and their feedback control

NASA Astrophysics Data System (ADS)

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

2016-05-01

In quantum optics, photonic Schrödinger cats are superpositions of two coherent states with opposite phases and with a significant number of photons. Recently, these states have been observed in the transient dynamics of driven-dissipative resonators subject to engineered two-photon processes. Here we present an exact analytical solution of the steady-state density matrix for this class of systems, including one-photon losses, which are considered detrimental for the achievement of cat states. We demonstrate that the unique steady state is a statistical mixture of two cat-like states with opposite parity, in spite of significant one-photon losses. The transient dynamics to the steady state depends dramatically on the initial state and can pass through a metastable regime lasting orders of magnitudes longer than the photon lifetime. By considering individual quantum trajectories in photon-counting configuration, we find that the system intermittently jumps between two cats. Finally, we propose and study a feedback protocol based on this behaviour to generate a pure cat-like steady state.

Blip decomposition of the path integral: exponential acceleration of real-time calculations on quantum dissipative systems.

PubMed

Makri, Nancy

2014-10-07

The real-time path integral representation of the reduced density matrix for a discrete system in contact with a dissipative medium is rewritten in terms of the number of blips, i.e., elementary time intervals over which the forward and backward paths are not identical. For a given set of blips, it is shown that the path sum with respect to the coordinates of all remaining time points is isomorphic to that for the wavefunction of a system subject to an external driving term and thus can be summed by an inexpensive iterative procedure. This exact decomposition reduces the number of terms by a factor that increases exponentially with propagation time. Further, under conditions (moderately high temperature and/or dissipation strength) that lead primarily to incoherent dynamics, the "fully incoherent limit" zero-blip term of the series provides a reasonable approximation to the dynamics, and the blip series converges rapidly to the exact result. Retention of only the blips required for satisfactory convergence leads to speedup of full-memory path integral calculations by many orders of magnitude.

Relaxation and thermalization in the one-dimensional Bose-Hubbard model: A case study for the interaction quantum quench from the atomic limit

NASA Astrophysics Data System (ADS)

Heidrich-Meisner, Fabian; Pollet, Lode; Sorg, Stefan; Vidmar, Lev

2015-03-01

We study the relaxation dynamics and thermalization in the one-dimensional Bose-Hubbard model induced by a global interaction quench. Specifically, we start from an initial state that has exactly one boson per site and is the ground state of a system with infinitely strong repulsive interactions at unit filling. The same interaction quench was realized in a recent experiment. Using exact diagonalization and the density-matrix renormalization-group method, we compute the time dependence of such observables as the multiple occupancy and the momentum distribution function. We discuss our numerical results in the framework of the eigenstate thermalization hypothesis and we observe that the microcanonical ensemble describes the time averages of many observables reasonably well for small and intermediate interaction strength. Moreover, the diagonal and the canonical ensembles are practically identical for our initial conditions already on the level of their respective energy distributions for small interaction strengths. Supported by the DFG through FOR 801 and the Alexander von Humboldt foundation.

Multi-cut solutions in Chern-Simons matrix models

NASA Astrophysics Data System (ADS)

Morita, Takeshi; Sugiyama, Kento

2018-04-01

We elaborate the Chern-Simons (CS) matrix models at large N. The saddle point equations of these matrix models have a curious structure which cannot be seen in the ordinary one matrix models. Thanks to this structure, an infinite number of multi-cut solutions exist in the CS matrix models. Particularly we exactly derive the two-cut solutions at finite 't Hooft coupling in the pure CS matrix model. In the ABJM matrix model, we argue that some of multi-cut solutions might be interpreted as a condensation of the D2-brane instantons.

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.

Development and application of a 2-electron reduced density matrix approach to electron transport via molecular junctions

NASA Astrophysics Data System (ADS)

Hoy, Erik P.; Mazziotti, David A.; Seideman, Tamar

2017-11-01

Can an electronic device be constructed using only a single molecule? Since this question was first asked by Aviram and Ratner in the 1970s [Chem. Phys. Lett. 29, 277 (1974)], the field of molecular electronics has exploded with significant experimental advancements in the understanding of the charge transport properties of single molecule devices. Efforts to explain the results of these experiments and identify promising new candidate molecules for molecular devices have led to the development of numerous new theoretical methods including the current standard theoretical approach for studying single molecule charge transport, i.e., the non-equilibrium Green's function formalism (NEGF). By pairing this formalism with density functional theory (DFT), a wide variety of transport problems in molecular junctions have been successfully treated. For some systems though, the conductance and current-voltage curves predicted by common DFT functionals can be several orders of magnitude above experimental results. In addition, since density functional theory relies on approximations to the exact exchange-correlation functional, the predicted transport properties can show significant variation depending on the functional chosen. As a first step to addressing this issue, the authors have replaced density functional theory in the NEGF formalism with a 2-electron reduced density matrix (2-RDM) method, creating a new approach known as the NEGF-RDM method. 2-RDM methods provide a more accurate description of electron correlation compared to density functional theory, and they have lower computational scaling compared to wavefunction based methods of similar accuracy. Additionally, 2-RDM methods are capable of capturing static electron correlation which is untreatable by existing NEGF-DFT methods. When studying dithiol alkane chains and dithiol benzene in model junctions, the authors found that the NEGF-RDM predicts conductances and currents that are 1-2 orders of magnitude below those of B3LYP and M06 DFT functionals. This suggests that the NEGF-RDM method could be a viable alternative to NEGF-DFT for molecular junction calculations.

Representation of the Coulomb Matrix Elements by Means of Appell Hypergeometric Function F 2

NASA Astrophysics Data System (ADS)

Bentalha, Zine el abidine

2018-06-01

Exact analytical representation for the Coulomb matrix elements by means of Appell's double series F 2 is derived. The finite sum obtained for the Appell function F 2 allows us to evaluate explicitly the matrix elements of the two-body Coulomb interaction in the lowest Landau level. An application requiring the matrix elements of Coulomb potential in quantum Hall effect regime is presented.

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.

Exact and approximate aspects of the boson expansion theories

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

Tamura, T.; Weeks, K.J.; Pedrocchi, V.G.

1981-03-01

It is shown that a boson expansion theory of the Kishimoto-Tamura type not only maps the operators exactly but also the space, and, consequently, the matrix elements of the fermion system onto those of the bosons. Significance of approximations made in calculations is also discussed.

Landscape of an exact energy functional

NASA Astrophysics Data System (ADS)

Cohen, Aron J.; Mori-Sánchez, Paula

2016-04-01

One of the great challenges of electronic structure theory is the quest for the exact functional of density functional theory. Its existence is proven, but it is a complicated multivariable functional that is almost impossible to conceptualize. In this paper the asymmetric two-site Hubbard model is studied, which has a two-dimensional universe of density matrices. The exact functional becomes a simple function of two variables whose three-dimensional energy landscape can be visualized and explored. A walk on this unique landscape, tilted to an angle defined by the one-electron Hamiltonian, gives a valley whose minimum is the exact total energy. This is contrasted with the landscape of some approximate functionals, explaining their failure for electron transfer in the strongly correlated limit. We show concrete examples of pure-state density matrices that are not v representable due to the underlying nonconvex nature of the energy landscape. The exact functional is calculated for all numbers of electrons, including fractional, allowing the derivative discontinuity to be visualized and understood. The fundamental gap for all possible systems is obtained solely from the derivatives of the exact functional.

Communication: Near-locality of exchange and correlation density functionals for 1- and 2-electron systems

NASA Astrophysics Data System (ADS)

Sun, Jianwei; Perdew, John P.; Yang, Zenghui; Peng, Haowei

2016-05-01

The uniform electron gas and the hydrogen atom play fundamental roles in condensed matter physics and quantum chemistry. The former has an infinite number of electrons uniformly distributed over the neutralizing positively charged background, and the latter only one electron bound to the proton. The uniform electron gas was used to derive the local spin density approximation to the exchange-correlation functional that undergirds the development of the Kohn-Sham density functional theory. We show here that the ground-state exchange-correlation energies of the hydrogen atom and many other 1- and 2-electron systems are modeled surprisingly well by a different local spin density approximation (LSDA0). LSDA0 is constructed to satisfy exact constraints but agrees surprisingly well with the exact results for a uniform two-electron density in a finite, curved three-dimensional space. We also apply LSDA0 to excited or noded 1-electron densities, where it works less well. Furthermore, we show that the localization of the exact exchange hole for a 1- or 2-electron ground state can be measured by the ratio of the exact exchange energy to its optimal lower bound.

Effect of atomic spontaneous decay on entanglement in the generalized Jaynes-Cummings model

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

Hessian, H.A.; Obada, A.-S.F.; Mohamed, A.-B.A.

2010-03-15

Some aspects of the irreversible dynamics of a generalized Jaynes-Cummings model are addressed. By working in the dressed-state representation, it is possible to split the dynamics of the entanglement and coherence. The exact solution of the master equation in the case of a high-Q cavity with atomic decay is found. Effects of the atomic spontaneous decay on the temporal evolution of partial entropies of the atom or the field and the total entropy as a quantitative measure entanglement are elucidated. The degree of entanglement, through the sum of the negative eigenvalues of the partially transposed density matrix and the negativemore » mutual information has been studied and compared with other measures.« less

Dynamic regime of coherent population trapping and optimization of frequency modulation parameters in atomic clocks.

PubMed

Yudin, V I; Taichenachev, A V; Basalaev, M Yu; Kovalenko, D V

2017-02-06

We theoretically investigate the dynamic regime of coherent population trapping (CPT) in the presence of frequency modulation (FM). We have formulated the criteria for quasi-stationary (adiabatic) and dynamic (non-adiabatic) responses of atomic system driven by this FM. Using the density matrix formalism for Λ system, the error signal is exactly calculated and optimized. It is shown that the optimal FM parameters correspond to the dynamic regime of atomic-field interaction, which significantly differs from conventional description of CPT resonances in the frame of quasi-stationary approach (under small modulation frequency). Obtained theoretical results are in good qualitative agreement with different experiments. Also we have found CPT-analogue of Pound-Driver-Hall regime of frequency stabilization.

Exact solution of some linear matrix equations using algebraic methods

NASA Technical Reports Server (NTRS)

Djaferis, T. E.; Mitter, S. K.

1979-01-01

Algebraic methods are used to construct the exact solution P of the linear matrix equation PA + BP = - C, where A, B, and C are matrices with real entries. The emphasis of this equation is on the use of finite algebraic procedures which are easily implemented on a digital computer and which lead to an explicit solution to the problem. The paper is divided into six sections which include the proof of the basic lemma, the Liapunov equation, and the computer implementation for the rational, integer and modular algorithms. Two numerical examples are given and the entire calculation process is depicted.

A Time Integration Algorithm Based on the State Transition Matrix for Structures with Time Varying and Nonlinear Properties

NASA Technical Reports Server (NTRS)

Bartels, Robert E.

2003-01-01

A variable order method of integrating the structural dynamics equations that is based on the state transition matrix has been developed. The method has been evaluated for linear time variant and nonlinear systems of equations. When the time variation of the system can be modeled exactly by a polynomial it produces nearly exact solutions for a wide range of time step sizes. Solutions of a model nonlinear dynamic response exhibiting chaotic behavior have been computed. Accuracy of the method has been demonstrated by comparison with solutions obtained by established methods.

Semilocal Exchange Energy Functional for Two-Dimensional Quantum Systems: A Step Beyond Generalized Gradient Approximations.

PubMed

Jana, Subrata; Samal, Prasanjit

2017-06-29

Semilocal density functionals for the exchange-correlation energy of electrons are extensively used as they produce realistic and accurate results for finite and extended systems. The choice of techniques plays a crucial role in constructing such functionals of improved accuracy and efficiency. An accurate and efficient semilocal exchange energy functional in two dimensions is constructed by making use of the corresponding hole which is derived based on the density matrix expansion. The exchange hole involved is localized under the generalized coordinate transformation and satisfies all the relevant constraints. Comprehensive testing and excellent performance of the functional is demonstrated versus exact exchange results. The accuracy of results obtained by using the newly constructed functional is quite remarkable as it substantially reduces the errors present in the local and nonempirical exchange functionals proposed so far for two-dimensional quantum systems. The underlying principles involved in the functional construction are physically appealing and hold promise for developing range separated and nonlocal exchange functionals in two dimensions.

Convex Banding of the Covariance Matrix

PubMed Central

Bien, Jacob; Bunea, Florentina; Xiao, Luo

2016-01-01

We introduce a new sparse estimator of the covariance matrix for high-dimensional models in which the variables have a known ordering. Our estimator, which is the solution to a convex optimization problem, is equivalently expressed as an estimator which tapers the sample covariance matrix by a Toeplitz, sparsely-banded, data-adaptive matrix. As a result of this adaptivity, the convex banding estimator enjoys theoretical optimality properties not attained by previous banding or tapered estimators. In particular, our convex banding estimator is minimax rate adaptive in Frobenius and operator norms, up to log factors, over commonly-studied classes of covariance matrices, and over more general classes. Furthermore, it correctly recovers the bandwidth when the true covariance is exactly banded. Our convex formulation admits a simple and efficient algorithm. Empirical studies demonstrate its practical effectiveness and illustrate that our exactly-banded estimator works well even when the true covariance matrix is only close to a banded matrix, confirming our theoretical results. Our method compares favorably with all existing methods, in terms of accuracy and speed. We illustrate the practical merits of the convex banding estimator by showing that it can be used to improve the performance of discriminant analysis for classifying sound recordings. PMID:28042189

Convex Banding of the Covariance Matrix.

PubMed

Bien, Jacob; Bunea, Florentina; Xiao, Luo

2016-01-01

We introduce a new sparse estimator of the covariance matrix for high-dimensional models in which the variables have a known ordering. Our estimator, which is the solution to a convex optimization problem, is equivalently expressed as an estimator which tapers the sample covariance matrix by a Toeplitz, sparsely-banded, data-adaptive matrix. As a result of this adaptivity, the convex banding estimator enjoys theoretical optimality properties not attained by previous banding or tapered estimators. In particular, our convex banding estimator is minimax rate adaptive in Frobenius and operator norms, up to log factors, over commonly-studied classes of covariance matrices, and over more general classes. Furthermore, it correctly recovers the bandwidth when the true covariance is exactly banded. Our convex formulation admits a simple and efficient algorithm. Empirical studies demonstrate its practical effectiveness and illustrate that our exactly-banded estimator works well even when the true covariance matrix is only close to a banded matrix, confirming our theoretical results. Our method compares favorably with all existing methods, in terms of accuracy and speed. We illustrate the practical merits of the convex banding estimator by showing that it can be used to improve the performance of discriminant analysis for classifying sound recordings.

Gravity Gradient Tensor of Arbitrary 3D Polyhedral Bodies with up to Third-Order Polynomial Horizontal and Vertical Mass Contrasts

NASA Astrophysics Data System (ADS)

Ren, Zhengyong; Zhong, Yiyuan; Chen, Chaojian; Tang, Jingtian; Kalscheuer, Thomas; Maurer, Hansruedi; Li, Yang

2018-03-01

During the last 20 years, geophysicists have developed great interest in using gravity gradient tensor signals to study bodies of anomalous density in the Earth. Deriving exact solutions of the gravity gradient tensor signals has become a dominating task in exploration geophysics or geodetic fields. In this study, we developed a compact and simple framework to derive exact solutions of gravity gradient tensor measurements for polyhedral bodies, in which the density contrast is represented by a general polynomial function. The polynomial mass contrast can continuously vary in both horizontal and vertical directions. In our framework, the original three-dimensional volume integral of gravity gradient tensor signals is transformed into a set of one-dimensional line integrals along edges of the polyhedral body by sequentially invoking the volume and surface gradient (divergence) theorems. In terms of an orthogonal local coordinate system defined on these edges, exact solutions are derived for these line integrals. We successfully derived a set of unified exact solutions of gravity gradient tensors for constant, linear, quadratic and cubic polynomial orders. The exact solutions for constant and linear cases cover all previously published vertex-type exact solutions of the gravity gradient tensor for a polygonal body, though the associated algorithms may differ in numerical stability. In addition, to our best knowledge, it is the first time that exact solutions of gravity gradient tensor signals are derived for a polyhedral body with a polynomial mass contrast of order higher than one (that is quadratic and cubic orders). Three synthetic models (a prismatic body with depth-dependent density contrasts, an irregular polyhedron with linear density contrast and a tetrahedral body with horizontally and vertically varying density contrasts) are used to verify the correctness and the efficiency of our newly developed closed-form solutions. Excellent agreements are obtained between our solutions and other published exact solutions. In addition, stability tests are performed to demonstrate that our exact solutions can safely be used to detect shallow subsurface targets.

A comparison of matrix methods for calculating eigenvalues in acoustically lined ducts

NASA Technical Reports Server (NTRS)

Watson, W.; Lansing, D. L.

1976-01-01

Three approximate methods - finite differences, weighted residuals, and finite elements - were used to solve the eigenvalue problem which arises in finding the acoustic modes and propagation constants in an absorptively lined two-dimensional duct without airflow. The matrix equations derived for each of these methods were solved for the eigenvalues corresponding to various values of wall impedance. Two matrix orders, 20 x 20 and 40 x 40, were used. The cases considered included values of wall admittance for which exact eigenvalues were known and for which several nearly equal roots were present. Ten of the lower order eigenvalues obtained from the three approximate methods were compared with solutions calculated from the exact characteristic equation in order to make an assessment of the relative accuracy and reliability of the three methods. The best results were given by the finite element method using a cubic polynomial. Excellent accuracy was consistently obtained, even for nearly equal eigenvalues, by using a 20 x 20 order matrix.

Transfer matrix approach to the persistent current in quantum rings: Application to hybrid normal-superconducting rings

NASA Astrophysics Data System (ADS)

Nava, Andrea; Giuliano, Rosa; Campagnano, Gabriele; Giuliano, Domenico

2016-11-01

Using the properties of the transfer matrix of one-dimensional quantum mechanical systems, we derive an exact formula for the persistent current across a quantum mechanical ring pierced by a magnetic flux Φ as a single integral of a known function of the system's parameters. Our approach provides exact results at zero temperature, which can be readily extended to a finite temperature T . We apply our technique to exactly compute the persistent current through p -wave and s -wave superconducting-normal hybrid rings, deriving full plots of the current as a function of the applied flux at various system's scales. Doing so, we recover at once a number of effects such as the crossover in the current periodicity on increasing the size of the ring and the signature of the topological phase transition in the p -wave case. In the limit of a large ring size, resorting to a systematic expansion in inverse powers of the ring length, we derive exact analytic closed-form formulas, applicable to a number of cases of physical interest.

The Augmented Lagrange Multipliers Method for Matrix Completion from Corrupted Samplings with Application to Mixed Gaussian-Impulse Noise Removal

PubMed Central

Meng, Fan; Yang, Xiaomei; Zhou, Chenghu

2014-01-01

This paper studies the problem of the restoration of images corrupted by mixed Gaussian-impulse noise. In recent years, low-rank matrix reconstruction has become a research hotspot in many scientific and engineering domains such as machine learning, image processing, computer vision and bioinformatics, which mainly involves the problem of matrix completion and robust principal component analysis, namely recovering a low-rank matrix from an incomplete but accurate sampling subset of its entries and from an observed data matrix with an unknown fraction of its entries being arbitrarily corrupted, respectively. Inspired by these ideas, we consider the problem of recovering a low-rank matrix from an incomplete sampling subset of its entries with an unknown fraction of the samplings contaminated by arbitrary errors, which is defined as the problem of matrix completion from corrupted samplings and modeled as a convex optimization problem that minimizes a combination of the nuclear norm and the -norm in this paper. Meanwhile, we put forward a novel and effective algorithm called augmented Lagrange multipliers to exactly solve the problem. For mixed Gaussian-impulse noise removal, we regard it as the problem of matrix completion from corrupted samplings, and restore the noisy image following an impulse-detecting procedure. Compared with some existing methods for mixed noise removal, the recovery quality performance of our method is dominant if images possess low-rank features such as geometrically regular textures and similar structured contents; especially when the density of impulse noise is relatively high and the variance of Gaussian noise is small, our method can outperform the traditional methods significantly not only in the simultaneous removal of Gaussian noise and impulse noise, and the restoration ability for a low-rank image matrix, but also in the preservation of textures and details in the image. PMID:25248103

Quantum dissipation theory and applications to quantum transport and quantum measurement in mesoscopic systems

NASA Astrophysics Data System (ADS)

Cui, Ping

The thesis comprises two major themes of quantum statistical dynamics. One is the development of quantum dissipation theory (QDT). It covers the establishment of some basic relations of quantum statistical dynamics, the construction of several nonequivalent complete second-order formulations, and the development of exact QDT. Another is related to the applications of quantum statistical dynamics to a variety of research fields. In particular, unconventional but novel theories of the electron transfer in Debye solvents, quantum transport, and quantum measurement are developed on the basis of QDT formulations. The thesis is organized as follows. In Chapter 1, we present some background knowledge in relation to the aforementioned two themes of this thesis. The key quantity in QDT is the reduced density operator rho(t) ≡ trBrho T(t); i.e., the partial trace of the total system and bath composite rhoT(t) over the bath degrees of freedom. QDT governs the evolution of reduced density operator, where the effects of bath are treated in a quantum statistical manner. In principle, the reduced density operator contains all dynamics information of interest. However, the conventional quantum transport theory is formulated in terms of nonequilibrium Green's function. The newly emerging field of quantum measurement in relation to quantum information and quantum computing does exploit a sort of QDT formalism. Besides the background of the relevant theoretical development, some representative experiments on molecular nanojunctions are also briefly discussed. In chapter 2, we outline some basic (including new) relations that highlight several important issues on QDT. The content includes the background of nonequilibrium quantum statistical mechanics, the general description of the total composite Hamiltonian with stochastic system-bath interaction, a novel parameterization scheme for bath correlation functions, a newly developed exact theory of driven Brownian oscillator (DBO) systems, and its closely related solvation mode transformation of system-bath coupling Hamiltonian in general. The exact QDT of DBO systems is also used to clarify the validity of conventional QDT formulations that involve Markovian approximation. In Chapter 3, we develop three nonequivalent but all complete second-order QDT (CS-QDT) formulations. Two of them are of the conventional prescriptions in terms of time-local dissipation and memory kernel, respectively. The third one is called the correlated driving-dissipation equations of motion (CODDE). This novel CS-QDT combines the merits of the former two for its advantages in both the application and numerical implementation aspects. Also highlighted is the importance of correlated driving-dissipation effects on the dynamics of the reduced system. In Chapter 4, we construct an exact QDT formalism via the calculus on path integrals. The new theory aims at the efficient evaluation of non-Markovian dissipation beyond the weak system-bath interaction regime in the presence of time-dependent external field. By adopting exponential-like expansions for bath correlation function, hierarchical equations of motion formalism and continued fraction Liouville-space Green's function formalism are established. The latter will soon be used together with the Dyson equation technique for an efficient evaluation of non-perturbative reduced density matrix dynamics. The interplay between system-bath interaction strength, non-Markovian property, and the required level of hierarchy is also studied with the aid of simple spin-boson systems, together with the three proposed schemes to truncate the infinite hierarchy. In Chapter 5, we develop a nonperturbative theory of electron transfer (ET) in Debye solvents. The resulting exact and analytical rate expression is constructed on the basis of the aforementioned continued fraction Liouville-space Green's function formalism, together with the Dyson equation technique. Not only does it recover the celebrated Marcus' inversion and Kramers' turnover behaviors, the new theory also shows some distinct quantum solvation effects that can alter the ET mechanism. Moreover, the present theory predicts further for the ET reaction thermodynamics, such as equilibrium Gibbs free-energy and entropy, some interesting solvent-dependent features that are calling for experimental verification. In Chapter 6, we discuss the constructed QDTs, in terms of their unified mathematical structure that supports a linear dynamics space, and thus facilitates their applications to various physical problems. The involving details are exemplified with the CODDE form of QDT. As the linear space is concerned, we identify the Schrodinger versus Heisenberg picture and the forward versus backward propagation of the reduced, dissipative Liouville dynamics. For applications we discuss the reduced linear response theory and the optimal control problems, in which the correlated effects of non-Markovian dissipation and field driving are shown to be important. In Chapter 7, we turn to quantum transport, i.e., electric current through molecular or mesoscopic systems under finite applied voltage. By viewing the nonequilibrium transport setup as a quantum open system, we develop a reduced-density-matrix approach to quantum transport. The resulting current is explicitly expressed in terms of the molecular reduced density matrix by tracing out the degrees of freedom of the electrodes at finite bias and temperature. We propose a conditional quantum master equation theory, which is an extension of the conventional (or unconditional) QDT by tracing out the well-defined bath subsets individually, instead of the entire bath degrees of freedom. Both the current and the noise spectrum can be conveniently analyzed in terms of the conditional reduced density matrix dynamics. By far, the QDT (including the conditional one) has only been exploited in second-order form. A self-consistent Born approximation for the system-electrode coupling is further proposed to recover all existing nonlinear current-voltage behaviors including the nonequilibrium Kondo effect. Transport theory based on the exact QDT formalism will be developed in future. In Chapter 8, we study the quantum measurement of a qubit with a quantum-point-contact detector. On the basis of a unified quantum master equation (a form of QDT), we study the measurement-induced relaxation and dephasing of the qubit. Our treatment pays particular attention on the detailed-balance relation, which is a consequence of properly accounting for the energy exchange between the qubit and detector during the measurement process. We also derive a conditional quantum master equation for quantum measurement in general, and study the readout characteristics of the qubit measurement. Our theory is applicable to the quantum measurement at arbitrary voltage and temperature. A number of remarkable new features are found and highlighted in concern with their possible relevance to future experiments. In Chapter 9, we discuss the further development of QDT, aiming at an efficient evaluation of many-electron systems. This will be carried out by reducing the many-particle (Fermion or Boson) QDT to a single-particle one by exploring, e.g. the Wick's contraction theorem. It also results in a time-dependent density functional theory (TDDFT) for transport through complex large-scale (e.g. molecules) systems. Primary results of the TDDFT-QDT are reported. In Chapter 10, we summary the thesis, and comment and remark on the future work on both the theoretical and application aspects of QDT.

Gedanken densities and exact constraints in density functional theory.

PubMed

Perdew, John P; Ruzsinszky, Adrienn; Sun, Jianwei; Burke, Kieron

2014-05-14

Approximations to the exact density functional for the exchange-correlation energy of a many-electron ground state can be constructed by satisfying constraints that are universal, i.e., valid for all electron densities. Gedanken densities are designed for the purpose of this construction, but need not be realistic. The uniform electron gas is an old gedanken density. Here, we propose a spherical two-electron gedanken density in which the dimensionless density gradient can be an arbitrary positive constant wherever the density is non-zero. The Lieb-Oxford lower bound on the exchange energy can be satisfied within a generalized gradient approximation (GGA) by bounding its enhancement factor or simplest GGA exchange-energy density. This enhancement-factor bound is well known to be sufficient, but our gedanken density shows that it is also necessary. The conventional exact exchange-energy density satisfies no such local bound, but energy densities are not unique, and the simplest GGA exchange-energy density is not an approximation to it. We further derive a strongly and optimally tightened bound on the exchange enhancement factor of a two-electron density, which is satisfied by the local density approximation but is violated by all published GGA's or meta-GGA's. Finally, some consequences of the non-uniform density-scaling behavior for the asymptotics of the exchange enhancement factor of a GGA or meta-GGA are given.

Electron correlation in Hooke's law atom in the high-density limit.

PubMed

Gill, P M W; O'Neill, D P

2005-03-01

Closed-form expressions for the first three terms in the perturbation expansion of the exact energy and Hartree-Fock energy of the lowest singlet and triplet states of the Hooke's law atom are found. These yield elementary formulas for the exact correlation energies (-49.7028 and -5.807 65 mE(h)) of the two states in the high-density limit and lead to a pair of necessary conditions on the exact correlation kernel G(w) in Hartree-Fock-Wigner theory.

DFT treatment of transport through Anderson junction: exact results and approximations

NASA Astrophysics Data System (ADS)

Burke, Kieron

2012-02-01

Since the pioneering break-junction experiments of Reed and Tour measuring the conductance of dithiolated benzene between gold leads, many researchers in physics and chemistry have been calculating conductance for such systems using density functional theory (DFT). Off resonance, the predicted current is often 10-100 times larger than that measured. This error is often ascribed to the application of ground-state DFT to a non-equilibrium problem. I will argue that, in fact, this is largely due to errors in the density functional approximations in popular use, rather than necessarily errors in the methodology. A stark illustration of this principle is the ability of DFT to reproduce the exact transmission through an Anderson junction at zero-temperature and weak bias, including the Kondo plateau, but only if the exact ground-state density functional is used. In fact, this case can be used to reverse-engineer the exact functional for this problem. Popular approximations can also be tested, including both smooth and discontinuous functionals of the density, as well as symmetry-broken approaches. [4pt] [1] Kondo effect given exactly by density functional theory, J. P. Bergfield, Z. Liu, K. Burke, and C. A. Stafford, arXiv:1106.3104; [0pt] [2] Broadening of the Derivative Discontinuity in Density Functional Theory, F. Evers, and P. Schmitteckert, arXiv:1106.3658; [0pt] [3] DFT-based transport calculations, Friedel's sum rule and the Kondo effect, P. Tr"oster, P. Schmitteckert, and F. Evers, arXiv:1106.3669; [0pt] [4] Towards a description of the Kondo effect using time-dependent density functional theory, G. Stefanucci, and S. Kurth, arXiv:1106.3728.

Coherent Backscattering by Polydisperse Discrete Random Media: Exact T-Matrix Results

NASA Technical Reports Server (NTRS)

Mishchenko, Michael I.; Dlugach, Janna M.; Mackowski, Daniel W.

2011-01-01

The numerically exact superposition T-matrix method is used to compute, for the first time to our knowledge, electromagnetic scattering by finite spherical volumes composed of polydisperse mixtures of spherical particles with different size parameters or different refractive indices. The backscattering patterns calculated in the far-field zone of the polydisperse multiparticle volumes reveal unequivocally the classical manifestations of the effect of weak localization of electromagnetic waves in discrete random media, thereby corroborating the universal interference nature of coherent backscattering. The polarization opposition effect is shown to be the least robust manifestation of weak localization fading away with increasing particle size parameter.

Applications of stochastic mechanics to polyatomic lattices

NASA Astrophysics Data System (ADS)

Beumée, J. G. B.; Vilallonga, E.; Rabitz, H.

1990-03-01

Stochastic quantization in the sense of Nelson provides an alternative interpretation of some aspects of quantum mechanics in the coordinate representation, and it was combined recently with the Ford, Kac, and Mazur (FKM) approximation [J. Math. Phys. 6, 504 (1965)] for large lattices to construct a quantum analog to the Brownian motion process. In this paper a similar approach is applied to model the effect of temperature fluctuations in a one-dimensional ordered chain of atoms with nearest-neighbor linear forces. However, we do not make use of the FKM approximation, and as a consequence the statistical properties of the involved processes are exactly determined by the lattice force field. In particular, we evaluate the covariance matrix for the fluctuations, and we examine its high- and low-temperature behavior. Because of the translation invariance of the interaction potential, the covariance matrix for the fluctuations becomes singular implying that the associated probability density has equal density along the zero eigenvector of the interaction matrix. This behavior is readily interpreted in terms of the motion of the center of mass of the system, which corresponds to a stochastically perturbed translation, while all other modes are bounded with a probability of 1. As is well known, the transformation to internal (bondlength) coordinates leads to a Hamiltonian specified by a nonsingular interaction matrix. We examine the variance of the fluctuations for the internal coordinates, and we show that in the high-temperature limit the result agrees with that of classical statistical mechanics. Both the position and bondlength of the surface atom decrease with time as is expected for a semi-infinite lattice. However, the position of the surface atom is less dependent on substrate-atom positions than is the surface bondlength on substrate bondlengths. Finally, the autocorrelation function of the surface bondlength in the case of a semi-infinite lattice limit is investigated for low- and high-temperature limits.

Fast radiative transfer models for retrieval of cloud properties in the back-scattering region: application to DSCOVR-EPIC sensor

NASA Astrophysics Data System (ADS)

Molina Garcia, Victor; Sasi, Sruthy; Efremenko, Dmitry; Doicu, Adrian; Loyola, Diego

2017-04-01

In this work, the requirements for the retrieval of cloud properties in the back-scattering region are described, and their application to the measurements taken by the Earth Polychromatic Imaging Camera (EPIC) on board the Deep Space Climate Observatory (DSCOVR) is shown. Various radiative transfer models and their linearizations are implemented, and their advantages and issues are analyzed. As radiative transfer calculations in the back-scattering region are computationally time-consuming, several acceleration techniques are also studied. The radiative transfer models analyzed include the exact Discrete Ordinate method with Matrix Exponential (DOME), the Matrix Operator method with Matrix Exponential (MOME), and the approximate asymptotic and equivalent Lambertian cloud models. To reduce the computational cost of the line-by-line (LBL) calculations, the k-distribution method, the Principal Component Analysis (PCA) and a combination of the k-distribution method plus PCA are used. The linearized radiative transfer models for retrieval of cloud properties include the Linearized Discrete Ordinate method with Matrix Exponential (LDOME), the Linearized Matrix Operator method with Matrix Exponential (LMOME) and the Forward-Adjoint Discrete Ordinate method with Matrix Exponential (FADOME). These models were applied to the EPIC oxygen-A band absorption channel at 764 nm. It is shown that the approximate asymptotic and equivalent Lambertian cloud models give inaccurate results, so an offline processor for the retrieval of cloud properties in the back-scattering region requires the use of exact models such as DOME and MOME, which behave similarly. The combination of the k-distribution method plus PCA presents similar accuracy to the LBL calculations, but it is up to 360 times faster, and the relative errors for the computed radiances are less than 1.5% compared to the results when the exact phase function is used. Finally, the linearized models studied show similar behavior, with relative errors less than 1% for the radiance derivatives, but FADOME is 2 times faster than LDOME and 2.5 times faster than LMOME.

Numerical simulations of electromagnetic scattering by Solar system objects

NASA Astrophysics Data System (ADS)

Dlugach, Janna M.

2016-11-01

Having been profoundly stimulated by the seminal work of Viktor V. Sobolev, I have been involved in multi-decadal research in the fields of radiative transfer, electromagnetic scattering by morphologically complex particles and particulate media, and planetary remote sensing. Much of this research has been done in close collaboration with other "descendants" of Academician Sobolev. This tutorial paper gives a representative overview of the results of extensive numerical simulations (in the vast majority carried out in collaboration with Michael Mishchenko) used to analyze remote-sensing observations of Solar system objects and based on highly accurate methods of the radiative transfer theory and direct computer solvers of the Maxwell equations. Using the atmosphere of Jupiter as a proving ground and performing T-matrix and radiative-transfer calculations helps demonstrate the strong effect of aerosol-particle shapes on the accuracy of remote-sensing retrievals. I then discuss the application of the T-matrix method, a numerically exact solution of the vector radiative transfer equation, and the theory of coherent backscattering to an analysis of polarimetric radar observations of Saturn's rings. Numerical modeling performed by using the superposition T-matrix method in application to cometary dust in the form of aggregates serves to reproduce the results of polarimetric observations of the distant comet C/2010 S1. On the basis of direct computer solutions of the Maxwell equations, it is demonstrated that all backscattering effects predicted by the low-density theories of radiative transfer and coherent backscattering can also be identified for media with volume packing densities typically encountered in natural and artificial environments. This result implies that spectacular opposition effects observed for some high-albedo atmoshereless Solar system bodies can be attributed to coherent backscattering of sunlight by regolith layers composed of microscopic particles.

Semi-exact concentric atomic density fitting: Reduced cost and increased accuracy compared to standard density fitting

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

Hollman, David S.; Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061; Schaefer, Henry F.

2014-02-14

A local density fitting scheme is considered in which atomic orbital (AO) products are approximated using only auxiliary AOs located on one of the nuclei in that product. The possibility of variational collapse to an unphysical “attractive electron” state that can affect such density fitting [P. Merlot, T. Kjærgaard, T. Helgaker, R. Lindh, F. Aquilante, S. Reine, and T. B. Pedersen, J. Comput. Chem. 34, 1486 (2013)] is alleviated by including atom-wise semidiagonal integrals exactly. Our approach leads to a significant decrease in the computational cost of density fitting for Hartree–Fock theory while still producing results with errors 2–5 timesmore » smaller than standard, nonlocal density fitting. Our method allows for large Hartree–Fock and density functional theory computations with exact exchange to be carried out efficiently on large molecules, which we demonstrate by benchmarking our method on 200 of the most widely used prescription drug molecules. Our new fitting scheme leads to smooth and artifact-free potential energy surfaces and the possibility of relatively simple analytic gradients.« less

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

Sun, Jianwei; Yang, Zenghui; Peng, Haowei

The uniform electron gas and the hydrogen atom play fundamental roles in condensed matter physics and quantum chemistry. The former has an infinite number of electrons uniformly distributed over the neutralizing positively charged background, and the latter only one electron bound to the proton. The uniform electron gas was used to derive the local spin density approximation to the exchange-correlation functional that undergirds the development of the Kohn-Sham density functional theory. We show here that the ground-state exchange-correlation energies of the hydrogen atom and many other 1- and 2-electron systems are modeled surprisingly well by a different local spin densitymore » approximation (LSDA0). LSDA0 is constructed to satisfy exact constraints but agrees surprisingly well with the exact results for a uniform two-electron density in a finite, curved three-dimensional space. We also apply LSDA0 to excited or noded 1-electron densities, where it works less well. Furthermore, we show that the localization of the exact exchange hole for a 1- or 2-electron ground state can be measured by the ratio of the exact exchange energy to its optimal lower bound.« less

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

Tang, Zhoufei; Ouyang, Xiaolong; Gong, Zhihao

An extended hierarchy equation of motion (HEOM) is proposed and applied to study the dynamics of the spin-boson model. In this approach, a complete set of orthonormal functions are used to expand an arbitrary bath correlation function. As a result, a complete dynamic basis set is constructed by including the system reduced density matrix and auxiliary fields composed of these expansion functions, where the extended HEOM is derived for the time derivative of each element. The reliability of the extended HEOM is demonstrated by comparison with the stochastic Hamiltonian approach under room-temperature classical ohmic and sub-ohmic noises and the multilayermore » multiconfiguration time-dependent Hartree theory under zero-temperature quantum ohmic noise. Upon increasing the order in the hierarchical expansion, the result obtained from the extended HOEM systematically converges to the numerically exact answer.« less

Exact conditions on the temperature dependence of density functionals

DOE PAGES

Burke, K.; Smith, J. C.; Grabowski, P. E.; ...

2016-05-15

Universal exact conditions guided the construction of most ground-state density functional approximations in use today. Here, we derive the relation between the entropy and Mermin free energy density functionals for thermal density functional theory. Both the entropy and sum of kinetic and electron-electron repulsion functionals are shown to be monotonically increasing with temperature, while the Mermin functional is concave downwards. Analogous relations are found for both exchange and correlation. The importance of these conditions is illustrated in two extremes: the Hubbard dimer and the uniform gas.

Obtaining highly excited eigenstates of the localized XX chain via DMRG-X.

PubMed

Devakul, Trithep; Khemani, Vedika; Pollmann, Frank; Huse, David A; Sondhi, S L

2017-12-13

We benchmark a variant of the recently introduced density matrix renormalization group (DMRG)-X algorithm against exact results for the localized random field XX chain. We find that the eigenstates obtained via DMRG-X exhibit a highly accurate l-bit description for system sizes much bigger than the direct, many-body, exact diagonalization in the spin variables is able to access. We take advantage of the underlying free fermion description of the XX model to accurately test the strengths and limitations of this algorithm for large system sizes. We discuss the theoretical constraints on the performance of the algorithm from the entanglement properties of the eigenstates, and its actual performance at different values of disorder. A small but significant improvement to the algorithm is also presented, which helps significantly with convergence. We find that, at high entanglement, DMRG-X shows a bias towards eigenstates with low entanglement, but can be improved with increased bond dimension. This result suggests that one must be careful when applying the algorithm for interacting many-body localized spin models near a transition.This article is part of the themed issue 'Breakdown of ergodicity in quantum systems: from solids to synthetic matter'. © 2017 The Author(s).

Obtaining highly excited eigenstates of the localized XX chain via DMRG-X

NASA Astrophysics Data System (ADS)

Devakul, Trithep; Khemani, Vedika; Pollmann, Frank; Huse, David A.; Sondhi, S. L.

2017-10-01

We benchmark a variant of the recently introduced density matrix renormalization group (DMRG)-X algorithm against exact results for the localized random field XX chain. We find that the eigenstates obtained via DMRG-X exhibit a highly accurate l-bit description for system sizes much bigger than the direct, many-body, exact diagonalization in the spin variables is able to access. We take advantage of the underlying free fermion description of the XX model to accurately test the strengths and limitations of this algorithm for large system sizes. We discuss the theoretical constraints on the performance of the algorithm from the entanglement properties of the eigenstates, and its actual performance at different values of disorder. A small but significant improvement to the algorithm is also presented, which helps significantly with convergence. We find that, at high entanglement, DMRG-X shows a bias towards eigenstates with low entanglement, but can be improved with increased bond dimension. This result suggests that one must be careful when applying the algorithm for interacting many-body localized spin models near a transition. This article is part of the themed issue 'Breakdown of ergodicity in quantum systems: from solids to synthetic matter'.

Finite-element time evolution operator for the anharmonic oscillator

NASA Technical Reports Server (NTRS)

Milton, Kimball A.

1995-01-01

The finite-element approach to lattice field theory is both highly accurate (relative errors approximately 1/N(exp 2), where N is the number of lattice points) and exactly unitary (in the sense that canonical commutation relations are exactly preserved at the lattice sites). In this talk I construct matrix elements for dynamical variables and for the time evolution operator for the anharmonic oscillator, for which the continuum Hamiltonian is H = p(exp 2)/2 + lambda q(exp 4)/4. Construction of such matrix elements does not require solving the implicit equations of motion. Low order approximations turn out to be extremely accurate. For example, the matrix element of the time evolution operator in the harmonic oscillator ground state gives a results for the anharmonic oscillator ground state energy accurate to better than 1 percent, while a two-state approximation reduces the error to less than 0.1 percent.

Partial transpose of random quantum states: Exact formulas and meanders

NASA Astrophysics Data System (ADS)

Fukuda, Motohisa; Śniady, Piotr

2013-04-01

We investigate the asymptotic behavior of the empirical eigenvalues distribution of the partial transpose of a random quantum state. The limiting distribution was previously investigated via Wishart random matrices indirectly (by approximating the matrix of trace 1 by the Wishart matrix of random trace) and shown to be the semicircular distribution or the free difference of two free Poisson distributions, depending on how dimensions of the concerned spaces grow. Our use of Wishart matrices gives exact combinatorial formulas for the moments of the partial transpose of the random state. We find three natural asymptotic regimes in terms of geodesics on the permutation groups. Two of them correspond to the above two cases; the third one turns out to be a new matrix model for the meander polynomials. Moreover, we prove the convergence to the semicircular distribution together with its extreme eigenvalues under weaker assumptions, and show large deviation bound for the latter.

Ground-state properties of Na2IrO3 determined from an ab initio Hamiltonian and its extensions containing Kitaev and extended Heisenberg interactions

NASA Astrophysics Data System (ADS)

Okubo, Tsuyoshi; Shinjo, Kazuya; Yamaji, Youhei; Kawashima, Naoki; Sota, Shigetoshi; Tohyama, Takami; Imada, Masatoshi

2017-08-01

We investigate the ground state properties of Na2IrO3 based on numerical calculations of the recently proposed ab initio Hamiltonian represented by Kitaev and extended Heisenberg interactions. To overcome the limitation posed by small tractable system sizes in the exact diagonalization study employed in a previous study [Y. Yamaji et al., Phys. Rev. Lett. 113, 107201 (2014), 10.1103/PhysRevLett.113.107201], we apply a two-dimensional density matrix renormalization group and an infinite-size tensor-network method. By calculating at much larger system sizes, we critically test the validity of the exact diagonalization results. The results consistently indicate that the ground state of Na2IrO3 is a magnetically ordered state with zigzag configuration in agreement with experimental observations and the previous diagonalization study. Applications of the two independent methods in addition to the exact diagonalization study further uncover a consistent and rich phase diagram near the zigzag phase beyond the accessibility of the exact diagonalization. For example, in the parameter space away from the ab initio value of Na2IrO3 controlled by the trigonal distortion, we find three phases: (i) an ordered phase with the magnetic moment aligned mutually in 120 degrees orientation on every third hexagon, (ii) a magnetically ordered phase with a 16-site unit cell, and (iii) an ordered phase with presumably incommensurate periodicity of the moment. It suggests that potentially rich magnetic structures may appear in A2IrO3 compounds for A other than Na. The present results also serve to establish the accuracy of the first-principles approach in reproducing the available experimental results thereby further contributing to finding a route to realize the Kitaev spin liquid.

Communication: Density functional theory model for multi-reference systems based on the exact-exchange hole normalization

NASA Astrophysics Data System (ADS)

Laqua, Henryk; Kussmann, Jörg; Ochsenfeld, Christian

2018-03-01

The correct description of multi-reference electronic ground states within Kohn-Sham density functional theory (DFT) requires an ensemble-state representation, employing fractionally occupied orbitals. However, the use of fractional orbital occupation leads to non-normalized exact-exchange holes, resulting in large fractional-spin errors for conventional approximative density functionals. In this communication, we present a simple approach to directly include the exact-exchange-hole normalization into DFT. Compared to conventional functionals, our model strongly improves the description for multi-reference systems, while preserving the accuracy in the single-reference case. We analyze the performance of our proposed method at the example of spin-averaged atoms and spin-restricted bond dissociation energy surfaces.

Communication: Density functional theory model for multi-reference systems based on the exact-exchange hole normalization.

PubMed

Laqua, Henryk; Kussmann, Jörg; Ochsenfeld, Christian

2018-03-28

The correct description of multi-reference electronic ground states within Kohn-Sham density functional theory (DFT) requires an ensemble-state representation, employing fractionally occupied orbitals. However, the use of fractional orbital occupation leads to non-normalized exact-exchange holes, resulting in large fractional-spin errors for conventional approximative density functionals. In this communication, we present a simple approach to directly include the exact-exchange-hole normalization into DFT. Compared to conventional functionals, our model strongly improves the description for multi-reference systems, while preserving the accuracy in the single-reference case. We analyze the performance of our proposed method at the example of spin-averaged atoms and spin-restricted bond dissociation energy surfaces.

Exact differential equation for the density and ionization energy of a many-particle system

NASA Technical Reports Server (NTRS)

Levy, M.; Perdew, J. P.; Sahni, V.

1984-01-01

The present investigation is concerned with relations studied by Hohenberg and Kohn (1964) and Kohn and Sham (1965). The properties of a ground-state many-electron system are determined by the electron density. The correct differential equation for the density, as dictated by density-functional theory, is presented. It is found that the ground-state density n of a many-electron system obeys a Schroedinger-like differential equation which may be solved by standard Kohn-Sham programs. Results are connected to the traditional exact Kohn-Sham theory. It is pointed out that the results of the current investigations are readily extended to spin-density functional theory.

An O(log sup 2 N) parallel algorithm for computing the eigenvalues of a symmetric tridiagonal matrix

NASA Technical Reports Server (NTRS)

Swarztrauber, Paul N.

1989-01-01

An O(log sup 2 N) parallel algorithm is presented for computing the eigenvalues of a symmetric tridiagonal matrix using a parallel algorithm for computing the zeros of the characteristic polynomial. The method is based on a quadratic recurrence in which the characteristic polynomial is constructed on a binary tree from polynomials whose degree doubles at each level. Intervals that contain exactly one zero are determined by the zeros of polynomials at the previous level which ensures that different processors compute different zeros. The exact behavior of the polynomials at the interval endpoints is used to eliminate the usual problems induced by finite precision arithmetic.

Exact diagonalization library for quantum electron models

NASA Astrophysics Data System (ADS)

Iskakov, Sergei; Danilov, Michael

2018-04-01

We present an exact diagonalization C++ template library (EDLib) for solving quantum electron models, including the single-band finite Hubbard cluster and the multi-orbital impurity Anderson model. The observables that can be computed using EDLib are single particle Green's functions and spin-spin correlation functions. This code provides three different types of Hamiltonian matrix storage that can be chosen based on the model.

Towards an exact correlated orbital theory for electrons

NASA Astrophysics Data System (ADS)

Bartlett, Rodney J.

2009-12-01

The formal and computational attraction of effective one-particle theories like Hartree-Fock and density functional theory raise the question of how far such approaches can be taken to offer exact results for selected properties of electrons in atoms, molecules, and solids. Some properties can be exactly described within an effective one-particle theory, like principal ionization potentials and electron affinities. This fact can be used to develop equations for a correlated orbital theory (COT) that guarantees a correct one-particle energy spectrum. They are built upon a coupled-cluster based frequency independent self-energy operator presented here, which distinguishes the approach from Dyson theory. The COT also offers an alternative to Kohn-Sham density functional theory (DFT), whose objective is to represent the electronic density exactly as a single determinant, while paying less attention to the energy spectrum. For any estimate of two-electron terms COT offers a litmus test of its accuracy for principal Ip's and Ea's. This feature for approximating the COT equations is illustrated numerically.

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.

Exactly solved mixed spin-(1,1/2) Ising-Heisenberg diamond chain with a single-ion anisotropy

NASA Astrophysics Data System (ADS)

Lisnyi, Bohdan; Strečka, Jozef

2015-03-01

The mixed spin-(1,1/2) Ising-Heisenberg diamond chain with a single-ion anisotropy is exactly solved through the generalized decoration-iteration transformation and the transfer-matrix method. The decoration-iteration transformation is first used for establishing a rigorous mapping equivalence with the corresponding spin-1 Blume-Emery-Griffiths chain, which is subsequently exactly treated within the transfer-matrix technique. Apart from three classical ground states the model exhibits three striking quantum ground states in which a singlet-dimer state of the interstitial Heisenberg spins is accompanied either with a frustrated state or a polarized state or a non-magnetic state of the nodal Ising spins. It is evidenced that two magnetization plateaus at zero and/or one-half of the saturation magnetization may appear in low-temperature magnetization curves. The specific heat may display remarkable temperature dependences with up to three and four distinct round maxima in a zero and non-zero magnetic field, respectively.

Optics of Water Microdroplets with Soot Inclusions: Exact Versus Approximate Results

NASA Technical Reports Server (NTRS)

Liu, Li; Mishchenko, Michael I.

2016-01-01

We use the recently generalized version of the multi-sphere superposition T-matrix method (STMM) to compute the scattering and absorption properties of microscopic water droplets contaminated by black carbon. The soot material is assumed to be randomly distributed throughout the droplet interior in the form of numerous small spherical inclusions. Our numerically-exact STMM results are compared with approximate ones obtained using the Maxwell-Garnett effective-medium approximation (MGA) and the Monte Carlo ray-tracing approximation (MCRTA). We show that the popular MGA can be used to calculate the droplet optical cross sections, single-scattering albedo, and asymmetry parameter provided that the soot inclusions are quasi-uniformly distributed throughout the droplet interior, but can fail in computations of the elements of the scattering matrix depending on the volume fraction of soot inclusions. The integral radiative characteristics computed with the MCRTA can deviate more significantly from their exact STMM counterparts, while accurate MCRTA computations of the phase function require droplet size parameters substantially exceeding 60.

Crossover ensembles of random matrices and skew-orthogonal polynomials

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

Kumar, Santosh, E-mail: skumar.physics@gmail.com; Pandey, Akhilesh, E-mail: ap0700@mail.jnu.ac.in

2011-08-15

Highlights: > We study crossover ensembles of Jacobi family of random matrices. > We consider correlations for orthogonal-unitary and symplectic-unitary crossovers. > We use the method of skew-orthogonal polynomials and quaternion determinants. > We prove universality of spectral correlations in crossover ensembles. > We discuss applications to quantum conductance and communication theory problems. - Abstract: In a recent paper (S. Kumar, A. Pandey, Phys. Rev. E, 79, 2009, p. 026211) we considered Jacobi family (including Laguerre and Gaussian cases) of random matrix ensembles and reported exact solutions of crossover problems involving time-reversal symmetry breaking. In the present paper we givemore » details of the work. We start with Dyson's Brownian motion description of random matrix ensembles and obtain universal hierarchic relations among the unfolded correlation functions. For arbitrary dimensions we derive the joint probability density (jpd) of eigenvalues for all transitions leading to unitary ensembles as equilibrium ensembles. We focus on the orthogonal-unitary and symplectic-unitary crossovers and give generic expressions for jpd of eigenvalues, two-point kernels and n-level correlation functions. This involves generalization of the theory of skew-orthogonal polynomials to crossover ensembles. We also consider crossovers in the circular ensembles to show the generality of our method. In the large dimensionality limit, correlations in spectra with arbitrary initial density are shown to be universal when expressed in terms of a rescaled symmetry breaking parameter. Applications of our crossover results to communication theory and quantum conductance problems are also briefly discussed.« less

Exact results of 1D traffic cellular automata: The low-density behavior of the Fukui-Ishibashi model

NASA Astrophysics Data System (ADS)

Salcido, Alejandro; Hernández-Zapata, Ernesto; Carreón-Sierra, Susana

2018-03-01

The maximum entropy states of the cellular automata models for traffic flow in a single-lane with no anticipation are presented and discussed. The exact analytical solutions for the low-density behavior of the stochastic Fukui-Ishibashi traffic model were obtained and compared with computer simulations of the model. An excellent agreement was found.

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.

Fine structure of the entanglement entropy in the O(2) model.

PubMed

Yang, Li-Ping; Liu, Yuzhi; Zou, Haiyuan; Xie, Z Y; Meurice, Y

2016-01-01

We compare two calculations of the particle density in the superfluid phase of the O(2) model with a chemical potential μ in 1+1 dimensions. The first relies on exact blocking formulas from the Tensor Renormalization Group (TRG) formulation of the transfer matrix. The second is a worm algorithm. We show that the particle number distributions obtained with the two methods agree well. We use the TRG method to calculate the thermal entropy and the entanglement entropy. We describe the particle density, the two entropies and the topology of the world lines as we increase μ to go across the superfluid phase between the first two Mott insulating phases. For a sufficiently large temporal size, this process reveals an interesting fine structure: the average particle number and the winding number of most of the world lines in the Euclidean time direction increase by one unit at a time. At each step, the thermal entropy develops a peak and the entanglement entropy increases until we reach half-filling and then decreases in a way that approximately mirrors the ascent. This suggests an approximate fermionic picture.

Entangled quantum electronic wavefunctions of the Mn₄CaO₅ cluster in photosystem II.

PubMed

Kurashige, Yuki; Chan, Garnet Kin-Lic; Yanai, Takeshi

2013-08-01

It is a long-standing goal to understand the reaction mechanisms of catalytic metalloenzymes at an entangled many-electron level, but this is hampered by the exponential complexity of quantum mechanics. Here, by exploiting the special structure of physical quantum states and using the density matrix renormalization group, we compute near-exact many-electron wavefunctions of the Mn4CaO5 cluster of photosystem II, with more than 1 × 10(18) quantum degrees of freedom. This is the first treatment of photosystem II beyond the single-electron picture of density functional theory. Our calculations support recent modifications to the structure determined by X-ray crystallography. We further identify multiple low-lying energy surfaces associated with the structural distortion seen using X-ray crystallography, highlighting multistate reactivity in the chemistry of the cluster. Direct determination of Mn spin-projections from our wavefunctions suggests that current candidates that have been recently distinguished using parameterized spin models should be reassessed. Through entanglement maps, we reveal rich information contained in the wavefunctions on bonding changes in the cycle.

Efficient evaluation of nonlocal operators in density functional theory

NASA Astrophysics Data System (ADS)

Chen, Ying-Chih; Chen, Jing-Zhe; Michaud-Rioux, Vincent; Shi, Qing; Guo, Hong

2018-02-01

We present a method which combines plane waves (PW) and numerical atomic orbitals (NAO) to efficiently evaluate nonlocal operators in density functional theory with periodic boundary conditions. Nonlocal operators are first expanded using PW and then transformed to NAO so that the problem of distance-truncation is avoided. The general formalism is implemented using the hybrid functional HSE06 where the nonlocal operator is the exact exchange. Comparison of electronic structures of a wide range of semiconductors to a pure PW scheme validates the accuracy of our method. Due to the locality of NAO, thus sparsity of matrix representations of the operators, the computational complexity of the method is asymptotically quadratic in the number of electrons. Finally, we apply the technique to investigate the electronic structure of the interface between a single-layer black phosphorous and the high-κ dielectric material c -HfO2 . We predict that the band offset between the two materials is 1.29 eV and 2.18 eV for valence and conduction band edges, respectively, and such offsets are suitable for 2D field-effect transistor applications.

Analytic nuclear forces and molecular properties from full configuration interaction quantum Monte Carlo

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

Thomas, Robert E.; Overy, Catherine; Opalka, Daniel

Unbiased stochastic sampling of the one- and two-body reduced density matrices is achieved in full configuration interaction quantum Monte Carlo with the introduction of a second, “replica” ensemble of walkers, whose population evolves in imaginary time independently from the first and which entails only modest additional computational overheads. The matrices obtained from this approach are shown to be representative of full configuration-interaction quality and hence provide a realistic opportunity to achieve high-quality results for a range of properties whose operators do not necessarily commute with the Hamiltonian. A density-matrix formulated quasi-variational energy estimator having been already proposed and investigated, themore » present work extends the scope of the theory to take in studies of analytic nuclear forces, molecular dipole moments, and polarisabilities, with extensive comparison to exact results where possible. These new results confirm the suitability of the sampling technique and, where sufficiently large basis sets are available, achieve close agreement with experimental values, expanding the scope of the method to new areas of investigation.« less

Single-molecule stochastic times in a reversible bimolecular reaction

NASA Astrophysics Data System (ADS)

Keller, Peter; Valleriani, Angelo

2012-08-01

In this work, we consider the reversible reaction between reactants of species A and B to form the product C. We consider this reaction as a prototype of many pseudobiomolecular reactions in biology, such as for instance molecular motors. We derive the exact probability density for the stochastic waiting time that a molecule of species A needs until the reaction with a molecule of species B takes place. We perform this computation taking fully into account the stochastic fluctuations in the number of molecules of species B. We show that at low numbers of participating molecules, the exact probability density differs from the exponential density derived by assuming the law of mass action. Finally, we discuss the condition of detailed balance in the exact stochastic and in the approximate treatment.

Matrix computations in MACSYMA

NASA Technical Reports Server (NTRS)

Wang, P. S.

1977-01-01

Facilities built into MACSYMA for manipulating matrices with numeric or symbolic entries are described. Computations will be done exactly, keeping symbols as symbols. Topics discussed include how to form a matrix and create other matrices by transforming existing matrices within MACSYMA; arithmetic and other computation with matrices; and user control of computational processes through the use of optional variables. Two algorithms designed for sparse matrices are given. The computing times of several different ways to compute the determinant of a matrix are compared.

Effect of Interaction on the Majorana Zero Modes in the Kitaev Chain at Half Filling

NASA Astrophysics Data System (ADS)

Li, Zhidan; Han, Qiang

2018-04-01

The one dimension interacting Kitaev chain at half filling is studied. The symmetry of the Hamiltonian is examined by dual transformations and various physical quantities as functions of the fermion-fermion interaction $U$ are calculated systematically using the density matrix renormalization group method. A special value of interaction $U_p$ is revealed in the topological region of the phase diagram. We show that at $U_p$ the ground states are strictly two-fold degenerate even though the chain length is finite and the zero-energy peak due to the Majorana zero modes is maximally enhanced and exactly localized at the end sites. $U_p$ may be attractive or repulsive depending on other system parameters. We also give a qualitative understanding of the effect of interaction under the self-consistent mean field framework.

The spin-temperature theory of dynamic nuclear polarization and nuclear spin-lattice relaxation

NASA Technical Reports Server (NTRS)

Byvik, C. E.; Wollan, D. S.

1974-01-01

A detailed derivation of the equations governing dynamic nuclear polarization (DNP) and nuclear spin lattice relaxation by use of the spin temperature theory has been carried to second order in a perturbation expansion of the density matrix. Nuclear spin diffusion in the rapid diffusion limit and the effects of the coupling of the electron dipole-dipole reservoir (EDDR) with the nuclear spins are incorporated. The complete expression for the dynamic nuclear polarization has been derived and then examined in detail for the limit of well resolved solid effect transitions. Exactly at the solid effect transition peaks, the conventional solid-effect DNP results are obtained, but with EDDR effects on the nuclear relaxation and DNP leakage factor included. Explicit EDDR contributions to DNP are discussed, and a new DNP effect is predicted.

Feedback controlled optics with wavefront compensation

NASA Technical Reports Server (NTRS)

Breckenridge, William G. (Inventor); Redding, David C. (Inventor)

1993-01-01

The sensitivity model of a complex optical system obtained by linear ray tracing is used to compute a control gain matrix by imposing the mathematical condition for minimizing the total wavefront error at the optical system's exit pupil. The most recent deformations or error states of the controlled segments or optical surfaces of the system are then assembled as an error vector, and the error vector is transformed by the control gain matrix to produce the exact control variables which will minimize the total wavefront error at the exit pupil of the optical system. These exact control variables are then applied to the actuators controlling the various optical surfaces in the system causing the immediate reduction in total wavefront error observed at the exit pupil of the optical system.

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.

Hyperfine coupling constants of the nitrogen and phosphorus atoms: A challenge for exact-exchange density-functional and post-Hartree-Fock methods

NASA Astrophysics Data System (ADS)

Kaupp, Martin; Arbuznikov, Alexei V.; Heßelmann, Andreas; Görling, Andreas

2010-05-01

The isotropic hyperfine coupling constants of the free N(S4) and P(S4) atoms have been evaluated with high-level post-Hartree-Fock and density-functional methods. The phosphorus hyperfine coupling presents a significant challenge to both types of methods. With large basis sets, MP2 and coupled-cluster singles and doubles calculations give much too small values for the phosphorus atom. Triple excitations are needed in coupled-cluster calculations to achieve reasonable agreement with experiment. None of the standard density functionals reproduce even the correct sign of this hyperfine coupling. Similarly, the computed hyperfine couplings depend crucially on the self-consistent treatment in exact-exchange density-functional theory within the optimized effective potential (OEP) method. Well-balanced auxiliary and orbital basis sets are needed for basis-expansion exact-exchange-only OEP approaches to come close to Hartree-Fock or numerical OEP data. Results from the localized Hartree-Fock and Krieger-Li-Iafrate approximations deviate notably from exact OEP data in spite of very similar total energies. Of the functionals tested, only full exact-exchange methods augmented by a correlation functional gave at least the correct sign of the P(S4) hyperfine coupling but with too low absolute values. The subtle interplay between the spin-polarization contributions of the different core shells has been analyzed, and the influence of even very small changes in the exchange-correlation potential could be identified.

Controllability of flow-conservation networks

NASA Astrophysics Data System (ADS)

Zhao, Chen; Zeng, An; Jiang, Rui; Yuan, Zhengzhong; Wang, Wen-Xu

2017-07-01

The ultimate goal of exploring complex networks is to control them. As such, controllability of complex networks has been intensively investigated. Despite recent advances in studying the impact of a network's topology on its controllability, a comprehensive understanding of the synergistic impact of network topology and dynamics on controllability is still lacking. Here, we explore the controllability of flow-conservation networks, trying to identify the minimal number of driver nodes that can guide the network to any desirable state. We develop a method to analyze the controllability on flow-conservation networks based on exact controllability theory, transforming the original analysis on adjacency matrix to Laplacian matrix. With this framework, we systematically investigate the impact of some key factors of networks, including link density, link directionality, and link polarity, on the controllability of these networks. We also obtain the analytical equations by investigating the network's structural properties approximatively and design the efficient tools. Finally, we consider some real networks with flow dynamics, finding that their controllability is significantly different from that predicted by only considering the topology. These findings deepen our understanding of network controllability with flow-conservation dynamics and provide a general framework to incorporate real dynamics in the analysis of network controllability.

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.

Exact solution of matricial Φ23 quantum field theory

NASA Astrophysics Data System (ADS)

Grosse, Harald; Sako, Akifumi; Wulkenhaar, Raimar

2017-12-01

We apply a recently developed method to exactly solve the Φ3 matrix model with covariance of a two-dimensional theory, also known as regularised Kontsevich model. Its correlation functions collectively describe graphs on a multi-punctured 2-sphere. We show how Ward-Takahashi identities and Schwinger-Dyson equations lead in a special large- N limit to integral equations that we solve exactly for all correlation functions. The solved model arises from noncommutative field theory in a special limit of strong deformation parameter. The limit defines ordinary 2D Schwinger functions which, however, do not satisfy reflection positivity.

Numerical study of a matrix-free trust-region SQP method for equality constrained optimization.

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

Heinkenschloss, Matthias; Ridzal, Denis; Aguilo, Miguel Antonio

2011-12-01

This is a companion publication to the paper 'A Matrix-Free Trust-Region SQP Algorithm for Equality Constrained Optimization' [11]. In [11], we develop and analyze a trust-region sequential quadratic programming (SQP) method that supports the matrix-free (iterative, in-exact) solution of linear systems. In this report, we document the numerical behavior of the algorithm applied to a variety of equality constrained optimization problems, with constraints given by partial differential equations (PDEs).

A minimal model for the structural energetics of VO2

NASA Astrophysics Data System (ADS)

Kim, Chanul; Marianetti, Chris; The Marianetti Group Team

Resolving the structural, magnetic, and electronic structure of VO2 from the first-principles of quantum mechanics is still a forefront problem despite decades of attention. Hybrid functionals have been shown to qualitatively ruin the structural energetics. While density functional theory (DFT) combined with cluster extensions of dynamical mean-field theory (DMFT) have demonstrated promising results in terms of the electronic properties, structural phase stability has not yet been addressed. In order to capture the basic physics of the structural transition, we propose a minimal model of VO2 based on the one dimensional Peierls-Hubbard model and parameterize this based on DFT calculations of VO2. The total energy versus dimerization in the minimal mode is then solved numerically exactly using density matrix renormalization group (DMRG) and compared to the Hartree-Fock solution. We demonstrate that the Hartree-Fock solution exhibits the same pathologies as DFT+U, and spin density functional theory for that matter, while the DMRG solution is consistent with experimental observation. Our results demonstrate the critical role of non-locality in the total energy, and this will need to be accounted for to obtain a complete description of VO2 from first-principles. The authors acknowledge support from FAME, one of six centers of STARnet, a Semiconductor Research Corporation program sponsored by MARCO and DARPA.

The free and forced vibrations of structures using the finite dynamic element method. Ph.D. Thesis, Aug. 1991 Final Report

NASA Technical Reports Server (NTRS)

Fergusson, Neil J.

1992-01-01

In addition to an extensive review of the literature on exact and corrective displacement based methods of vibration analysis, a few theorems are proven concerning the various structural matrices involved in such analyses. In particular, the consistent mass matrix and the quasi-static mass matrix are shown to be equivalent, in the sense that the terms in their respective Taylor expansions are proportional to one another, and that they both lead to the same dynamic stiffness matrix when used with the appropriate stiffness matrix.

Unitary-matrix models as exactly solvable string theories

NASA Technical Reports Server (NTRS)

Periwal, Vipul; Shevitz, Danny

1990-01-01

Exact differential equations are presently found for the scaling functions of models of unitary matrices which are solved in a double-scaling limit, using orthogonal polynomials on a circle. For the case of the simplest, k = 1 model, the Painleve II equation with constant 0 is obtained; possible nonperturbative phase transitions exist for these models. Equations are presented for k = 2 and 3, and discussed with a view to asymptotic behavior.

Core-softened potentials, multiple liquid-liquid critical points, and density anomaly regions: An exact solution

NASA Astrophysics Data System (ADS)

Rizzatti, Eduardo O.; Barbosa, Marco Aurélio A.; Barbosa, Marcia C.

2018-02-01

The pressure versus temperature phase diagram of a system of particles interacting through a multiscale shoulder-like potential is exactly computed in one dimension. The N-shoulder potential exhibits N density anomaly regions in the phase diagram if the length scales can be connected by a convex curve. The result is analyzed in terms of the convexity of the Gibbs free energy.

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.

The vector radiative transfer numerical model of coupled ocean-atmosphere system using the matrix-operator method

NASA Astrophysics Data System (ADS)

Xianqiang, He; Delu, Pan; Yan, Bai; Qiankun, Zhu

2005-10-01

The numerical model of the vector radiative transfer of the coupled ocean-atmosphere system is developed based on the matrix-operator method, which is named PCOART. In PCOART, using the Fourier analysis, the vector radiative transfer equation (VRTE) splits up into a set of independent equations with zenith angle as only angular coordinate. Using the Gaussian-Quadrature method, VRTE is finally transferred into the matrix equation, which is calculated by using the adding-doubling method. According to the reflective and refractive properties of the ocean-atmosphere interface, the vector radiative transfer numerical model of ocean and atmosphere is coupled in PCOART. By comparing with the exact Rayleigh scattering look-up-table of MODIS(Moderate-resolution Imaging Spectroradiometer), it is shown that PCOART is an exact numerical calculation model, and the processing methods of the multi-scattering and polarization are correct in PCOART. Also, by validating with the standard problems of the radiative transfer in water, it is shown that PCOART could be used to calculate the underwater radiative transfer problems. Therefore, PCOART is a useful tool to exactly calculate the vector radiative transfer of the coupled ocean-atmosphere system, which can be used to study the polarization properties of the radiance in the whole ocean-atmosphere system and the remote sensing of the atmosphere and ocean.

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

Donangelo, R.J.

An integral representation for the classical limit of the quantum mechanical S-matrix is developed and applied to heavy-ion Coulomb excitation and Coulomb-nuclear interference. The method combines the quantum principle of superposition with exact classical dynamics to describe the projectile-target system. A detailed consideration of the classical trajectories and of the dimensionless parameters that characterize the system is carried out. The results are compared, where possible, to exact quantum mechanical calculations and to conventional semiclassical calculations. It is found that in the case of backscattering the classical limit S-matrix method is able to almost exactly reproduce the quantum-mechanical S-matrix elements, andmore » therefore the transition probabilities, even for projectiles as light as protons. The results also suggest that this approach should be a better approximation for heavy-ion multiple Coulomb excitation than earlier semiclassical methods, due to a more accurate description of the classical orbits in the electromagnetic field of the target nucleus. Calculations using this method indicate that the rotational excitation probabilities in the Coulomb-nuclear interference region should be very sensitive to the details of the potential at the surface of the nucleus, suggesting that heavy-ion rotational excitation could constitute a sensitive probe of the nuclear potential in this region. The application to other problems as well as the present limits of applicability of the formalism are also discussed.« less

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.

A study of some non-equilibrium driven models and their contribution to the understanding of molecular motors

NASA Astrophysics Data System (ADS)

Mazilu, Irina; Gonzalez, Joshua

2008-03-01

From the point of view of a physicist, a bio-molecular motor represents an interesting non-equilibrium system and it is directly amenable to an analysis using standard methods of non-equilibrium statistical physics. We conduct a rigorous Monte Carlo study of three different driven lattice gas models that retain the basic behavior of three types of cytoskeletal molecular motors. Our models incorporate novel features such as realistic dynamics rules and complex motor-motor interactions. We are interested to have a deeper understanding of how various parameters influence the macroscopic behavior of these systems, what is the density profile and if the system undergoes a phase transition. On the analytical front, we computed the steady-state probability distributions exactly for the one of the models using the matrix method that was established in 1993 by B. Derrida et al. We also explored the possibilities offered by the ``Bethe ansatz'' method by mapping some well studied spin models into asymmetric simple exclusion models (already analyzed using computer simulations), and to use the results obtained for the spin models in finding an exact solution for our problem. We have exhaustive computational studies of the kinesin and dynein molecular motor models that prove to be very useful in checking our analytical work.

Fermionic entanglement in superconducting systems

NASA Astrophysics Data System (ADS)

Di Tullio, M.; Gigena, N.; Rossignoli, R.

2018-06-01

We examine distinct measures of fermionic entanglement in the exact ground state of a finite superconducting system. It is first shown that global measures such as the one-body entanglement entropy, which represents the minimum relative entropy between the exact ground state and the set of fermionic Gaussian states, exhibit a close correlation with the BCS gap, saturating in the strong superconducting regime. The same behavior is displayed by the bipartite entanglement between the set of all single-particle states k of positive quasimomenta and their time-reversed partners k ¯. In contrast, the entanglement associated with the reduced density matrix of four single-particle modes k ,k ¯ , k',k¯' , which can be measured through a properly defined fermionic concurrence, exhibits a different behavior, showing a peak in the vicinity of the superconducting transition for states k ,k' close to the Fermi level and becoming small in the strong coupling regime. In the latter, such reduced state exhibits, instead, a finite mutual information and quantum discord. While the first measures can be correctly estimated with the BCS approximation, the previous four-level concurrence lies strictly beyond the latter, requiring at least a particle-number projected BCS treatment for its description. Formal properties of all previous entanglement measures are as well discussed.

Numerically Exact Long Time Magnetization Dynamics Near the Nonequilibrium Kondo Regime

NASA Astrophysics Data System (ADS)

Cohen, Guy; Gull, Emanuel; Reichman, David; Millis, Andrew; Rabani, Eran

2013-03-01

The dynamical and steady-state spin response of the nonequilibrium Anderson impurity model to magnetic fields, bias voltages, and temperature is investigated by a numerically exact method which allows access to unprecedentedly long times. The method is based on using real, continuous time bold Monte Carlo techniques--quantum Monte Carlo sampling of diagrammatic corrections to a partial re-summation--in order to compute the kernel of a memory function, which is then used to determine the reduced density matrix. The method owes its effectiveness to the fact that the memory kernel is dominated by relatively short-time properties even when the system's dynamics are long-ranged. We make predictions regarding the non-monotonic temperature dependence of the system at high bias voltage and the oscillatory quench dynamics at high magnetic fields. We also discuss extensions of the method to the computation of transport properties and correlation functions, and its suitability as an impurity solver free from the need for analytical continuation in the context of dynamical mean field theory. This work is supported by the US Department of Energy under grant DE-SC0006613, by NSF-DMR-1006282 and by the US-Israel Binational Science Foundation. GC is grateful to the Yad Hanadiv-Rothschild Foundation for the award of a Rothschild Fellowship.

Non-equilibrium steady states in the Klein-Gordon theory

NASA Astrophysics Data System (ADS)

Doyon, Benjamin; Lucas, Andrew; Schalm, Koenraad; Bhaseen, M. J.

2015-03-01

We construct non-equilibrium steady states in the Klein-Gordon theory in arbitrary space dimension d following a local quench. We consider the approach where two independently thermalized semi-infinite systems, with temperatures {{T}L} and {{T}R}, are connected along a d-1-dimensional hypersurface. A current-carrying steady state, described by thermally distributed modes with temperatures {{T}L} and {{T}R} for left and right-moving modes, respectively, emerges at late times. The non-equilibrium density matrix is the exponential of a non-local conserved charge. We obtain exact results for the average energy current and the complete distribution of energy current fluctuations. The latter shows that the long-time energy transfer can be described by a continuum of independent Poisson processes, for which we provide the exact weights. We further describe the full time evolution of local observables following the quench. Averages of generic local observables, including the stress-energy tensor, approach the steady state with a power-law in time, where the exponent depends on the initial conditions at the connection hypersurface. We describe boundary conditions and special operators for which the steady state is reached instantaneously on the connection hypersurface. A semiclassical analysis of freely propagating modes yields the average energy current at large distances and late times. We conclude by comparing and contrasting our findings with results for interacting theories and provide an estimate for the timescale governing the crossover to hydrodynamics. As a modification of our Klein-Gordon analysis we also include exact results for free Dirac fermions.

Direct Measurement of the Density Matrix of a Quantum System

NASA Astrophysics Data System (ADS)

Thekkadath, G. S.; Giner, L.; Chalich, Y.; Horton, M. J.; Banker, J.; Lundeen, J. S.

2016-09-01

One drawback of conventional quantum state tomography is that it does not readily provide access to single density matrix elements since it requires a global reconstruction. Here, we experimentally demonstrate a scheme that can be used to directly measure individual density matrix elements of general quantum states. The scheme relies on measuring a sequence of three observables, each complementary to the last. The first two measurements are made weak to minimize the disturbance they cause to the state, while the final measurement is strong. We perform this joint measurement on polarized photons in pure and mixed states to directly measure their density matrix. The weak measurements are achieved using two walk-off crystals, each inducing a polarization-dependent spatial shift that couples the spatial and polarization degrees of freedom of the photons. This direct measurement method provides an operational meaning to the density matrix and promises to be especially useful for large dimensional states.

Direct Measurement of the Density Matrix of a Quantum System.

PubMed

Thekkadath, G S; Giner, L; Chalich, Y; Horton, M J; Banker, J; Lundeen, J S

2016-09-16

One drawback of conventional quantum state tomography is that it does not readily provide access to single density matrix elements since it requires a global reconstruction. Here, we experimentally demonstrate a scheme that can be used to directly measure individual density matrix elements of general quantum states. The scheme relies on measuring a sequence of three observables, each complementary to the last. The first two measurements are made weak to minimize the disturbance they cause to the state, while the final measurement is strong. We perform this joint measurement on polarized photons in pure and mixed states to directly measure their density matrix. The weak measurements are achieved using two walk-off crystals, each inducing a polarization-dependent spatial shift that couples the spatial and polarization degrees of freedom of the photons. This direct measurement method provides an operational meaning to the density matrix and promises to be especially useful for large dimensional states.

The effects of isotope-labeled analogs on the LC-IDMS measurement by comparison of ESI responses and matrix effect of melamine, 13C3-melamine, 13C3+15N3-melamine, and 15N3-melamine.

PubMed

Li, Xiu Qin; Zhang, Qing He; Yang, Zong; Li, Hong Mei; Huang, Dong Feng

2017-05-01

In this paper, the effect of isotope-labeled analogs on the liquid chromatography-isotope dilution mass spectrometry (LC-IDMS) measurement was evaluated based on the comparison research of electrospray ionization responses (ESI) and matrix effect of melamine, 13 C 3 -melamine, 13 C 3 + 15 N 3 -melamine, and 15 N 3 -melamine. The isotope-labeled melamines had similar ionization efficiency with melamine in the electrospray ionization source, but the intensity of corresponding quantitative fragment ions had distinctive differences. Based on the density functional theory at the B3LYP/6-311+G** level, this phenomenon was explained very well. The rare cleavage pathways of melamine, which just could be exactly identified by 15 N-labeled melamines, resulted in the difference of quantitative fragment ions between 15 N-labeled melamines and melamine. The interaction of ESI response between melamine and isotope-labeled melamines was investigated using MRM monitor mode. 15 N-labeled melamine had significant ion inter-suppression effect on melamine, while 13 C-labeled melamine had little influence on melamine. Finally, the influence of different isotope-labeled melamines on the LC-IDMS result was evaluated using the IDMS correction factor (θ). Taking the determination of melamine in milk powder as an example, the matrix effects of different isotope-labeled melamines and melamine had notable difference and the impact of this difference on the measurement results depended on the concentrations of analyte and matrix solution. It was worth noting that 15 N 3 -melamine exhibited significant ion suppression to melamine in matrix solution. The deviation of the results from IDMS method might reach 59% using 15 N 3 -melamine as internal standard in special matrix solution. Graphical Abstract The comparison of ESI responses of melamine, 13 C 3 -melamine, 13 C 3 + 15 N 3 -melamine and 15 N 3 -melamine.

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.

The sagitta and lens thickness: the exact solution and a matrix approximation for lenses with toric, spherical, and cylindrical surfaces.

PubMed

Harris, W F

1989-03-01

The exact equation for sagitta of spherical surfaces is generalized to toric surfaces which include spherical and cylindrical surfaces as special cases. Lens thickness, therefore, can be calculated accurately anywhere on a lens even in cases of extreme spherical and cylindrical powers and large diameters. The sagittae of tire- and barrel-form toric surfaces differ off the principal meridians, as is shown by a numerical example. The same holds for pulley- and capstan-form toric surfaces. A general expression is given for thickness at an arbitrary point on a toric lens. Approximate expressions are derived and re-expressed in terms of matrices. The matrix provides an elegant means of generalizing equations for spherical surfaces and lenses to toric surfaces and lenses.

Analytical approximations to the Hotelling trace for digital x-ray detectors

NASA Astrophysics Data System (ADS)

Clarkson, Eric; Pineda, Angel R.; Barrett, Harrison H.

2001-06-01

The Hotelling trace is the signal-to-noise ratio for the ideal linear observer in a detection task. We provide an analytical approximation for this figure of merit when the signal is known exactly and the background is generated by a stationary random process, and the imaging system is an ideal digital x-ray detector. This approximation is based on assuming that the detector is infinite in extent. We test this approximation for finite-size detectors by comparing it to exact calculations using matrix inversion of the data covariance matrix. After verifying the validity of the approximation under a variety of circumstances, we use it to generate plots of the Hotelling trace as a function of pairs of parameters of the system, the signal and the background.

Compressed sensing of hyperspectral images based on scrambled block Hadamard ensemble

NASA Astrophysics Data System (ADS)

Wang, Li; Feng, Yan

2016-11-01

A fast measurement matrix based on scrambled block Hadamard ensemble for compressed sensing (CS) of hyperspectral images (HSI) is investigated. The proposed measurement matrix offers several attractive features. First, the proposed measurement matrix possesses Gaussian behavior, which illustrates that the matrix is universal and requires a near-optimal number of samples for exact reconstruction. In addition, it could be easily implemented in the optical domain due to its integer-valued elements. More importantly, the measurement matrix only needs small memory for storage in the sampling process. Experimental results on HSIs reveal that the reconstruction performance of the proposed measurement matrix is comparable or better than Gaussian matrix and Bernoulli matrix using different reconstruction algorithms while consuming less computational time. The proposed matrix could be used in CS of HSI, which would save the storage memory on board, improve the sampling efficiency, and ameliorate the reconstruction quality.

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.

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.

A real-time extension of density matrix embedding theory for non-equilibrium electron dynamics

NASA Astrophysics Data System (ADS)

Kretchmer, Joshua S.; Chan, Garnet Kin-Lic

2018-02-01

We introduce real-time density matrix embedding theory (DMET), a dynamical quantum embedding theory for computing non-equilibrium electron dynamics in strongly correlated systems. As in the previously developed static DMET, real-time DMET partitions the system into an impurity corresponding to the region of interest coupled to the surrounding environment, which is efficiently represented by a quantum bath of the same size as the impurity. In this work, we focus on a simplified single-impurity time-dependent formulation as a first step toward a multi-impurity theory. The equations of motion of the coupled impurity and bath embedding problem are derived using the time-dependent variational principle. The accuracy of real-time DMET is compared to that of time-dependent complete active space self-consistent field (TD-CASSCF) theory and time-dependent Hartree-Fock (TDHF) theory for a variety of quantum quenches in the single impurity Anderson model (SIAM), in which the Hamiltonian is suddenly changed (quenched) to induce a non-equilibrium state. Real-time DMET shows a marked improvement over the mean-field TDHF, converging to the exact answer even in the non-trivial Kondo regime of the SIAM. However, as expected from analogous behavior in static DMET, the constrained structure of the real-time DMET wavefunction leads to a slower convergence with respect to active space size, in the single-impurity formulation, relative to TD-CASSCF. Our initial results suggest that real-time DMET provides a promising framework to simulate non-equilibrium electron dynamics in which strong electron correlation plays an important role, and lays the groundwork for future multi-impurity formulations.

A real-time extension of density matrix embedding theory for non-equilibrium electron dynamics.

PubMed

Kretchmer, Joshua S; Chan, Garnet Kin-Lic

2018-02-07

We introduce real-time density matrix embedding theory (DMET), a dynamical quantum embedding theory for computing non-equilibrium electron dynamics in strongly correlated systems. As in the previously developed static DMET, real-time DMET partitions the system into an impurity corresponding to the region of interest coupled to the surrounding environment, which is efficiently represented by a quantum bath of the same size as the impurity. In this work, we focus on a simplified single-impurity time-dependent formulation as a first step toward a multi-impurity theory. The equations of motion of the coupled impurity and bath embedding problem are derived using the time-dependent variational principle. The accuracy of real-time DMET is compared to that of time-dependent complete active space self-consistent field (TD-CASSCF) theory and time-dependent Hartree-Fock (TDHF) theory for a variety of quantum quenches in the single impurity Anderson model (SIAM), in which the Hamiltonian is suddenly changed (quenched) to induce a non-equilibrium state. Real-time DMET shows a marked improvement over the mean-field TDHF, converging to the exact answer even in the non-trivial Kondo regime of the SIAM. However, as expected from analogous behavior in static DMET, the constrained structure of the real-time DMET wavefunction leads to a slower convergence with respect to active space size, in the single-impurity formulation, relative to TD-CASSCF. Our initial results suggest that real-time DMET provides a promising framework to simulate non-equilibrium electron dynamics in which strong electron correlation plays an important role, and lays the groundwork for future multi-impurity formulations.

On corrected formula for irradiated graphene quantum conductivity

NASA Astrophysics Data System (ADS)

Firsova, N. E.

2017-09-01

Graphene membrane irradiated by weak activating periodic electric field in terahertz range is considered. The corrected formula for the graphene quantum conductivity is found. The obtained formula gives complex conjugate results when radiation polarization direction is clockwise or it is opposite clockwise. The found formula allows us to see that the graphene membrane is an oscillating contour. Its eigen frequency coincides with a singularity point of the conductivity and depends on the electrons concentration. So the graphene membrane could be used as an antenna or a transistor and its eigen frequency could be tuned by doping in a large terahertz-infrared frequency range. The obtained formula allows us also to calculate the graphene membrane quantum inductivity and capacitance. The found dependence on electrons concentration is consistent with experiments. The method of the proof is based on study of the time-dependent density matrix. The exact solution of von Neumann equation for density matrix is found for our case in linear approximation on the external field. On this basis the induced current is studied and then the formula for quantum conductivity as a function of external field frequency and temperature is obtained. The method of the proof suggested in this paper could be used to study other problems. The found formula for quantum conductivity can be used to correct the SPPs Dispersion Relation and for the description of radiation process. It would be useful to take the obtained results into account when constructing devices containing graphene membrane nanoantenna. Such project could make it possible to create wireless communications among nanosystems. This would be promising research area of energy harvesting applications.

The analytical transfer matrix method for PT-symmetric complex potential

NASA Astrophysics Data System (ADS)

Naceri, Leila; Hammou, Amine B.

2017-07-01

We have extended the analytical transfer matrix (ATM) method to solve quantum mechanical bound state problems with complex PT-symmetric potentials. Our work focuses on a class of models studied by Bender and Jones, we calculate the energy eigenvalues, discuss the critical values of g and compare the results with those obtained from other methods such as exact numerical computation and WKB approximation method.

Simple and Accurate Method for Central Spin Problems

NASA Astrophysics Data System (ADS)

Lindoy, Lachlan P.; Manolopoulos, David E.

2018-06-01

We describe a simple quantum mechanical method that can be used to obtain accurate numerical results over long timescales for the spin correlation tensor of an electron spin that is hyperfine coupled to a large number of nuclear spins. This method does not suffer from the statistical errors that accompany a Monte Carlo sampling of the exact eigenstates of the central spin Hamiltonian obtained from the algebraic Bethe ansatz, or from the growth of the truncation error with time in the time-dependent density matrix renormalization group (TDMRG) approach. As a result, it can be applied to larger central spin problems than the algebraic Bethe ansatz, and for longer times than the TDMRG algorithm. It is therefore an ideal method to use to solve central spin problems, and we expect that it will also prove useful for a variety of related problems that arise in a number of different research fields.

The dynamics of the optically driven Lambda transition of the 15N-V- center in diamond.

PubMed

González, Gabriel; Leuenberger, Michael N

2010-07-09

Recent experimental results demonstrate the possibility of writing quantum information in the ground state triplet of the (15)N-V(-) center in diamond by means of an optically driven spin non-conserving two-photon Lambda transition in the presence of a strong applied electric field. Our calculations show that the hyperfine interaction in the (15)N-V(-) center is capable of mediating such a transition. We use a density matrix approach to describe the exact dynamics for the allowed optical spin non-conserving transitions between two sublevels of the ground state triplet. This approach allows us to calculate the Rabi oscillations, by means of which we obtain a Rabi frequency with an upper bound determined by the hyperfine interaction. This result is crucial for the success of implementing optically driven quantum information processing with the N-V center in diamond.

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.

Emergence of chiral spin liquids via quantum melting of noncoplanar magnetic orders

DOE PAGES

Hickey, Ciarán; Cincio, Lukasz; Papić, Zlatko; ...

2017-09-11

Quantum spin liquids (QSLs) are highly entangled states of quantum magnets which lie beyond the Landau paradigm of classifying phases of matter via broken symmetries. A physical route to arriving at QSLs is via frustration-induced quantum melting of ordered states such as valence bond crystals or magnetic orders. Using extensive exact diagonalization (ED) and density-matrix renormalization group (DMRG)we show studies of concrete S U ( 2 ) invariant spin models on honeycomb, triangular, and square lattices, that chiral spin liquids (CSLs) emerge as descendants of triple- Q spin crystals with tetrahedral magnetic order and a large scalar spin chirality. Suchmore » ordered-to-CSL melting transitions may yield lattice realizations of effective Chern-Simons-Higgs field theories. We provides a distinct unifying perspective on the emergence of CSLs and suggests that materials with certain noncoplanar magnetic orders might provide a good starting point to search for CSLs.« less

Emergence of chiral spin liquids via quantum melting of noncoplanar magnetic orders

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

Hickey, Ciarán; Cincio, Lukasz; Papić, Zlatko

Quantum spin liquids (QSLs) are highly entangled states of quantum magnets which lie beyond the Landau paradigm of classifying phases of matter via broken symmetries. A physical route to arriving at QSLs is via frustration-induced quantum melting of ordered states such as valence bond crystals or magnetic orders. Using extensive exact diagonalization (ED) and density-matrix renormalization group (DMRG)we show studies of concrete S U ( 2 ) invariant spin models on honeycomb, triangular, and square lattices, that chiral spin liquids (CSLs) emerge as descendants of triple- Q spin crystals with tetrahedral magnetic order and a large scalar spin chirality. Suchmore » ordered-to-CSL melting transitions may yield lattice realizations of effective Chern-Simons-Higgs field theories. We provides a distinct unifying perspective on the emergence of CSLs and suggests that materials with certain noncoplanar magnetic orders might provide a good starting point to search for CSLs.« less

Electric field effect on the second-order nonlinear optical properties of parabolic and semiparabolic quantum wells

NASA Astrophysics Data System (ADS)

Zhang, Li; Xie, Hong-Jing

2003-12-01

By using the compact-density-matrix approach and iterative procedure, a detailed procedure for the calculation of the second-harmonic generation (SHG) susceptibility tensor is given in the electric-field-biased parabolic and semiparabolic quantum wells (QW’s). The simple analytical formula for the SHG susceptibility in the systems is also deduced. By adopting the methods of envelope wave function and displacement harmonic oscillation, the electronic states in parabolic and semi parabolic QW’s with applied electric fields are exactly solved. Numerical results on typical AlxGa1-xAl/GaAs materials show that, for the same effective widths, the SHG susceptibility in semiparabolic QW is larger than that in parabolic QW due to the self-asymmetry of the semiparabolic QW, and the applied electric field can make the SHG susceptibilities in both systems enhance remarkably. Moreover, the SHG susceptibility also sensitively depends on the relaxation rate of the systems.

New Exact Solutions of Relativistic Hydrodynamics for Longitudinally Expanding Fireballs

NASA Astrophysics Data System (ADS)

Csörgő, Tamás; Kasza, Gábor; Csanád, Máté; Jiang, Zefang

2018-06-01

We present new, exact, finite solutions of relativistic hydrodynamics for longitudinally expanding fireballs for arbitrary constant value of the speed of sound. These new solutions generalize earlier, longitudinally finite, exact solutions, from an unrealistic to a reasonable equation of state, characterized by a temperature independent (average) value of the speed of sound. Observables like the rapidity density and the pseudorapidity density are evaluated analytically, resulting in simple and easy to fit formulae that can be matched to the high energy proton-proton and heavy ion collision data at RHIC and LHC. In the longitudinally boost-invariant limit, these new solutions approach the Hwa-Bjorken solution and the corresponding rapidity distributions approach a rapidity plateaux.

Generalized nonequilibrium vertex correction method in coherent medium theory for quantum transport simulation of disordered nanoelectronics

NASA Astrophysics Data System (ADS)

Yan, Jiawei; Ke, Youqi

2016-07-01

Electron transport properties of nanoelectronics can be significantly influenced by the inevitable and randomly distributed impurities/defects. For theoretical simulation of disordered nanoscale electronics, one is interested in both the configurationally averaged transport property and its statistical fluctuation that tells device-to-device variability induced by disorder. However, due to the lack of an effective method to do disorder averaging under the nonequilibrium condition, the important effects of disorders on electron transport remain largely unexplored or poorly understood. In this work, we report a general formalism of Green's function based nonequilibrium effective medium theory to calculate the disordered nanoelectronics. In this method, based on a generalized coherent potential approximation for the Keldysh nonequilibrium Green's function, we developed a generalized nonequilibrium vertex correction method to calculate the average of a two-Keldysh-Green's-function correlator. We obtain nine nonequilibrium vertex correction terms, as a complete family, to express the average of any two-Green's-function correlator and find they can be solved by a set of linear equations. As an important result, the averaged nonequilibrium density matrix, averaged current, disorder-induced current fluctuation, and averaged shot noise, which involve different two-Green's-function correlators, can all be derived and computed in an effective and unified way. To test the general applicability of this method, we applied it to compute the transmission coefficient and its fluctuation with a square-lattice tight-binding model and compared with the exact results and other previously proposed approximations. Our results show very good agreement with the exact results for a wide range of disorder concentrations and energies. In addition, to incorporate with density functional theory to realize first-principles quantum transport simulation, we have also derived a general form of conditionally averaged nonequilibrium Green's function for multicomponent disorders.

Linearly exact parallel closures for slab geometry

NASA Astrophysics Data System (ADS)

Ji, Jeong-Young; Held, Eric D.; Jhang, Hogun

2013-08-01

Parallel closures are obtained by solving a linearized kinetic equation with a model collision operator using the Fourier transform method. The closures expressed in wave number space are exact for time-dependent linear problems to within the limits of the model collision operator. In the adiabatic, collisionless limit, an inverse Fourier transform is performed to obtain integral (nonlocal) parallel closures in real space; parallel heat flow and viscosity closures for density, temperature, and flow velocity equations replace Braginskii's parallel closure relations, and parallel flow velocity and heat flow closures for density and temperature equations replace Spitzer's parallel transport relations. It is verified that the closures reproduce the exact linear response function of Hammett and Perkins [Phys. Rev. Lett. 64, 3019 (1990)] for Landau damping given a temperature gradient. In contrast to their approximate closures where the vanishing viscosity coefficient numerically gives an exact response, our closures relate the heat flow and nonvanishing viscosity to temperature and flow velocity (gradients).

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.

Nonzero θ13 from the Triangular Ansatz and Leptogenesis

NASA Astrophysics Data System (ADS)

Benaoum, H. B.

2012-08-01

Recent experiments indicate a departure from the exact tri-bimaximal mixing by measure ring definitive nonzero value of θ13. Within the framework of type I seesaw mechanism, we reconstruct the triangular Dirac neutrino mass matrix from the μ - τ symmetric mass matrix. The deviation from μ - τ symmetry is then parametrized by adding dimensionless parameters yi in the triangular mass matrix. In this parametrization of the neutrino mass matrix, the nonzero value θ13 is controlled by Δy = y4 - y6. We also calculate the resulting leptogenesis and show that the triangular texture can generate the observed baryon asymmetry in the universe via leptogenesis scenario.

Comprehensive T-Matrix Reference Database: A 2007-2009 Update

NASA Technical Reports Server (NTRS)

Mishchenko, Michael I.; Zakharova, Nadia T.; Videen, Gorden; Khlebtsov, Nikolai G.; Wriedt, Thomas

2010-01-01

The T-matrix method is among the most versatile, efficient, and widely used theoretical techniques for the numerically exact computation of electromagnetic scattering by homogeneous and composite particles, clusters of particles, discrete random media, and particles in the vicinity of an interface separating two half-spaces with different refractive indices. This paper presents an update to the comprehensive database of T-matrix publications compiled by us previously and includes the publications that appeared since 2007. It also lists several earlier publications not included in the original database.

On the Daubechies-based wavelet differentiation matrix

NASA Technical Reports Server (NTRS)

Jameson, Leland

1993-01-01

The differentiation matrix for a Daubechies-based wavelet basis is constructed and superconvergence is proven. That is, it will be proven that under the assumption of periodic boundary conditions that the differentiation matrix is accurate of order 2M, even though the approximation subspace can represent exactly only polynomials up to degree M-1, where M is the number of vanishing moments of the associated wavelet. It is illustrated that Daubechies-based wavelet methods are equivalent to finite difference methods with grid refinement in regions of the domain where small-scale structure is present.

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.

Some Fundamental Issues in Ground-State Density Functional Theory: A Guide for the Perplexed.

PubMed

Perdew, John P; Ruzsinszky, Adrienn; Constantin, Lucian A; Sun, Jianwei; Csonka, Gábor I

2009-04-14

Some fundamental issues in ground-state density functional theory are discussed without equations: (1) The standard Hohenberg-Kohn and Kohn-Sham theorems were proven for a Hamiltonian that is not quite exact for real atoms, molecules, and solids. (2) The density functional for the exchange-correlation energy, which must be approximated, arises from the tendency of electrons to avoid one another as they move through the electron density. (3) In the absence of a magnetic field, either spin densities or total electron density can be used, although the former choice is better for approximations. (4) "Spin contamination" of the determinant of Kohn-Sham orbitals for an open-shell system is not wrong but right. (5) Only to the extent that symmetries of the interacting wave function are reflected in the spin densities should those symmetries be respected by the Kohn-Sham noninteracting or determinantal wave function. Functionals below the highest level of approximations should however sometimes break even those symmetries, for good physical reasons. (6) Simple and commonly used semilocal (lower-level) approximations for the exchange-correlation energy as a functional of the density can be accurate for closed systems near equilibrium and yet fail for open systems of fluctuating electron number. (7) The exact Kohn-Sham noninteracting state need not be a single determinant, but common approximations can fail when it is not. (8) Over an open system of fluctuating electron number, connected to another such system by stretched bonds, semilocal approximations make the exchange-correlation energy and hole-density sum rule too negative. (9) The gap in the exact Kohn-Sham band structure of a crystal underestimates the real fundamental gap but may approximate the first exciton energy in the large-gap limit. (10) Density functional theory is not really a mean-field theory, although it looks like one. The exact functional includes strong correlation, and semilocal approximations often overestimate the strength of static correlation through their semilocal exchange contributions. (11) Only under rare conditions can excited states arise directly from a ground-state theory.

Comparison of SOM point densities based on different criteria.

PubMed

Kohonen, T

1999-11-15

Point densities of model (codebook) vectors in self-organizing maps (SOMs) are evaluated in this article. For a few one-dimensional SOMs with finite grid lengths and a given probability density function of the input, the numerically exact point densities have been computed. The point density derived from the SOM algorithm turned out to be different from that minimizing the SOM distortion measure, showing that the model vectors produced by the basic SOM algorithm in general do not exactly coincide with the optimum of the distortion measure. A new computing technique based on the calculus of variations has been introduced. It was applied to the computation of point densities derived from the distortion measure for both the classical vector quantization and the SOM with general but equal dimensionality of the input vectors and the grid, respectively. The power laws in the continuum limit obtained in these cases were found to be identical.

Tensor spherical harmonics theories on the exact nature of the elastic fields of a spherically anisotropic multi-inhomogeneous inclusion

NASA Astrophysics Data System (ADS)

Shodja, H. M.; Khorshidi, A.

2013-04-01

Eshelby's theories on the nature of the disturbance strains due to polynomial eigenstrains inside an isotropic ellipsoidal inclusion, and the form of homogenizing eigenstrains corresponding to remote polynomial loadings in the equivalent inclusion method (EIM) are not valid for spherically anisotropic inclusions and inhomogeneities. Materials with spherically anisotropic behavior are frequently encountered in nature, for example, some graphite particles or polyethylene spherulites. Moreover, multi-inclusions/inhomogeneities/inhomogeneous inclusions have abundant engineering and scientific applications and their exact theoretical treatment would be of great value. The present work is devoted to the development of a mathematical framework for the exact treatment of a spherical multi-inhomogeneous inclusion with spherically anisotropic constituents embedded in an unbounded isotropic matrix. The formulations herein are based on tensor spherical harmonics having orthogonality and completeness properties. For polynomial eigenstrain field and remote applied loading, several theorems on the exact closed-form expressions of the elastic fields associated with the matrix and all the phases of the inhomogeneous inclusion are stated and proved. Several classes of impotent eigenstrain fields associated to a generally anisotropic inclusion as well as isotropic and spherically anisotropic multi-inclusions are also introduced. The presented theories are useful for obtaining highly accurate solutions of desired accuracy when the constituent phases of the multi-inhomogeneous inclusion are made of functionally graded materials (FGMs).

Transformation matrices between non-linear and linear differential equations

NASA Technical Reports Server (NTRS)

Sartain, R. L.

1983-01-01

In the linearization of systems of non-linear differential equations, those systems which can be exactly transformed into the second order linear differential equation Y"-AY'-BY=0 where Y, Y', and Y" are n x 1 vectors and A and B are constant n x n matrices of real numbers were considered. The 2n x 2n matrix was used to transform the above matrix equation into the first order matrix equation X' = MX. Specially the matrix M and the conditions which will diagonalize or triangularize M were studied. Transformation matrices P and P sub -1 were used to accomplish this diagonalization or triangularization to return to the solution of the second order matrix differential equation system from the first order system.

A parallel algorithm for computing the eigenvalues of a symmetric tridiagonal matrix

NASA Technical Reports Server (NTRS)

Swarztrauber, Paul N.

1993-01-01

A parallel algorithm, called polysection, is presented for computing the eigenvalues of a symmetric tridiagonal matrix. The method is based on a quadratic recurrence in which the characteristic polynomial is constructed on a binary tree from polynomials whose degree doubles at each level. Intervals that contain exactly one zero are determined by the zeros of polynomials at the previous level which ensures that different processors compute different zeros. The signs of the polynomials at the interval endpoints are determined a priori and used to guarantee that all zeros are found. The use of finite-precision arithmetic may result in multiple zeros; however, in this case, the intervals coalesce and their number determines exactly the multiplicity of the zero. For an N x N matrix the eigenvalues can be determined in O(log-squared N) time with N-squared processors and O(N) time with N processors. The method is compared with a parallel variant of bisection that requires O(N-squared) time on a single processor, O(N) time with N processors, and O(log N) time with N-squared processors.

The Green's matrix and the boundary integral equations for analysis of time-harmonic dynamics of elastic helical springs.

PubMed

Sorokin, Sergey V

2011-03-01

Helical springs serve as vibration isolators in virtually any suspension system. Various exact and approximate methods may be employed to determine the eigenfrequencies of vibrations of these structural elements and their dynamic transfer functions. The method of boundary integral equations is a meaningful alternative to obtain exact solutions of problems of the time-harmonic dynamics of elastic springs in the framework of Bernoulli-Euler beam theory. In this paper, the derivations of the Green's matrix, of the Somigliana's identities, and of the boundary integral equations are presented. The vibrational power transmission in an infinitely long spring is analyzed by means of the Green's matrix. The eigenfrequencies and the dynamic transfer functions are found by solving the boundary integral equations. In the course of analysis, the essential features and advantages of the method of boundary integral equations are highlighted. The reported analytical results may be used to study the time-harmonic motion in any wave guide governed by a system of linear differential equations in a single spatial coordinate along its axis. © 2011 Acoustical Society of America

Information loss in effective field theory: Entanglement and thermal entropies

NASA Astrophysics Data System (ADS)

Boyanovsky, Daniel

2018-03-01

Integrating out high energy degrees of freedom to yield a low energy effective field theory leads to a loss of information with a concomitant increase in entropy. We obtain the effective field theory of a light scalar field interacting with heavy fields after tracing out the heavy degrees of freedom from the time evolved density matrix. The initial density matrix describes the light field in its ground state and the heavy fields in equilibrium at a common temperature T . For T =0 , we obtain the reduced density matrix in a perturbative expansion; it reveals an emergent mixed state as a consequence of the entanglement between light and heavy fields. We obtain the effective action that determines the time evolution of the reduced density matrix for the light field in a nonperturbative Dyson resummation of one-loop correlations of the heavy fields. The Von-Neumann entanglement entropy associated with the reduced density matrix is obtained for the nonresonant and resonant cases in the asymptotic long time limit. In the nonresonant case the reduced density matrix displays an incipient thermalization albeit with a wave-vector, time and coupling dependent effective temperature as a consequence of memory of initial conditions. The entanglement entropy is time independent and is the thermal entropy for this effective, nonequilibrium temperature. In the resonant case the light field fully thermalizes with the heavy fields, the reduced density matrix loses memory of the initial conditions and the entanglement entropy becomes the thermal entropy of the light field. We discuss the relation between the entanglement entropy ultraviolet divergences and renormalization.

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.

ac-driven vortices and the Hall effect in a superconductor with a tilted washboard pinning potential

NASA Astrophysics Data System (ADS)

Shklovskij, Valerij A.; Dobrovolskiy, Oleksandr V.

2008-09-01

The Langevin equation for a two-dimensional (2D) nonlinear guided vortex motion in a tilted cosine pinning potential in the presence of an ac is exactly solved in terms of a matrix continued fraction at arbitrary value of the Hall effect. The influence of an ac of arbitrary amplitude and frequency on the dc and ac magnetoresistivity tensors is analyzed. The ac density and frequency dependence of the overall shape and the number and position of the Shapiro steps on the anisotropic current-voltage characteristics are considered. The influence of a subcritical or overcritical dc on the time-dependent stationary ac longitudinal and transverse resistive vortex responses (on the frequency of an ac drive Ω ) in terms of the nonlinear impedance tensor Ẑ and the nonlinear ac response at Ω harmonics are studied. Analytical formulas for 2D temperature-dependent linear impedance tensor ẐL in the presence of a dc which depend on the angle α between the current-density vector and the guiding direction of the washboard planar pinning potential are derived and analyzed. Influence of α anisotropy and the Hall effect on the nonlinear power absorption by vortices is discussed.

The Poisson-Boltzmann theory for the two-plates problem: some exact results.

PubMed

Xing, Xiang-Jun

2011-12-01

The general solution to the nonlinear Poisson-Boltzmann equation for two parallel charged plates, either inside a symmetric electrolyte, or inside a 2q:-q asymmetric electrolyte, is found in terms of Weierstrass elliptic functions. From this we derive some exact asymptotic results for the interaction between charged plates, as well as the exact form of the renormalized surface charge density.

Dielectric properties of proteins from simulations: tools and techniques

NASA Astrophysics Data System (ADS)

Simonson, Thomas; Perahia, David

1995-09-01

Tools and techniques to analyze the dielectric properties of proteins are described. Microscopic dielectric properties are determined by a susceptibility tensor of order 3 n, where n is the number of protein atoms. For perturbing charges not too close to the protein, the dielectric relaxation free energy is directly related to the dipole-dipole correlation matrix of the unperturbed protein, or equivalently to the covariance matrix of its atomic displacements. These are straightforward to obtain from existing molecular dynamics packages such as CHARMM or X- PLOR. Macroscopic dielectric properties can be derived from the dipolar fluctuations of the protein, by idealizing the protein as one or more spherical media. The dipolar fluctuations are again directly related to the covariance matrix of the atomic displacements. An interesting consequence is that the quasiharmonic approximation, which by definition exactly reproduces this covariance matrix, gives the protein dielectric constant exactly. Finally a technique is reviewed to obtain normal or quasinormal modes of vibration of symmetric protein assemblies. Using elementary group theory, and eliminating the high-frequency modes of vibration of each monomer, the limiting step in terms of memory and computation is finding the normal modes of a single monomer, with the other monomers held fixed. This technique was used to study the dielectric properties of the Tobacco Mosaic Virus protein disk.

Dynamics of a spin-boson model with structured spectral density

NASA Astrophysics Data System (ADS)

Kurt, Arzu; Eryigit, Resul

2018-05-01

We report the results of a study of the dynamics of a two-state system coupled to an environment with peaked spectral density. An exact analytical expression for the bath correlation function is obtained. Validity range of various approximations to the correlation function for calculating the population difference of the system is discussed as function of tunneling splitting, oscillator frequency, coupling constant, damping rate and the temperature of the bath. An exact expression for the population difference, for a limited range of parameters, is derived.

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.

Optimized Projection Matrix for Compressive Sensing

NASA Astrophysics Data System (ADS)

Xu, Jianping; Pi, Yiming; Cao, Zongjie

2010-12-01

Compressive sensing (CS) is mainly concerned with low-coherence pairs, since the number of samples needed to recover the signal is proportional to the mutual coherence between projection matrix and sparsifying matrix. Until now, papers on CS always assume the projection matrix to be a random matrix. In this paper, aiming at minimizing the mutual coherence, a method is proposed to optimize the projection matrix. This method is based on equiangular tight frame (ETF) design because an ETF has minimum coherence. It is impossible to solve the problem exactly because of the complexity. Therefore, an alternating minimization type method is used to find a feasible solution. The optimally designed projection matrix can further reduce the necessary number of samples for recovery or improve the recovery accuracy. The proposed method demonstrates better performance than conventional optimization methods, which brings benefits to both basis pursuit and orthogonal matching pursuit.

Eigenvalue Attraction

NASA Astrophysics Data System (ADS)

Movassagh, Ramis

2016-02-01

We prove that the complex conjugate (c.c.) eigenvalues of a smoothly varying real matrix attract (Eq. 15). We offer a dynamical perspective on the motion and interaction of the eigenvalues in the complex plane, derive their governing equations and discuss applications. C.c. pairs closest to the real axis, or those that are ill-conditioned, attract most strongly and can collide to become exactly real. As an application we consider random perturbations of a fixed matrix M. If M is Normal, the total expected force on any eigenvalue is shown to be only the attraction of its c.c. (Eq. 24) and when M is circulant the strength of interaction can be related to the power spectrum of white noise. We extend this by calculating the expected force (Eq. 41) for real stochastic processes with zero-mean and independent intervals. To quantify the dominance of the c.c. attraction, we calculate the variance of other forces. We apply the results to the Hatano-Nelson model and provide other numerical illustrations. It is our hope that the simple dynamical perspective herein might help better understanding of the aggregation and low density of the eigenvalues of real random matrices on and near the real line respectively. In the appendix we provide a Matlab code for plotting the trajectories of the eigenvalues.

Thermodynamic Bethe ansatz for non-equilibrium steady states: exact energy current and fluctuations in integrable QFT

NASA Astrophysics Data System (ADS)

Castro-Alvaredo, Olalla; Chen, Yixiong; Doyon, Benjamin; Hoogeveen, Marianne

2014-03-01

We evaluate the exact energy current and scaled cumulant generating function (related to the large-deviation function) in non-equilibrium steady states with energy flow, in any integrable model of relativistic quantum field theory (IQFT) with diagonal scattering. Our derivations are based on various recent results of Bernard and Doyon. The steady states are built by connecting homogeneously two infinite halves of the system thermalized at different temperatures Tl, Tr, and waiting for a long time. We evaluate the current J(Tl, Tr) using the exact QFT density matrix describing these non-equilibrium steady states and using Zamolodchikov’s method of the thermodynamic Bethe ansatz (TBA). The scaled cumulant generating function is obtained from the extended fluctuation relations which hold in integrable models. We verify our formula in particular by showing that the conformal field theory (CFT) result is obtained in the high-temperature limit. We analyze numerically our non-equilibrium steady-state TBA equations for three models: the sinh-Gordon model, the roaming trajectories model, and the sine-Gordon model at a particular reflectionless point. Based on the numerics, we conjecture that an infinite family of non-equilibrium c-functions, associated with the scaled cumulants, can be defined, which we interpret physically. We study the full scaled distribution function and find that it can be described by a set of independent Poisson processes. Finally, we show that the ‘additivity’ property of the current, which is known to hold in CFT and was proposed to hold more generally, does not hold in general IQFT—that is, J(Tl, Tr) is not of the form f(Tl) - f(Tr).

Ultrahigh-resolution spectroscopy with atomic or molecular dark resonances: Exact steady-state line shapes and asymptotic profiles in the adiabatic pulsed regime

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

Zanon-Willette, Thomas; Clercq, Emeric de; Arimondo, Ennio

2011-12-15

Exact and asymptotic line shape expressions are derived from the semiclassical density matrix representation describing a set of closed three-level {Lambda} atomic or molecular states including decoherences, relaxation rates, and light shifts. An accurate analysis of the exact steady-state dark-resonance profile describing the Autler-Townes doublet, the electromagnetically induced transparency or coherent population trapping resonance, and the Fano-Feshbach line shape leads to the linewidth expression of the two-photon Raman transition and frequency shifts associated to the clock transition. From an adiabatic analysis of the dynamical optical Bloch equations in the weak field limit, a pumping time required to efficiently trap amore » large number of atoms into a coherent superposition of long-lived states is established. For a highly asymmetrical configuration with different decay channels, a strong two-photon resonance based on a lower states population inversion is established when the driving continuous-wave laser fields are greatly unbalanced. When time separated resonant two-photon pulses are applied in the adiabatic pulsed regime for atomic or molecular clock engineering, where the first pulse is long enough to reach a coherent steady-state preparation and the second pulse is very short to avoid repumping into a new dark state, dark-resonance fringes mixing continuous-wave line shape properties and coherent Ramsey oscillations are created. Those fringes allow interrogation schemes bypassing the power broadening effect. Frequency shifts affecting the central clock fringe computed from asymptotic profiles and related to the Raman decoherence process exhibit nonlinear shapes with the three-level observable used for quantum measurement. We point out that different observables experience different shifts on the lower-state clock transition.« less

Momentum distribution of the uniform electron gas: Improved parametrization and exact limits of the cumulant expansion

NASA Astrophysics Data System (ADS)

Gori-Giorgi, Paola; Ziesche, Paul

2002-12-01

The momentum distribution of the unpolarized uniform electron gas in its Fermi-liquid regime, n(k,rs), with the momenta k measured in units of the Fermi wave number kF and with the density parameter rs, is constructed with the help of the convex Kulik function G(x). It is assumed that n(0,rs),n(1±,rs), the on-top pair density g(0,rs), and the kinetic energy t(rs) are known (respectively, from accurate calculations for rs=1,…,5, from the solution of the Overhauser model, and from quantum Monte Carlo calculations via the virial theorem). Information from the high- and the low-density limit, corresponding to the random-phase approximation and to the Wigner crystal limit, is used. The result is an accurate parametrization of n(k,rs), which fulfills most of the known exact constraints. It is in agreement with the effective-potential calculations of Takada and Yasuhara [Phys. Rev. B 44, 7879 (1991)], is compatible with quantum Monte Carlo data, and is valid in the density range rs≲12. The corresponding cumulant expansions of the pair density and of the static structure factor are discussed, and some exact limits are derived.

Integrable flows between exact CFTs

NASA Astrophysics Data System (ADS)

Georgiou, George; Sfetsos, Konstantinos

2017-11-01

We explicitly construct families of integrable σ-model actions smoothly inter-polating between exact CFTs. In the ultraviolet the theory is the direct product of two current algebras at levels k 1 and k 2. In the infrared and for the case of two deformation matrices the CFT involves a coset CFT, whereas for a single matrix deformation it is given by the ultraviolet direct product theories but at levels k 1 and k 2 - k 1. For isotropic deformations we demonstrate integrability. In this case we also compute the exact beta-function for the deformation parameters using gravitational methods. This is shown to coincide with previous results obtained using perturbation theory and non-perturbative symmetries.

Using monomer vibrational wavefunctions to compute numerically exact (12D) rovibrational levels of water dimer

NASA Astrophysics Data System (ADS)

Wang, Xiao-Gang; Carrington, Tucker

2018-02-01

We compute numerically exact rovibrational levels of water dimer, with 12 vibrational coordinates, on the accurate CCpol-8sf ab initio flexible monomer potential energy surface [C. Leforestier et al., J. Chem. Phys. 137, 014305 (2012)]. It does not have a sum-of-products or multimode form and therefore quadrature in some form must be used. To do the calculation, it is necessary to use an efficient basis set and to develop computational tools, for evaluating the matrix-vector products required to calculate the spectrum, that obviate the need to store the potential on a 12D quadrature grid. The basis functions we use are products of monomer vibrational wavefunctions and standard rigid-monomer basis functions (which involve products of three Wigner functions). Potential matrix-vector products are evaluated using the F matrix idea previously used to compute rovibrational levels of 5-atom and 6-atom molecules. When the coupling between inter- and intra-monomer coordinates is weak, this crude adiabatic type basis is efficient (only a few monomer vibrational wavefunctions are necessary), although the calculation of matrix elements is straightforward. It is much easier to use than an adiabatic basis. The product structure of the basis is compatible with the product structure of the kinetic energy operator and this facilitates computation of matrix-vector products. Compared with the results obtained using a [6 + 6]D adiabatic approach, we find good agreement for the inter-molecular levels and larger differences for the intra-molecular water bend levels.

Using monomer vibrational wavefunctions to compute numerically exact (12D) rovibrational levels of water dimer.

PubMed

Wang, Xiao-Gang; Carrington, Tucker

2018-02-21

We compute numerically exact rovibrational levels of water dimer, with 12 vibrational coordinates, on the accurate CCpol-8sf ab initio flexible monomer potential energy surface [C. Leforestier et al., J. Chem. Phys. 137, 014305 (2012)]. It does not have a sum-of-products or multimode form and therefore quadrature in some form must be used. To do the calculation, it is necessary to use an efficient basis set and to develop computational tools, for evaluating the matrix-vector products required to calculate the spectrum, that obviate the need to store the potential on a 12D quadrature grid. The basis functions we use are products of monomer vibrational wavefunctions and standard rigid-monomer basis functions (which involve products of three Wigner functions). Potential matrix-vector products are evaluated using the F matrix idea previously used to compute rovibrational levels of 5-atom and 6-atom molecules. When the coupling between inter- and intra-monomer coordinates is weak, this crude adiabatic type basis is efficient (only a few monomer vibrational wavefunctions are necessary), although the calculation of matrix elements is straightforward. It is much easier to use than an adiabatic basis. The product structure of the basis is compatible with the product structure of the kinetic energy operator and this facilitates computation of matrix-vector products. Compared with the results obtained using a [6 + 6]D adiabatic approach, we find good agreement for the inter-molecular levels and larger differences for the intra-molecular water bend levels.

Uniform Recovery Bounds for Structured Random Matrices in Corrupted Compressed Sensing

NASA Astrophysics Data System (ADS)

Zhang, Peng; Gan, Lu; Ling, Cong; Sun, Sumei

2018-04-01

We study the problem of recovering an $s$-sparse signal $\\mathbf{x}^{\\star}\\in\\mathbb{C}^n$ from corrupted measurements $\\mathbf{y} = \\mathbf{A}\\mathbf{x}^{\\star}+\\mathbf{z}^{\\star}+\\mathbf{w}$, where $\\mathbf{z}^{\\star}\\in\\mathbb{C}^m$ is a $k$-sparse corruption vector whose nonzero entries may be arbitrarily large and $\\mathbf{w}\\in\\mathbb{C}^m$ is a dense noise with bounded energy. The aim is to exactly and stably recover the sparse signal with tractable optimization programs. In this paper, we prove the uniform recovery guarantee of this problem for two classes of structured sensing matrices. The first class can be expressed as the product of a unit-norm tight frame (UTF), a random diagonal matrix and a bounded columnwise orthonormal matrix (e.g., partial random circulant matrix). When the UTF is bounded (i.e. $\\mu(\\mathbf{U})\\sim1/\\sqrt{m}$), we prove that with high probability, one can recover an $s$-sparse signal exactly and stably by $l_1$ minimization programs even if the measurements are corrupted by a sparse vector, provided $m = \\mathcal{O}(s \\log^2 s \\log^2 n)$ and the sparsity level $k$ of the corruption is a constant fraction of the total number of measurements. The second class considers randomly sub-sampled orthogonal matrix (e.g., random Fourier matrix). We prove the uniform recovery guarantee provided that the corruption is sparse on certain sparsifying domain. Numerous simulation results are also presented to verify and complement the theoretical results.

Efficient exact-exchange time-dependent density-functional theory methods and their relation to time-dependent Hartree-Fock.

PubMed

Hesselmann, Andreas; Görling, Andreas

2011-01-21

A recently introduced time-dependent exact-exchange (TDEXX) method, i.e., a response method based on time-dependent density-functional theory that treats the frequency-dependent exchange kernel exactly, is reformulated. In the reformulated version of the TDEXX method electronic excitation energies can be calculated by solving a linear generalized eigenvalue problem while in the original version of the TDEXX method a laborious frequency iteration is required in the calculation of each excitation energy. The lowest eigenvalues of the new TDEXX eigenvalue equation corresponding to the lowest excitation energies can be efficiently obtained by, e.g., a version of the Davidson algorithm appropriate for generalized eigenvalue problems. Alternatively, with the help of a series expansion of the new TDEXX eigenvalue equation, standard eigensolvers for large regular eigenvalue problems, e.g., the standard Davidson algorithm, can be used to efficiently calculate the lowest excitation energies. With the help of the series expansion as well, the relation between the TDEXX method and time-dependent Hartree-Fock is analyzed. Several ways to take into account correlation in addition to the exact treatment of exchange in the TDEXX method are discussed, e.g., a scaling of the Kohn-Sham eigenvalues, the inclusion of (semi)local approximate correlation potentials, or hybrids of the exact-exchange kernel with kernels within the adiabatic local density approximation. The lowest lying excitations of the molecules ethylene, acetaldehyde, and pyridine are considered as examples.

Light Scattering by Wavelength-Sized Particles "Dusted" with Subwavelength-Sized Grains

NASA Technical Reports Server (NTRS)

Mishchenko, Michael I.; Dlugach, Janna M.; Mackowski, Daniel W.

2011-01-01

The numerically exact superposition T-matrix method is used to compute the scattering cross sections and the Stokes scattering matrix for polydisperse spherical particles covered with a large number of much smaller grains. We show that the optical effect of the presence of microscopic dust on the surfaces of wavelength-sized, weakly absorbing particles is much less significant than that of a major overall asphericity of the particle shape.

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

Complete devil's staircase and crystal-superfluid transitions in a dipolar XXZ spin chain: a trapped ion quantum simulation

NASA Astrophysics Data System (ADS)

Hauke, Philipp; Cucchietti, Fernando M.; Müller-Hermes, Alexander; Bañuls, Mari-Carmen; Cirac, J. Ignacio; Lewenstein, Maciej

2010-11-01

Systems with long-range interactions show a variety of intriguing properties: they typically accommodate many metastable states, they can give rise to spontaneous formation of supersolids, and they can lead to counterintuitive thermodynamic behavior. However, the increased complexity that comes with long-range interactions strongly hinders theoretical studies. This makes a quantum simulator for long-range models highly desirable. Here, we show that a chain of trapped ions can be used to quantum simulate a one-dimensional (1D) model of hard-core bosons with dipolar off-site interaction and tunneling, equivalent to a dipolar XXZ spin-1/2 chain. We explore the rich phase diagram of this model in detail, employing perturbative mean-field theory, exact diagonalization and quasi-exact numerical techniques (density-matrix renormalization group and infinite time-evolving block decimation). We find that the complete devil's staircase—an infinite sequence of crystal states existing at vanishing tunneling—spreads to a succession of lobes similar to the Mott lobes found in Bose-Hubbard models. Investigating the melting of these crystal states at increased tunneling, we do not find (contrary to similar 2D models) clear indications of supersolid behavior in the region around the melting transition. However, we find that inside the insulating lobes there are quasi-long-range (algebraic) correlations, as opposed to models with nearest-neighbor tunneling, that show exponential decay of correlations.

Dynamics of Coupled Electron-Boson Systems with the Multiple Davydov D1 Ansatz and the Generalized Coherent State.

PubMed

Chen, Lipeng; Borrelli, Raffaele; Zhao, Yang

2017-11-22

The dynamics of a coupled electron-boson system is investigated by employing a multitude of the Davydov D 1 trial states, also known as the multi-D 1 Ansatz, and a second trial state based on a superposition of the time-dependent generalized coherent state (GCS Ansatz). The two Ansätze are applied to study population dynamics in the spin-boson model and the Holstein molecular crystal model, and a detailed comparison with numerically exact results obtained by the (multilayer) multiconfiguration time-dependent Hartree method and the hierarchy equations of motion approach is drawn. It is found that the two methodologies proposed here have significantly improved over that with the single D 1 Ansatz, yielding quantitatively accurate results even in the critical cases of large energy biases and large transfer integrals. The two methodologies provide new effective tools for accurate, efficient simulation of many-body quantum dynamics thanks to a relatively small number of parameters which characterize the electron-nuclear wave functions. The wave-function-based approaches are capable of tracking explicitly detailed bosonic dynamics, which is absent by construct in approaches based on the reduced density matrix. The efficiency and flexibility of our methods are also advantages as compared with numerically exact approaches such as QUAPI and HEOM, especially at low temperatures and in the strong coupling regime.

Frustrated S = 1/2 Two-Leg Ladder with Different Leg Interactions

NASA Astrophysics Data System (ADS)

Tonegawa, Takashi; Okamoto, Kiyomi; Hikihara, Toshiya; Sakai, Tôru

2017-04-01

We explore the ground-state phase diagram of the S = 1/2 two-leg ladder. The isotropic leg interactions J1,a and J1,b between nearest neighbor spins in the legs a and b, respectively, are different from each other. The xy and z components of the uniform rung interactions are denoted by Jr and ΔJr, respectively, where Δ is the XXZ anisotropy parameter. This system has a frustration when J1,aJ1,b < 0 irrespective of the sign of Jr. The phase diagrams on the Δ (0≤Δ<1) versus J1,b plane in the cases of J1,a = - 0.2 and J1,a = 0.2 with Jr = -1 are determined numerically. We employ the physical consideration, the level spectroscopy analysis of the results obtained by the exact diagonalization method and also the density-matrix renormalization-group method. It is found that the non-collinear ferrimagnetic (NCFR) state appears as the ground state in the frustrated region of the parameters. Furthermore, the direct-product triplet-dimer (TD) state in which all rungs form the TD pair is the exact ground state, when J1,a + J1,b = 0 and 0≤ Δ ≲ 0.83. The obtained phase diagrams consist of the TD, XY and Haldane phases as well as the NCFR phase.

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.

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...

Communication: Correct charge transfer in CT complexes from the Becke'05 density functional

NASA Astrophysics Data System (ADS)

Becke, Axel D.; Dale, Stephen G.; Johnson, Erin R.

2018-06-01

It has been known for over twenty years that density functionals of the generalized-gradient approximation (GGA) type and exact-exchange-GGA hybrids with low exact-exchange mixing fraction yield enormous errors in the properties of charge-transfer (CT) complexes. Manifestations of this error have also plagued computations of CT excitation energies. GGAs transfer far too much charge in CT complexes. This error has therefore come to be called "delocalization" error. It remains, to this day, a vexing unsolved problem in density-functional theory (DFT). Here we report that a 100% exact-exchange-based density functional known as Becke'05 or "B05" [A. D. Becke, J. Chem. Phys. 119, 2972 (2003); 122, 064101 (2005)] predicts excellent charge transfers in classic CT complexes involving the electron donors NH3, C2H4, HCN, and C2H2 and electron acceptors F2 and Cl2. Our approach is variational, as in our recent "B05min" dipole moments paper [Dale et al., J. Chem. Phys. 147, 154103 (2017)]. Therefore B05 is not only an accurate DFT for thermochemistry but is promising as a solution to the delocalization problem as well.

Evaluation of Several Approximate Methods for Calculating the Symmetrical Bending-Moment Response of Flexible Airplanes to Isotropic Atmospheric Turbulence

NASA Technical Reports Server (NTRS)

Bennett, Floyd V.; Yntema, Robert T.

1959-01-01

Several approximate procedures for calculating the bending-moment response of flexible airplanes to continuous isotropic turbulence are presented and evaluated. The modal methods (the mode-displacement and force-summation methods) and a matrix method (segmented-wing method) are considered. These approximate procedures are applied to a simplified airplane for which an exact solution to the equation of motion can be obtained. The simplified airplane consists of a uniform beam with a concentrated fuselage mass at the center. Airplane motions are limited to vertical rigid-body translation and symmetrical wing bending deflections. Output power spectra of wing bending moments based on the exact transfer-function solutions are used as a basis for the evaluation of the approximate methods. It is shown that the force-summation and the matrix methods give satisfactory accuracy and that the mode-displacement method gives unsatisfactory accuracy.

Radiative transfer models for retrieval of cloud parameters from EPIC/DSCOVR measurements

NASA Astrophysics Data System (ADS)

Molina García, Víctor; Sasi, Sruthy; Efremenko, Dmitry S.; Doicu, Adrian; Loyola, Diego

2018-07-01

In this paper we analyze the accuracy and efficiency of several radiative transfer models for inferring cloud parameters from radiances measured by the Earth Polychromatic Imaging Camera (EPIC) on board the Deep Space Climate Observatory (DSCOVR). The radiative transfer models are the exact discrete ordinate and matrix operator methods with matrix exponential, and the approximate asymptotic and equivalent Lambertian cloud models. To deal with the computationally expensive radiative transfer calculations, several acceleration techniques such as, for example, the telescoping technique, the method of false discrete ordinate, the correlated k-distribution method and the principal component analysis (PCA) are used. We found that, for the EPIC oxygen A-band absorption channel at 764 nm, the exact models using the correlated k-distribution in conjunction with PCA yield an accuracy better than 1.5% and a computation time of 18 s for radiance calculations at 5 viewing zenith angles.

Path integral approach to the Wigner representation of canonical density operators for discrete systems coupled to harmonic baths.

PubMed

Montoya-Castillo, Andrés; Reichman, David R

2017-01-14

We derive a semi-analytical form for the Wigner transform for the canonical density operator of a discrete system coupled to a harmonic bath based on the path integral expansion of the Boltzmann factor. The introduction of this simple and controllable approach allows for the exact rendering of the canonical distribution and permits systematic convergence of static properties with respect to the number of path integral steps. In addition, the expressions derived here provide an exact and facile interface with quasi- and semi-classical dynamical methods, which enables the direct calculation of equilibrium time correlation functions within a wide array of approaches. We demonstrate that the present method represents a practical path for the calculation of thermodynamic data for the spin-boson and related systems. We illustrate the power of the present approach by detailing the improvement of the quality of Ehrenfest theory for the correlation function C zz (t)=Re⟨σ z (0)σ z (t)⟩ for the spin-boson model with systematic convergence to the exact sampling function. Importantly, the numerically exact nature of the scheme presented here and its compatibility with semiclassical methods allows for the systematic testing of commonly used approximations for the Wigner-transformed canonical density.

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.

Multi-jet Merging with NLO Matrix Elements

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

Siegert, Frank; /Freiburg U.; Hoche, Stefan

2011-08-18

In the algorithm presented here, the ME+PS approach to merge samples of tree-level matrix elements into inclusive event samples is combined with the POWHEG method, which includes exact next-to-leading order matrix elements in the parton shower. The advantages of the method are discussed and the quality of its implementation in SHERPA is exemplified by results for e{sup +}e{sup -} annihilation into hadrons at LEP, for deep-inelastic lepton-nucleon scattering at HERA, for Drell-Yan lepton-pair production at the Tevatron and for W{sup +}W{sup -}-production at LHC energies. The simulation of hard QCD radiation in parton-shower Monte Carlos has seen tremendous progress overmore » the last years. It was largely stimulated by the need for more precise predictions at LHC energies where the large available phase space allows additional hard QCD radiation alongside known Standard Model processes or even signals from new physics. Two types of algorithms have been developed, which allow to improve upon the soft-collinear approximations made in the parton shower, such that hard radiation is simulated according to exact matrix elements. In the ME+PS approach [1] higher-order tree-level matrix elements for different final-state jet multiplicity are merged with each other and with subsequent parton shower emissions to generate an inclusive sample. Such a prescription is invaluable for analyses which are sensitive to final states with a large jet multiplicity. The only remaining deficiency of such tree-level calculations is the large uncertainty stemming from scale variations. The POWHEG method [2] solves this problem for the lowest multiplicity subprocess by combining full NLO matrix elements with the parton shower. While this leads to NLO accuracy in the inclusive cross section and the exact radiation pattern for the first emission, it fails to describe higher-order emissions with improved accuracy. Thus it is not sufficient if final states with high jet multiplicities are considered. With the complementary advantages of these two approaches, the question arises naturally whether it would be possible to combine them into an even more powerful one. Such a combined algorithm was independently developed in [5] and [6]. Here a summary of the algorithm is given and predictions from corresponding Monte-Carlo predictions are presented.« less

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.

Exact density functional theory for ideal polymer fluids with nearest neighbor bonding constraints.

PubMed

Woodward, Clifford E; Forsman, Jan

2008-08-07

We present a new density functional theory of ideal polymer fluids, assuming nearest-neighbor bonding constraints. The free energy functional is expressed in terms of end site densities of chain segments and thus has a simpler mathematical structure than previously used expressions using multipoint distributions. This work is based on a formalism proposed by Tripathi and Chapman [Phys. Rev. Lett. 94, 087801 (2005)]. Those authors obtain an approximate free energy functional for ideal polymers in terms of monomer site densities. Calculations on both repulsive and attractive surfaces show that their theory is reasonably accurate in some cases, but does differ significantly from the exact result for longer polymers with attractive surfaces. We suggest that segment end site densities, rather than monomer site densities, are the preferred choice of "site functions" for expressing the free energy functional of polymer fluids. We illustrate the application of our theory to derive an expression for the free energy of an ideal fluid of infinitely long polymers.

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

Constantin, Lucian A.; Fabiano, Eduardo; Della Sala, Fabio

We introduce a novel non-local ingredient for the construction of exchange density functionals: the reduced Hartree parameter, which is invariant under the uniform scaling of the density and represents the exact exchange enhancement factor for one- and two-electron systems. The reduced Hartree parameter is used together with the conventional meta-generalized gradient approximation (meta-GGA) semilocal ingredients (i.e., the electron density, its gradient, and the kinetic energy density) to construct a new generation exchange functional, termed u-meta-GGA. This u-meta-GGA functional is exact for the exchange of any one- and two-electron systems, is size-consistent and non-empirical, satisfies the uniform density scaling relation, andmore » recovers the modified gradient expansion derived from the semiclassical atom theory. For atoms, ions, jellium spheres, and molecules, it shows a good accuracy, being often better than meta-GGA exchange functionals. Our construction validates the use of the reduced Hartree ingredient in exchange-correlation functional development, opening the way to an additional rung in the Jacob’s ladder classification of non-empirical density functionals.« less

Exact analytic solution for non-linear density fluctuation in a ΛCDM universe

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

Yoo, Jaiyul; Gong, Jinn-Ouk, E-mail: jyoo@physik.uzh.ch, E-mail: jinn-ouk.gong@apctp.org

We derive the exact third-order analytic solution of the matter density fluctuation in the proper-time hypersurface in a ΛCDM universe, accounting for the explicit time-dependence and clarifying the relation to the initial condition. Furthermore, we compare our analytic solution to the previous calculation in the comoving gauge, and to the standard Newtonian perturbation theory by providing Fourier kernels for the relativistic effects. Our results provide an essential ingredient for a complete description of galaxy bias in the relativistic context.

An exact solution for a thick domain wall in general relativity

NASA Technical Reports Server (NTRS)

Goetz, Guenter; Noetzold, Dirk

1989-01-01

An exact solution of the Einstein equations for a static, planar domain wall with finite thickness is presented. At infinity, density and pressure vanish and the space-time tends to the Minkowski vacuum on one side of the wall and to the Taub vacuum on the other side. A surprising feature of this solution is that the density and pressure distribution are symmetric about the central plane of the wall whereas the space-time metric and therefore also the gravitational field experienced by a test particle is asymmetric.

Are Low-order Covariance Estimates Useful in Error Analyses?

NASA Astrophysics Data System (ADS)

Baker, D. F.; Schimel, D.

2005-12-01

Atmospheric trace gas inversions, using modeled atmospheric transport to infer surface sources and sinks from measured concentrations, are most commonly done using least-squares techniques that return not only an estimate of the state (the surface fluxes) but also the covariance matrix describing the uncertainty in that estimate. Besides allowing one to place error bars around the estimate, the covariance matrix may be used in simulation studies to learn what uncertainties would be expected from various hypothetical observing strategies. This error analysis capability is routinely used in designing instrumentation, measurement campaigns, and satellite observing strategies. For example, Rayner, et al (2002) examined the ability of satellite-based column-integrated CO2 measurements to constrain monthly-average CO2 fluxes for about 100 emission regions using this approach. Exact solutions for both state vector and covariance matrix become computationally infeasible, however, when the surface fluxes are solved at finer resolution (e.g., daily in time, under 500 km in space). It is precisely at these finer scales, however, that one would hope to be able to estimate fluxes using high-density satellite measurements. Non-exact estimation methods such as variational data assimilation or the ensemble Kalman filter could be used, but they achieve their computational savings by obtaining an only approximate state estimate and a low-order approximation of the true covariance. One would like to be able to use this covariance matrix to do the same sort of error analyses as are done with the full-rank covariance, but is it correct to do so? Here we compare uncertainties and `information content' derived from full-rank covariance matrices obtained from a direct, batch least squares inversion to those from the incomplete-rank covariance matrices given by a variational data assimilation approach solved with a variable metric minimization technique (the Broyden-Fletcher- Goldfarb-Shanno algorithm). Two cases are examined: a toy problem in which CO2 fluxes for 3 latitude bands are estimated for only 2 time steps per year, and for the monthly fluxes for 22 regions across 1988-2003 solved for in the TransCom3 interannual flux inversion of Baker, et al (2005). The usefulness of the uncertainty estimates will be assessed as a function of the number of minimization steps used in the variational approach; this will help determine whether they will also be useful in the high-resolution cases that we would most like to apply the non-exact methods to. Baker, D.F., et al., TransCom3 inversion intercomparison: Impact of transport model errors on the interannual variability of regional CO2 fluxes, 1988-2003, Glob. Biogeochem. Cycles, doi:10.1029/2004GB002439, 2005, in press. Rayner, P.J., R.M. Law, D.M. O'Brien, T.M. Butler, and A.C. Dilley, Global observations of the carbon budget, 3, Initial assessment of the impact of satellite orbit, scan geometry, and cloud on measuring CO2 from space, J. Geophys. Res., 107(D21), 4557, doi:10.1029/2001JD000618, 2002.

A constitutive law for continuous fiber reinforced brittle matrix composites with fiber fragmentation and stress recovery

NASA Astrophysics Data System (ADS)

Neumeister, Jonas M.

1993-08-01

THE TENSILE BEHAVIOR of a brittle matrix composite is studied for post matrix crack saturation conditions. Scatter of fiber strength following the Weibull distribution as well as the influence of the major microstructural variables is considered. The stress in a fiber is assumed to recover linearly around a failure due to a fiber-matrix interface behavior mainly ruled by friction. The constitutive behavior for such a composite is analysed. Results are given for a simplified and a refined approximate description and compared with an analysis resulting from the exact analytical theory of fiber fragmentation. It is shown that the stress-strain relation for the refined model excellently follows the exact solution and gives the location of the maximum to within 1% in both stress and strain; for most materials the agreement is even better. Also it is shown that all relations can be normalized to depend on only two variables; a stress reference and the Weibull exponent. For systems with low scatter in fiber strength the simplified model is sufficient to determine the stress maximum but not the postcritical behavior. In addition, the simplified model gives explicit analytical expressions for the maximum stress and corresponding strain. None of the models contain any volume dependence or statistical scatter, but the maximum stress given by the stress-strain relation constitutes an upper bound for the ultimate tensile strength of the composite.

Two dimensional J-matrix approach to quantum scattering

NASA Astrophysics Data System (ADS)

Olumegbon, Ismail Adewale

We present an extension of the J-matrix method of scattering to two dimensions in cylindrical coordinates. In the J-matrix approach we select a zeroth order Hamiltonian, H0, which is exactly solvable in the sense that we select a square integrable basis set that enable us to have an infinite tridiagonal representation for H0. Expanding the wavefunction in this basis makes the wave equation equivalent to a three-term recursion relation for the expansion coefficients. Consequently, finding solutions of the recursion relation is equivalent to solving the original H0 problem (i.e., determining the expansion coefficients of the system's wavefunction). The part of the original potential interaction which cannot be brought to an exact tridiagonal form is cut in an NxN basis space and its matrix elements are computed numerically using Gauss quadrature approach. Hence, this approach embodies powerful tools in the analysis of solutions of the wave equation by exploiting the intimate connection and interplay between tridiagonal matrices and the theory of orthogonal polynomials. In such analysis, one is at liberty to employ a wide range of well established methods and numerical techniques associated with these settings such as quadrature approximation and continued fractions. To demonstrate the utility, usefulness, and accuracy of the extended method we use it to obtain the bound states for an illustrative short range potential problem.

Two dimensional J-matrix approach to quantum scattering

NASA Astrophysics Data System (ADS)

Olumegbon, Ismail Adewale

2013-01-01

We present an extension of the J-matrix method of scattering to two dimensions in cylindrical coordinates. In the J-matrix approach we select a zeroth order Hamiltonian, H0, which is exactly solvable in the sense that we select a square integrable basis set that enable us to have an infinite tridiagonal representation for H0. Expanding the wavefunction in this basis makes the wave equation equivalent to a three-term recursion relation for the expansion coefficients. Consequently, finding solutions of the recursion relation is equivalent to solving the original H0 problem (i.e., determining the expansion coefficients of the system's wavefunction). The part of the original potential interaction which cannot be brought to an exact tridiagonal form is cut in an NxN basis space and its matrix elements are computed numerically using Gauss quadrature approach. Hence, this approach embodies powerful tools in the analysis of solutions of the wave equation by exploiting the intimate connection and interplay between tridiagonal matrices and the theory of orthogonal polynomials. In such analysis, one is at liberty to employ a wide range of well established methods and numerical techniques associated with these settings such as quadrature approximation and continued fractions. To demonstrate the utility, usefulness, and accuracy of the extended method we use it to obtain the bound states for an illustrative short range potential problem.

Sparse PCA with Oracle Property.

PubMed

Gu, Quanquan; Wang, Zhaoran; Liu, Han

In this paper, we study the estimation of the k -dimensional sparse principal subspace of covariance matrix Σ in the high-dimensional setting. We aim to recover the oracle principal subspace solution, i.e., the principal subspace estimator obtained assuming the true support is known a priori. To this end, we propose a family of estimators based on the semidefinite relaxation of sparse PCA with novel regularizations. In particular, under a weak assumption on the magnitude of the population projection matrix, one estimator within this family exactly recovers the true support with high probability, has exact rank- k , and attains a [Formula: see text] statistical rate of convergence with s being the subspace sparsity level and n the sample size. Compared to existing support recovery results for sparse PCA, our approach does not hinge on the spiked covariance model or the limited correlation condition. As a complement to the first estimator that enjoys the oracle property, we prove that, another estimator within the family achieves a sharper statistical rate of convergence than the standard semidefinite relaxation of sparse PCA, even when the previous assumption on the magnitude of the projection matrix is violated. We validate the theoretical results by numerical experiments on synthetic datasets.

Sparse PCA with Oracle Property

PubMed Central

Gu, Quanquan; Wang, Zhaoran; Liu, Han

2014-01-01

In this paper, we study the estimation of the k-dimensional sparse principal subspace of covariance matrix Σ in the high-dimensional setting. We aim to recover the oracle principal subspace solution, i.e., the principal subspace estimator obtained assuming the true support is known a priori. To this end, we propose a family of estimators based on the semidefinite relaxation of sparse PCA with novel regularizations. In particular, under a weak assumption on the magnitude of the population projection matrix, one estimator within this family exactly recovers the true support with high probability, has exact rank-k, and attains a s/n statistical rate of convergence with s being the subspace sparsity level and n the sample size. Compared to existing support recovery results for sparse PCA, our approach does not hinge on the spiked covariance model or the limited correlation condition. As a complement to the first estimator that enjoys the oracle property, we prove that, another estimator within the family achieves a sharper statistical rate of convergence than the standard semidefinite relaxation of sparse PCA, even when the previous assumption on the magnitude of the projection matrix is violated. We validate the theoretical results by numerical experiments on synthetic datasets. PMID:25684971

Interior radiances in optically deep absorbing media. 1: Exact solutions for one-dimensional model

NASA Technical Reports Server (NTRS)

Kattawar, G. W.; Plass, G. N.

1973-01-01

The exact solutions are obtained for a one dimensional model of a scattering and absorbing medium. The results are given for both the reflected and transmitted radiance for any arbitrary surface albedo as well as for the interior radiance. These same quantities are calculated by the matrix operator method. The relative error of the solutions is obtained by comparison with the exact solutions as well as by an error analysis of the equations. The importance of an accurate starting value for the reflection and transmission operators is shown. A fourth order Runge-Kutta method can be used to solve the differential equations satisfied by these operators in order to obtain such accurate starting values.

Solving Modal Equations of Motion with Initial Conditions Using MSC/NASTRAN DMAP. Part 2; Coupled Versus Uncoupled Integration

NASA Technical Reports Server (NTRS)

Barnett, Alan R.; Ibrahim, Omar M.; Abdallah, Ayman A.; Sullivan, Timothy L.

1993-01-01

By utilizing MSC/NASTRAN DMAP (Direct Matrix Abstraction Program) in an existing NASA Lewis Research Center coupled loads methodology, solving modal equations of motion with initial conditions is possible using either coupled (Newmark-Beta) or uncoupled (exact mode superposition) integration available within module TRD1. Both the coupled and newly developed exact mode superposition methods have been used to perform transient analyses of various space systems. However, experience has shown that in most cases, significant time savings are realized when the equations of motion are integrated using the uncoupled solver instead of the coupled solver. Through the results of a real-world engineering analysis, advantages of using the exact mode superposition methodology are illustrated.

Comprehensive T-Matrix Reference Database: A 2012 - 2013 Update

NASA Technical Reports Server (NTRS)

Mishchenko, Michael I.; Videen, Gorden; Khlebtsov, Nikolai G.; Wriedt, Thomas

2013-01-01

The T-matrix method is one of the most versatile, efficient, and accurate theoretical techniques widely used for numerically exact computer calculations of electromagnetic scattering by single and composite particles, discrete random media, and particles imbedded in complex environments. This paper presents the fifth update to the comprehensive database of peer-reviewed T-matrix publications initiated by us in 2004 and includes relevant publications that have appeared since 2012. It also lists several earlier publications not incorporated in the original database, including Peter Waterman's reports from the 1960s illustrating the history of the T-matrix approach and demonstrating that John Fikioris and Peter Waterman were the true pioneers of the multi-sphere method otherwise known as the generalized Lorenz - Mie theory.

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.

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.

Matrix superpotentials

NASA Astrophysics Data System (ADS)

Nikitin, Anatoly G.; Karadzhov, Yuri

2011-07-01

We present a collection of matrix-valued shape invariant potentials which give rise to new exactly solvable problems of SUSY quantum mechanics. It includes all irreducible matrix superpotentials of the generic form W=kQ+\\frac{1}{k} R+P, where k is a variable parameter, Q is the unit matrix multiplied by a real-valued function of independent variable x, and P and R are the Hermitian matrices depending on x. In particular, we recover the Pron'ko-Stroganov 'matrix Coulomb potential' and all known scalar shape invariant potentials of SUSY quantum mechanics. In addition, five new shape invariant potentials are presented. Three of them admit a dual shape invariance, i.e. the related Hamiltonians can be factorized using two non-equivalent superpotentials. We find discrete spectrum and eigenvectors for the corresponding Schrödinger equations and prove that these eigenvectors are normalizable.

Thermal density functional theory, ensemble density functional theory, and potential functional theory for warm dense matter

NASA Astrophysics Data System (ADS)

Pribram-Jones, Aurora

Warm dense matter (WDM) is a high energy phase between solids and plasmas, with characteristics of both. It is present in the centers of giant planets, within the earth's core, and on the path to ignition of inertial confinement fusion. The high temperatures and pressures of warm dense matter lead to complications in its simulation, as both classical and quantum effects must be included. One of the most successful simulation methods is density functional theory-molecular dynamics (DFT-MD). Despite great success in a diverse array of applications, DFT-MD remains computationally expensive and it neglects the explicit temperature dependence of electron-electron interactions known to exist within exact DFT. Finite-temperature density functional theory (FT DFT) is an extension of the wildly successful ground-state DFT formalism via thermal ensembles, broadening its quantum mechanical treatment of electrons to include systems at non-zero temperatures. Exact mathematical conditions have been used to predict the behavior of approximations in limiting conditions and to connect FT DFT to the ground-state theory. An introduction to FT DFT is given within the context of ensemble DFT and the larger field of DFT is discussed for context. Ensemble DFT is used to describe ensembles of ground-state and excited systems. Exact conditions in ensemble DFT and the performance of approximations depend on ensemble weights. Using an inversion method, exact Kohn-Sham ensemble potentials are found and compared to approximations. The symmetry eigenstate Hartree-exchange approximation is in good agreement with exact calculations because of its inclusion of an ensemble derivative discontinuity. Since ensemble weights in FT DFT are temperature-dependent Fermi weights, this insight may help develop approximations well-suited to both ground-state and FT DFT. A novel, highly efficient approach to free energy calculations, finite-temperature potential functional theory, is derived, which has the potential to transform the simulation of warm dense matter. As a semiclassical method, it connects the normally disparate regimes of cold condensed matter physics and hot plasma physics. This orbital-free approach captures the smooth classical density envelope and quantum density oscillations that are both crucial to accurate modeling of materials where temperature and pressure effects are influential.

Exact transition probabilities in a 6-state Landau–Zener system with path interference

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

Sinitsyn, Nikolai A.

2015-04-23

In this paper, we identify a nontrivial multistate Landau–Zener (LZ) model for which transition probabilities between any pair of diabatic states can be determined analytically and exactly. In the semiclassical picture, this model features the possibility of interference of different trajectories that connect the same initial and final states. Hence, transition probabilities are generally not described by the incoherent successive application of the LZ formula. Finally, we discuss reasons for integrability of this system and provide numerical tests of the suggested expression for the transition probability matrix.

Condensates of p-wave pairs are exact solutions for rotating two-component Bose gases.

PubMed

Papenbrock, T; Reimann, S M; Kavoulakis, G M

2012-02-17

We derive exact analytical results for the wave functions and energies of harmonically trapped two-component Bose-Einstein condensates with weakly repulsive interactions under rotation. The isospin symmetric wave functions are universal and do not depend on the matrix elements of the two-body interaction. The comparison with the results from numerical diagonalization shows that the ground state and low-lying excitations consist of condensates of p-wave pairs for repulsive contact interactions, Coulomb interactions, and the repulsive interactions between aligned dipoles.

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.

Exact kinetic energy enables accurate evaluation of weak interactions by the FDE-vdW method.

PubMed

Sinha, Debalina; Pavanello, Michele

2015-08-28

The correlation energy of interaction is an elusive and sought-after interaction between molecular systems. By partitioning the response function of the system into subsystem contributions, the Frozen Density Embedding (FDE)-vdW method provides a computationally amenable nonlocal correlation functional based on the adiabatic connection fluctuation dissipation theorem applied to subsystem density functional theory. In reproducing potential energy surfaces of weakly interacting dimers, we show that FDE-vdW, either employing semilocal or exact nonadditive kinetic energy functionals, is in quantitative agreement with high-accuracy coupled cluster calculations (overall mean unsigned error of 0.5 kcal/mol). When employing the exact kinetic energy (which we term the Kohn-Sham (KS)-vdW method), the binding energies are generally closer to the benchmark, and the energy surfaces are also smoother.

Exact kinetic energy enables accurate evaluation of weak interactions by the FDE-vdW method

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

Sinha, Debalina; Pavanello, Michele, E-mail: m.pavanello@rutgers.edu

2015-08-28

The correlation energy of interaction is an elusive and sought-after interaction between molecular systems. By partitioning the response function of the system into subsystem contributions, the Frozen Density Embedding (FDE)-vdW method provides a computationally amenable nonlocal correlation functional based on the adiabatic connection fluctuation dissipation theorem applied to subsystem density functional theory. In reproducing potential energy surfaces of weakly interacting dimers, we show that FDE-vdW, either employing semilocal or exact nonadditive kinetic energy functionals, is in quantitative agreement with high-accuracy coupled cluster calculations (overall mean unsigned error of 0.5 kcal/mol). When employing the exact kinetic energy (which we term themore » Kohn-Sham (KS)-vdW method), the binding energies are generally closer to the benchmark, and the energy surfaces are also smoother.« less

Probing the 5 f electrons in Am-I by hybrid density functional theory

NASA Astrophysics Data System (ADS)

Atta-Fynn, Raymond; Ray, Asok K.

2009-11-01

The ground states of the actinides and their compounds continue to be matters of considerable controversies. Experimentally, Americium-I (Am-I) is a non-magnetic dhcp metal whereas theoretically an anti-ferromagnetic ground state is predicted. We show that hybrid density functional theory, which admixes a fraction, λ, of exact Hartree-Fock (HF) exchange with approximate DFT exchange, can correctly reproduce the ground state properties of Am. In particular, for λ=0.40, we obtain a non-magnetic ground state with equilibrium atomic volume, bulk modulus, 5 f electron population, and the density of electronic states all in good agreement with experimental data. We argue that the exact HF exchange corrects the overestimation of the approximate DFT exchange interaction.

Gaussian memory in kinematic matrix theory for self-propellers.

PubMed

Nourhani, Amir; Crespi, Vincent H; Lammert, Paul E

2014-12-01

We extend the kinematic matrix ("kinematrix") formalism [Phys. Rev. E 89, 062304 (2014)], which via simple matrix algebra accesses ensemble properties of self-propellers influenced by uncorrelated noise, to treat Gaussian correlated noises. This extension brings into reach many real-world biological and biomimetic self-propellers for which inertia is significant. Applying the formalism, we analyze in detail ensemble behaviors of a 2D self-propeller with velocity fluctuations and orientation evolution driven by an Ornstein-Uhlenbeck process. On the basis of exact results, a variety of dynamical regimes determined by the inertial, speed-fluctuation, orientational diffusion, and emergent disorientation time scales are delineated and discussed.

Comprehensive Thematic T-Matrix Reference Database: A 2015-2017 Update

NASA Technical Reports Server (NTRS)

Mishchenko, Michael I.; Zakharova, Nadezhda; Khlebtsov, Nikolai G.; Videen, Gorden; Wriedt, Thomas

2017-01-01

The T-matrix method pioneered by Peter C. Waterman is one of the most versatile and efficient numerically exact computer solvers of the time-harmonic macroscopic Maxwell equations. It is widely used for the computation of electromagnetic scattering by single and composite particles, discrete random media, periodic structures (including metamaterials), and particles in the vicinity of plane or rough interfaces separating media with different refractive indices. This paper is the eighth update to the comprehensive thematic database of peer-reviewed T-matrix publications initiated in 2004 and lists relevant publications that have appeared since 2015. It also references a small number of earlier publications overlooked previously.

Comprehensive thematic T-matrix reference database: A 2015-2017 update

NASA Astrophysics Data System (ADS)

Mishchenko, Michael I.; Zakharova, Nadezhda T.; Khlebtsov, Nikolai G.; Videen, Gorden; Wriedt, Thomas

2017-11-01

The T-matrix method pioneered by Peter C. Waterman is one of the most versatile and efficient numerically exact computer solvers of the time-harmonic macroscopic Maxwell equations. It is widely used for the computation of electromagnetic scattering by single and composite particles, discrete random media, periodic structures (including metamaterials), and particles in the vicinity of plane or rough interfaces separating media with different refractive indices. This paper is the eighth update to the comprehensive thematic database of peer-reviewed T-matrix publications initiated in 2004 and lists relevant publications that have appeared since 2015. It also references a small number of earlier publications overlooked previously.

Discontinuous functional for linear-response time-dependent density-functional theory: The exact-exchange kernel and approximate forms

NASA Astrophysics Data System (ADS)

Hellgren, Maria; Gross, E. K. U.

2013-11-01

We present a detailed study of the exact-exchange (EXX) kernel of time-dependent density-functional theory with an emphasis on its discontinuity at integer particle numbers. It was recently found that this exact property leads to sharp peaks and step features in the kernel that diverge in the dissociation limit of diatomic systems [Hellgren and Gross, Phys. Rev. APLRAAN1050-294710.1103/PhysRevA.85.022514 85, 022514 (2012)]. To further analyze the discontinuity of the kernel, we here make use of two different approximations to the EXX kernel: the Petersilka Gossmann Gross (PGG) approximation and a common energy denominator approximation (CEDA). It is demonstrated that whereas the PGG approximation neglects the discontinuity, the CEDA includes it explicitly. By studying model molecular systems it is shown that the so-called field-counteracting effect in the density-functional description of molecular chains can be viewed in terms of the discontinuity of the static kernel. The role of the frequency dependence is also investigated, highlighting its importance for long-range charge-transfer excitations as well as inner-shell excitations.

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.

Symmetry-Resolved Entanglement in Many-Body Systems.

PubMed

Goldstein, Moshe; Sela, Eran

2018-05-18

Similarly to the system Hamiltonian, a subsystem's reduced density matrix is composed of blocks characterized by symmetry quantum numbers (charge sectors). We present a geometric approach for extracting the contribution of individual charge sectors to the subsystem's entanglement measures within the replica trick method, via threading appropriate conjugate Aharonov-Bohm fluxes through a multisheet Riemann surface. Specializing to the case of 1+1D conformal field theory, we obtain general exact results for the entanglement entropies and spectrum, and apply them to a variety of systems, ranging from free and interacting fermions to spin and parafermion chains, and verify them numerically. We find that the total entanglement entropy, which scales as lnL, is composed of sqrt[lnL] contributions of individual subsystem charge sectors for interacting fermion chains, or even O(L^{0}) contributions when total spin conservation is also accounted for. We also explain how measurements of the contribution to the entanglement from separate charge sectors can be performed experimentally with existing techniques.

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

Mackowski, Daniel W.; Mishchenko, Michael I.

The conventional orientation-averaging procedure developed in the framework of the superposition T-matrix approach is generalized to include the case of illumination by a Gaussian beam (GB). The resulting computer code is parallelized and used to perform extensive numerically exact calculations of electromagnetic scattering by volumes of discrete random medium consisting of monodisperse spherical particles. The size parameters of the scattering volumes are 40, 50, and 60, while their packing density is fixed at 5%. We demonstrate that all scattering patterns observed in the far-field zone of a random multisphere target and their evolution with decreasing width of the incident GBmore » can be interpreted in terms of idealized theoretical concepts such as forward-scattering interference, coherent backscattering (CB), and diffuse multiple scattering. It is shown that the increasing violation of electromagnetic reciprocity with decreasing GB width suppresses and eventually eradicates all observable manifestations of CB. This result supplements the previous demonstration of the effects of broken reciprocity in the case of magneto-optically active particles subjected to an external magnetic field.« less

Infinite projected entangled-pair state algorithm for ruby and triangle-honeycomb lattices

NASA Astrophysics Data System (ADS)

Jahromi, Saeed S.; Orús, Román; Kargarian, Mehdi; Langari, Abdollah

2018-03-01

The infinite projected entangled-pair state (iPEPS) algorithm is one of the most efficient techniques for studying the ground-state properties of two-dimensional quantum lattice Hamiltonians in the thermodynamic limit. Here, we show how the algorithm can be adapted to explore nearest-neighbor local Hamiltonians on the ruby and triangle-honeycomb lattices, using the corner transfer matrix (CTM) renormalization group for 2D tensor network contraction. Additionally, we show how the CTM method can be used to calculate the ground-state fidelity per lattice site and the boundary density operator and entanglement entropy (EE) on an infinite cylinder. As a benchmark, we apply the iPEPS method to the ruby model with anisotropic interactions and explore the ground-state properties of the system. We further extract the phase diagram of the model in different regimes of the couplings by measuring two-point correlators, ground-state fidelity, and EE on an infinite cylinder. Our phase diagram is in agreement with previous studies of the model by exact diagonalization.

Entanglement in the Anisotropic Kondo Necklace Model

NASA Astrophysics Data System (ADS)

Mendoza-Arenas, J. J.; Franco, R.; Silva-Valencia, J.

We study the entanglement in the one-dimensional Kondo necklace model with exact diagonalization, calculating the concurrence as a function of the Kondo coupling J and an anisotropy η in the interaction between conduction spins, and we review some results previously obtained in the limiting cases η = 0 and 1. We observe that as J increases, localized and conduction spins get more entangled, while neighboring conduction spins diminish their concurrence; localized spins require a minimum concurrence between conduction spins to be entangled. The anisotropy η diminishes the entanglement for neighboring spins when it increases, driving the system to the Ising limit η = 1 where conduction spins are not entangled. We observe that the concurrence does not give information about the quantum phase transition in the anisotropic Kondo necklace model (between a Kondo singlet and an antiferromagnetic state), but calculating the von Neumann block entropy with the density matrix renormalization group in a chain of 100 sites for the Ising limit indicates that this quantity is useful for locating the quantum critical point.

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

Song, Xue-ke; Wu, Tao; Xu, Shuai

In this paper, we have investigated the dynamical behaviors of the two important quantum correlation witnesses, i.e. geometric quantum discord (GQD) and Bell–CHSH inequality in the XXZ model with DM interaction by employing the quantum renormalization group (QRG) method. The results have shown that the anisotropy suppresses the quantum correlations while the DM interaction can enhance them. Meanwhile, using the QRG method we have studied the quantum phase transition of GQD and obtained two saturated values, which are associated with two different phases: spin-fluid phase and the Néel phase. It is worth mentioning that the block–block correlation is not strongmore » enough to violate the Bell–CHSH inequality in the whole iteration steps. Moreover, the nonanalytic phenomenon and scaling behavior of Bell inequality are discussed in detail. As a byproduct, the conjecture that the exact lower and upper bounds of Bell inequality versus GQD can always be established for this spin system although the given density matrix is a general X state.« less

Strong-coupling phases of the spin-orbit-coupled spin-1 Bose-Hubbard chain: Odd-integer Mott lobes and helical magnetic phases

NASA Astrophysics Data System (ADS)

Pixley, J. H.; Cole, William S.; Spielman, I. B.; Rizzi, Matteo; Das Sarma, S.

2017-10-01

We study the odd-integer filled Mott phases of a spin-1 Bose-Hubbard chain and determine their fate in the presence of a Raman induced spin-orbit coupling which has been achieved in ultracold atomic gases; this system is described by a quantum spin-1 chain with a spiral magnetic field. The spiral magnetic field initially induces helical order with either ferromagnetic or dimer order parameters, giving rise to a spiral paramagnet at large field. The spiral ferromagnet-to-paramagnet phase transition is in a universality class with critical exponents associated with the divergence of the correlation length ν ≈2 /3 and the order-parameter susceptibility γ ≈1 /2 . We solve the effective spin model exactly using the density-matrix renormalization group, and compare with both a large-S classical solution and a phenomenological Landau theory. We discuss how these exotic bosonic magnetic phases can be produced and probed in ultracold atomic experiments in optical lattices.

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

Dubetsky, Boris; Libby, Stephen; Berman, Paul

The influence of an external test mass on the phase of the signal of an atom interferometer is studied theoretically. Using traditional techniques in atom optics based on the density matrix equations in the Wigner representation, we are able to extract the various contributions to the phase of the signal associated with the classical motion of the atoms, the quantum correction to this motion resulting from atomic recoil that is produced when the atoms interact with Raman field pulses and quantum corrections to the atomic motion that occur in the time between the Raman field pulses. Thus, by increasing themore » effective wave vector associated with the Raman field pulses using modified field parameters, we can increase the sensitivity of the signal to the point where such quantum corrections can be measured. Furthermore, the expressions that are derived can be evaluated numerically to isolate the contribution to the signal from an external test mass. The regions of validity of the exact and approximate expressions are determined.« less

Atom Interferometry in the Presence of an External Test Mass

DOE PAGES

Dubetsky, Boris; Libby, Stephen; Berman, Paul

2016-04-21

The influence of an external test mass on the phase of the signal of an atom interferometer is studied theoretically. Using traditional techniques in atom optics based on the density matrix equations in the Wigner representation, we are able to extract the various contributions to the phase of the signal associated with the classical motion of the atoms, the quantum correction to this motion resulting from atomic recoil that is produced when the atoms interact with Raman field pulses and quantum corrections to the atomic motion that occur in the time between the Raman field pulses. Thus, by increasing themore » effective wave vector associated with the Raman field pulses using modified field parameters, we can increase the sensitivity of the signal to the point where such quantum corrections can be measured. Furthermore, the expressions that are derived can be evaluated numerically to isolate the contribution to the signal from an external test mass. The regions of validity of the exact and approximate expressions are determined.« less

Free-time and fixed end-point optimal control theory in dissipative media: application to entanglement generation and maintenance.

PubMed

Mishima, K; Yamashita, K

2009-07-07

We develop monotonically convergent free-time and fixed end-point optimal control theory (OCT) in the density-matrix representation to deal with quantum systems showing dissipation. Our theory is more general and flexible for tailoring optimal laser pulses in order to control quantum dynamics with dissipation than the conventional fixed-time and fixed end-point OCT in that the optimal temporal duration of laser pulses can also be optimized exactly. To show the usefulness of our theory, it is applied to the generation and maintenance of the vibrational entanglement of carbon monoxide adsorbed on the copper (100) surface, CO/Cu(100). We demonstrate the numerical results and clarify how to combat vibrational decoherence as much as possible by the tailored shapes of the optimal laser pulses. It is expected that our theory will be general enough to be applied to a variety of dissipative quantum dynamics systems because the decoherence is one of the quantum phenomena sensitive to the temporal duration of the quantum dynamics.

Symmetry-Resolved Entanglement in Many-Body Systems

NASA Astrophysics Data System (ADS)

Goldstein, Moshe; Sela, Eran

2018-05-01

Similarly to the system Hamiltonian, a subsystem's reduced density matrix is composed of blocks characterized by symmetry quantum numbers (charge sectors). We present a geometric approach for extracting the contribution of individual charge sectors to the subsystem's entanglement measures within the replica trick method, via threading appropriate conjugate Aharonov-Bohm fluxes through a multisheet Riemann surface. Specializing to the case of 1 +1 D conformal field theory, we obtain general exact results for the entanglement entropies and spectrum, and apply them to a variety of systems, ranging from free and interacting fermions to spin and parafermion chains, and verify them numerically. We find that the total entanglement entropy, which scales as ln L , is composed of √{ln L } contributions of individual subsystem charge sectors for interacting fermion chains, or even O (L0) contributions when total spin conservation is also accounted for. We also explain how measurements of the contribution to the entanglement from separate charge sectors can be performed experimentally with existing techniques.

Conditions where random phase approximation becomes exact in the high-density limit

NASA Astrophysics Data System (ADS)

Morawetz, Klaus; Ashokan, Vinod; Bala, Renu; Pathak, Kare Narain

2018-04-01

It is shown that, in d -dimensional systems, the vertex corrections beyond the random phase approximation (RPA) or G W approximation scales with the power d -β -α of the Fermi momentum if the relation between Fermi energy and Fermi momentum is ɛf˜pfβ and the interacting potential possesses a momentum power law of ˜p-α . The condition d -β -α <0 specifies systems where RPA is exact in the high-density limit. The one-dimensional structure factor is found to be the interaction-free one in the high-density limit for contact interaction. A cancellation of RPA and vertex corrections render this result valid up to second order in contact interaction. For finite-range potentials of cylindrical wires a large-scale cancellation appears and is found to be independent of the width parameter of the wire. The proposed high-density expansion agrees with the quantum Monte Carlo simulations.

Electromagnetic energy momentum in dispersive media

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

Philbin, T. G.

2011-01-15

The standard derivations of electromagnetic energy and momentum in media take Maxwell's equations as the starting point. It is well known that for dispersive media this approach does not directly yield exact expressions for the energy and momentum densities. Although Maxwell's equations fully describe electromagnetic fields, the general approach to conserved quantities in field theory is not based on the field equations, but rather on the action. Here an action principle for macroscopic electromagnetism in dispersive, lossless media is used to derive the exact conserved energy-momentum tensor. The time-averaged energy density reduces to Brillouin's simple formula when the fields aremore » monochromatic. The time-averaged momentum density for monochromatic fields corresponds to the familiar Minkowski expression DxB, but for general fields in dispersive media the momentum density does not have the Minkowski value. The results are unaffected by the debate over momentum balance in light-matter interactions.« less

Density-Dependent Conformable Space-time Fractional Diffusion-Reaction Equation and Its Exact Solutions

NASA Astrophysics Data System (ADS)

Hosseini, Kamyar; Mayeli, Peyman; Bekir, Ahmet; Guner, Ozkan

2018-01-01

In this article, a special type of fractional differential equations (FDEs) named the density-dependent conformable fractional diffusion-reaction (DDCFDR) equation is studied. Aforementioned equation has a significant role in the modelling of some phenomena arising in the applied science. The well-organized methods, including the \\exp (-φ (\\varepsilon )) -expansion and modified Kudryashov methods are exerted to generate the exact solutions of this equation such that some of the solutions are new and have been reported for the first time. Results illustrate that both methods have a great performance in handling the DDCFDR equation.

Exact time-dependent nonlinear dispersive wave solutions in compressible magnetized plasmas exhibiting collapse.

PubMed

Chakrabarti, Nikhil; Maity, Chandan; Schamel, Hans

2011-04-08

Compressional waves in a magnetized plasma of arbitrary resistivity are treated with the lagrangian fluid approach. An exact nonlinear solution with a nontrivial space and time dependence is obtained with boundary conditions as in Harris' current sheet. The solution shows competition among hydrodynamic convection, magnetic field diffusion, and dispersion. This results in a collapse of density and the magnetic field in the absence of dispersion. The dispersion effects arrest the collapse of density but not of the magnetic field. A possible application is in the early stage of magnetic star formation.

Exact joint density-current probability function for the asymmetric exclusion process.

PubMed

Depken, Martin; Stinchcombe, Robin

2004-07-23

We study the asymmetric simple exclusion process with open boundaries and derive the exact form of the joint probability function for the occupation number and the current through the system. We further consider the thermodynamic limit, showing that the resulting distribution is non-Gaussian and that the density fluctuations have a discontinuity at the continuous phase transition, while the current fluctuations are continuous. The derivations are performed by using the standard operator algebraic approach and by the introduction of new operators satisfying a modified version of the original algebra. Copyright 2004 The American Physical Society

Theoretical and lidar studies of the density response of the mesospheric sodium layer to gravity wave perturbations

NASA Technical Reports Server (NTRS)

Shelton, J. D.; Gardner, C. S.

1981-01-01

The density response of atmospheric layers to gravity waves is developed in two forms, an exact solution and a perturbation series solution. The degree of nonlinearity in the layer density response is described by the series solution whereas the exact solution gives insight into the nature of the responses. Density perturbation in an atmospheric layer are shown to be substantially greater than the atmospheric density perturbation associated with the propagation of a gravity wave. Because of the density gradients present in atmospheric layers, interesting effects were observed such as a phase reversal in the linear layer response which occurs near the layer peak. Once the layer response is understood, the sodium layer can be used as a tracer of atmospheric wave motions. A two dimensional digital signal processing technique was developed. Both spatial and temporal filtering are utilized to enhance the resolution by decreasing shot noise by more han 10 dB. Many of the features associated with a layer density response to gravity waves were observed in high resolution density profiles of the mesospheric sodium layer. These include nonlinearities as well as the phase reversal in the linear layer response.

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.

Universal functions of nuclear proximity potential for Skyrme nucleus-nucleus interaction in a semiclassical approach

NASA Astrophysics Data System (ADS)

Gupta, Raj K.; Singh, Dalip; Kumar, Raj; Greiner, Walter

2009-07-01

The universal function of the nuclear proximity potential is obtained for the Skyrme nucleus-nucleus interaction in the semiclassical extended Thomas-Fermi (ETF) approach. This is obtained as a sum of the spin-orbit-density-independent and spin-orbit-density-dependent parts of the Hamiltonian density, since the two terms behave differently, the spin-orbit-density-independent part mainly attractive and the spin-orbit-density-dependent part mainly repulsive. The semiclassical expansions of kinetic energy density and spin-orbit density are allowed up to second order, and the two-parameter Fermi density, with its parameters fitted to experiments, is used for the nuclear density. The universal functions or the resulting nuclear proximity potential reproduce the 'exact' Skyrme nucleus-nucleus interaction potential in the semiclassical approach, within less than ~1 MeV of difference, both at the maximum attraction and in the surface region. An application of the resulting interaction potential to fusion excitation functions shows clearly that the parameterized universal functions of nuclear proximity potential substitute completely the 'exact' potential in the Skyrme energy density formalism based on the semiclassical ETF method, including also the modifications of interaction barriers at sub-barrier energies in terms of modifying the constants of the universal functions.

Many-Body Perturbation Theory (MBPT) and Time-Dependent Density-Functional Theory (TD-DFT): MBPT Insights About What Is Missing In, and Corrections To, the TD-DFT Adiabatic Approximation.

PubMed

Casida, Mark E; Huix-Rotllant, Miquel

2016-01-01

In their famous paper, Kohn and Sham formulated a formally exact density-functional theory (DFT) for the ground-state energy and density of a system of N interacting electrons, albeit limited at the time by certain troubling representability questions. As no practical exact form of the exchange-correlation (xc) energy functional was known, the xc-functional had to be approximated, ideally by a local or semilocal functional. Nowadays, however, the realization that Nature is not always so nearsighted has driven us up Perdew's Jacob's ladder to find increasingly nonlocal density/wavefunction hybrid functionals. Time-dependent (TD-) DFT is a younger development which allows DFT concepts to be used to describe the temporal evolution of the density in the presence of a perturbing field. Linear response (LR) theory then allows spectra and other information about excited states to be extracted from TD-DFT. Once again the exact TD-DFT xc-functional must be approximated in practical calculations and this has historically been done using the TD-DFT adiabatic approximation (AA) which is to TD-DFT very similar to what the local density approximation (LDA) is to conventional ground-state DFT. Although some of the recent advances in TD-DFT focus on what can be done within the AA, others explore ways around the AA. After giving an overview of DFT, TD-DFT, and LR-TD-DFT, this chapter focuses on many-body corrections to LR-TD-DFT as one way to build hybrid density-functional/wavefunction methodology for incorporating aspects of nonlocality in time not present in the AA.

Universal shocks in the Wishart random-matrix ensemble.

PubMed

Blaizot, Jean-Paul; Nowak, Maciej A; Warchoł, Piotr

2013-05-01

We show that the derivative of the logarithm of the average characteristic polynomial of a diffusing Wishart matrix obeys an exact partial differential equation valid for an arbitrary value of N, the size of the matrix. In the large N limit, this equation generalizes the simple inviscid Burgers equation that has been obtained earlier for Hermitian or unitary matrices. The solution, through the method of characteristics, presents singularities that we relate to the precursors of shock formation in the Burgers equation. The finite N effects appear as a viscosity term in the Burgers equation. Using a scaling analysis of the complete equation for the characteristic polynomial, in the vicinity of the shocks, we recover in a simple way the universal Bessel oscillations (so-called hard-edge singularities) familiar in random-matrix theory.

Exact results for models of multichannel quantum nonadiabatic transitions

DOE PAGES

Sinitsyn, N. A.

2014-12-11

We consider nonadiabatic transitions in explicitly time-dependent systems with Hamiltonians of the form Hˆ(t)=Aˆ+Bˆt+Cˆ/t, where t is time and Aˆ,Bˆ,Cˆ are Hermitian N × N matrices. We show that in any model of this type, scattering matrix elements satisfy nontrivial exact constraints that follow from the absence of the Stokes phenomenon for solutions with specific conditions at t→–∞. This allows one to continue such solutions analytically to t→+∞, and connect their asymptotic behavior at t→–∞ and t→+∞. This property becomes particularly useful when a model shows additional discrete symmetries. Specifically, we derive a number of simple exact constraints and explicitmore » expressions for scattering probabilities in such systems.« less

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.

Study on the mechanism of liquid phase sintering (M-12)

NASA Technical Reports Server (NTRS)

Kohara, S.

1993-01-01

The objectives were to (1) obtain the data representing the growth rate of solid particles in a liquid matrix without the effect of gravity; and (2) reveal the growth behavior of solid particles during liquid phase sintering using the data obtained. Nickel and tungsten are used as the constituent materials in liquid phase sintering. The properties of the constituent metals are given. When a compact of the mixture of tungsten and nickel powders is heated and kept at 1550 C, nickel melts down but tungsten stays solid. As the density of tungsten is much greater than that of nickel, the sedimentation of tungsten particles occurs in the experiment on Earth. The difference between the experiments on Earth and in space is illustrated. The tungsten particles sink to the bottom and are brought into contact with each other. The resulting pressure at the contact point causes the accelerated dissolution of tungsten. Consequently, flat surfaces are formed at the contact sites. As a result of dissolution and reprecipitation of tungsten, the shape of particles changes to a polygon. This phenomenon is called 'flattening.' An example of flattening of tungsten particles is shown. Thus, the data obtained by the experiment on Earth may not represent the exact growth behavior of the solid particles in a liquid matrix. If the experiments were done in a microgravity environment, the data corresponding to the theoretical growth behavior of solid particles could be achieved.

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

Expression and clinical significance of matrix metalloproteinase-9 in lymphatic invasiveness and metastasis of breast cancer.

PubMed

Wu, Qiu-Wan; Yang, Qing-Mo; Huang, Yu-Fan; She, Hong-Qiang; Liang, Jing; Yang, Qiao-Lu; Zhang, Zhi-Ming

2014-01-01

Matrix metalloproteinase 9 (MMP-9) is a type-IV collagenase that is highly expressed in breast cancer, but its exact role in tumor progression and metastasis is unclear. MMP-9 mRNA and protein expression was examined by real-time reverse transcriptase PCR and immunohistochemical staining, respectively, in 41 breast cancer specimens with matched peritumoral benign breast epithelial tissue and suspicious metastatic axillary lymph nodes. Lymph vessels were labeled with D2-40 and lymphatic microvessel density (LMVD) was calculated. Correlation of MMP-9 protein expression with clinicopathological parameters and LMVD was also evaluated. MMP-9(+) staining in breast cancer specimens (35/41, 85.4%) was higher than in matched epithelium (21/41, 51.2%; P<0.05) and lymph nodes (13/41, 31.7%; P<0.001). Higher MMP-9 mRNA expression was also detected in tumor specimens compared with matched epithelial tissues and lymph nodes (P<0.05). Elevated MMP-9 expression was correlated with lymph node metastasis and LMVD (P<0.05). MMP-9 was overexpressed in breast cancer specimens compared with peritumoral benign breast epithelium and lymph nodes. Moreover, its expression in the matched epithelium and lymph nodes was positively associated with lymph node metastasis, and its expression in lymph nodes was positively associated with lymphangiogenesis in breast cancer. Thus, MMP-9 is a potential marker for breast cancer progression.

A Kalman filter for a two-dimensional shallow-water model

NASA Technical Reports Server (NTRS)

Parrish, D. F.; Cohn, S. E.

1985-01-01

A two-dimensional Kalman filter is described for data assimilation for making weather forecasts. The filter is regarded as superior to the optimal interpolation method because the filter determines the forecast error covariance matrix exactly instead of using an approximation. A generalized time step is defined which includes expressions for one time step of the forecast model, the error covariance matrix, the gain matrix, and the evolution of the covariance matrix. Subsequent time steps are achieved by quantifying the forecast variables or employing a linear extrapolation from a current variable set, assuming the forecast dynamics are linear. Calculations for the evolution of the error covariance matrix are banded, i.e., are performed only with the elements significantly different from zero. Experimental results are provided from an application of the filter to a shallow-water simulation covering a 6000 x 6000 km grid.

Variational optimization algorithms for uniform matrix product states

NASA Astrophysics Data System (ADS)

Zauner-Stauber, V.; Vanderstraeten, L.; Fishman, M. T.; Verstraete, F.; Haegeman, J.

2018-01-01

We combine the density matrix renormalization group (DMRG) with matrix product state tangent space concepts to construct a variational algorithm for finding ground states of one-dimensional quantum lattices in the thermodynamic limit. A careful comparison of this variational uniform matrix product state algorithm (VUMPS) with infinite density matrix renormalization group (IDMRG) and with infinite time evolving block decimation (ITEBD) reveals substantial gains in convergence speed and precision. We also demonstrate that VUMPS works very efficiently for Hamiltonians with long-range interactions and also for the simulation of two-dimensional models on infinite cylinders. The new algorithm can be conveniently implemented as an extension of an already existing DMRG implementation.

Two-lane traffic-flow model with an exact steady-state solution.

PubMed

Kanai, Masahiro

2010-12-01

We propose a stochastic cellular-automaton model for two-lane traffic flow based on the misanthrope process in one dimension. The misanthrope process is a stochastic process allowing for an exact steady-state solution; hence, we have an exact flow-density diagram for two-lane traffic. In addition, we introduce two parameters that indicate, respectively, driver's driving-lane preference and passing-lane priority. Due to the additional parameters, the model shows a deviation of the density ratio for driving-lane use and a biased lane efficiency in flow. Then, a mean-field approach explicitly describes the asymmetric flow by the hop rates, the driving-lane preference, and the passing-lane priority. Meanwhile, the simulation results are in good agreement with an observational data, and we thus estimate these parameters. We conclude that the proposed model successfully produces two-lane traffic flow particularly with the driving-lane preference and the passing-lane priority.

General Exact Solution to the Problem of the Probability Density for Sums of Random Variables

NASA Astrophysics Data System (ADS)

Tribelsky, Michael I.

2002-07-01

The exact explicit expression for the probability density pN(x) for a sum of N random, arbitrary correlated summands is obtained. The expression is valid for any number N and any distribution of the random summands. Most attention is paid to application of the developed approach to the case of independent and identically distributed summands. The obtained results reproduce all known exact solutions valid for the, so called, stable distributions of the summands. It is also shown that if the distribution is not stable, the profile of pN(x) may be divided into three parts, namely a core (small x), a tail (large x), and a crossover from the core to the tail (moderate x). The quantitative description of all three parts as well as that for the entire profile is obtained. A number of particular examples are considered in detail.

General exact solution to the problem of the probability density for sums of random variables.

PubMed

Tribelsky, Michael I

2002-08-12

The exact explicit expression for the probability density p(N)(x) for a sum of N random, arbitrary correlated summands is obtained. The expression is valid for any number N and any distribution of the random summands. Most attention is paid to application of the developed approach to the case of independent and identically distributed summands. The obtained results reproduce all known exact solutions valid for the, so called, stable distributions of the summands. It is also shown that if the distribution is not stable, the profile of p(N)(x) may be divided into three parts, namely a core (small x), a tail (large x), and a crossover from the core to the tail (moderate x). The quantitative description of all three parts as well as that for the entire profile is obtained. A number of particular examples are considered in detail.

A B-spline Galerkin method for the Dirac equation

NASA Astrophysics Data System (ADS)

Froese Fischer, Charlotte; Zatsarinny, Oleg

2009-06-01

The B-spline Galerkin method is first investigated for the simple eigenvalue problem, y=-λy, that can also be written as a pair of first-order equations y=λz, z=-λy. Expanding both y(r) and z(r) in the B basis results in many spurious solutions such as those observed for the Dirac equation. However, when y(r) is expanded in the B basis and z(r) in the dB/dr basis, solutions of the well-behaved second-order differential equation are obtained. From this analysis, we propose a stable method ( B,B) basis for the Dirac equation and evaluate its accuracy by comparing the computed and exact R-matrix for a wide range of nuclear charges Z and angular quantum numbers κ. When splines of the same order are used, many spurious solutions are found whereas none are found for splines of different order. Excellent agreement is obtained for the R-matrix and energies for bound states for low values of Z. For high Z, accuracy requires the use of a grid with many points near the nucleus. We demonstrate the accuracy of the bound-state wavefunctions by comparing integrals arising in hyperfine interaction matrix elements with exact analytic expressions. We also show that the Thomas-Reiche-Kuhn sum rule is not a good measure of the quality of the solutions obtained by the B-spline Galerkin method whereas the R-matrix is very sensitive to the appearance of pseudo-states.

A Non-Perturbative Treatment of Quantum Impurity Problems in Real Lattices

NASA Astrophysics Data System (ADS)

Allerdt, Andrew C.

Historically, the RKKY or indirect exchange, interaction has been accepted as being able to be described by second order perturbation theory. A typical universal expression is usually given in this context. This approach, however, fails to incorporate many body effects, quantum fluctuations, and other important details. In Chapter 2, a novel numerical approach is developed to tackle these problems in a quasi-exact, non-perturbative manner. Behind the method lies the main concept of being able to exactly map an n-dimensional lattice problem onto a 1-dimensional chain. The density matrix renormalization group algorithm is then employed to solve the newly cast Hamiltonian. In the following chapters, it is demonstrated that conventional RKKY theory does not capture the crucial physics. It is found that the Kondo effect, i.e. the screening of an impurity spin, tends to dominate over a ferromagnetic interaction between impurity spins. Furthermore, it is found that the indirect exchange interaction does not decay algebraically. Instead, there is a crossover upon increasing JK, where impurities favor forming their own independent Kondo states after just a few lattice spacings. This is not a trivial result, as one may naively expect impurities to interact when their conventional Kondo clouds overlap. The spin structure around impurities coupled to the edge of a 2D topological insulator is investigated in Chapter 7. Modeled after materials such as silicine, germanene, and stanene, it is shown with spatial resolution of the lattice that the specific impurity placement plays a key role. Effects of spin-orbit interactions are also discussed. Finally, in the last chapter, transition metal complexes are studied. This really shows the power and versatility of the method developed throughout the work. The spin states of an iron atom in the molecule FeN4C 10 are calculated and compared to DFT, showing the importance of inter-orbital coulomb interactions. Using dynamical DMRG, the density of states for the 3d-orbitals can also be obtained.

Wilson loops in supersymmetric gauge theories

NASA Astrophysics Data System (ADS)

Pestun, Vasily

This thesis is devoted to several exact computations in four-dimensional supersymmetric gauge field theories. In the first part of the thesis we prove conjecture due to Erickson-Semenoff-Zarembo and Drukker-Gross which relates supersymmetric circular Wilson loop operators in the N = 4 supersymmetric Yang-Mills theory with a Gaussian matrix model. We also compute the partition function and give a new matrix model formula for the expectation value of a supersymmetric circular Wilson loop operator for the pure N = 2 and the N* = 2 supersymmetric Yang-Mills theory on a four-sphere. Circular supersymmetric Wilson loops in four-dimensional N = 2 superconformal gauge theory are treated similarly. In the second part we consider supersymmetric Wilson loops of arbitrary shape restricted to a two-dimensional sphere in the four-dimensional N = 4 supersymmetric Yang-Mills theory. We show that expectation value for these Wilson loops can be exactly computed using a two-dimensional theory closely related to the topological two-dimensional Higgs-Yang-Mills theory, or two-dimensional Yang-Mills theory for the complexified gauge group.

Applications of automatic differentiation in computational fluid dynamics

NASA Technical Reports Server (NTRS)

Green, Lawrence L.; Carle, A.; Bischof, C.; Haigler, Kara J.; Newman, Perry A.

1994-01-01

Automatic differentiation (AD) is a powerful computational method that provides for computing exact sensitivity derivatives (SD) from existing computer programs for multidisciplinary design optimization (MDO) or in sensitivity analysis. A pre-compiler AD tool for FORTRAN programs called ADIFOR has been developed. The ADIFOR tool has been easily and quickly applied by NASA Langley researchers to assess the feasibility and computational impact of AD in MDO with several different FORTRAN programs. These include a state-of-the-art three dimensional multigrid Navier-Stokes flow solver for wings or aircraft configurations in transonic turbulent flow. With ADIFOR the user specifies sets of independent and dependent variables with an existing computer code. ADIFOR then traces the dependency path throughout the code, applies the chain rule to formulate derivative expressions, and generates new code to compute the required SD matrix. The resulting codes have been verified to compute exact non-geometric and geometric SD for a variety of cases. in less time than is required to compute the SD matrix using centered divided differences.

Direct Analysis of Triterpenes from High-Salt Fermented Cucumbers Using Infrared Matrix-Assisted Laser Desorption Electrospray Ionization (IR-MALDESI)

NASA Astrophysics Data System (ADS)

Ekelöf, Måns; McMurtrie, Erin K.; Nazari, Milad; Johanningsmeier, Suzanne D.; Muddiman, David C.

2017-02-01

High-salt samples present a challenge to mass spectrometry (MS) analysis, particularly when electrospray ionization (ESI) is used, requiring extensive sample preparation steps such as desalting, extraction, and purification. In this study, infrared matrix-assisted laser desorption electrospray ionization (IR-MALDESI) coupled to a Q Exactive Plus mass spectrometer was used to directly analyze 50-μm thick slices of cucumber fermented and stored in 1 M sodium chloride brine. From the several hundred unique substances observed, three triterpenoid lipids produced by cucumbers, β-sitosterol, stigmasterol, and lupeol, were putatively identified based on exact mass and selected for structural analysis. The spatial distribution of the lipids were imaged, and the putative assignments were confirmed by tandem mass spectrometry performed directly on the same cucumber, demonstrating the capacity of the technique to deliver confident identifications from highly complex samples in molar concentrations of salt without the need for sample preparation.

Exact solution of a one-dimensional model of strained epitaxy on a periodically modulated substrate

NASA Astrophysics Data System (ADS)

Tokar, V. I.; Dreyssé, H.

2005-03-01

We consider a one-dimensional lattice gas model of strained epitaxy with the elastic strain accounted for through a finite number of cluster interactions comprising contiguous atomic chains. Interactions of this type arise in the models of strained epitaxy based on the Frenkel-Kontorova model. Furthermore, the deposited atoms interact with the substrate via an arbitrary periodic potential of period L . This model is solved exactly with the use of an appropriately adopted technique developed recently in the theory of protein folding. The advantage of the proposed approach over the standard transfer-matrix method is that it reduces the problem to finding the largest eigenvalue of a matrix of size L instead of 2L-1 , which is vital in the case of nanostructures where L may measure in hundreds of interatomic distances. Our major conclusion is that the substrate modulation always facilitates the size calibration of self-assembled nanoparticles in one- and two-dimensional systems.

Spectral functions of strongly correlated extended systems via an exact quantum embedding

NASA Astrophysics Data System (ADS)

Booth, George H.; Chan, Garnet Kin-Lic

2015-04-01

Density matrix embedding theory (DMET) [Phys. Rev. Lett. 109, 186404 (2012), 10.1103/PhysRevLett.109.186404], introduced an approach to quantum cluster embedding methods whereby the mapping of strongly correlated bulk problems to an impurity with finite set of bath states was rigorously formulated to exactly reproduce the entanglement of the ground state. The formalism provided similar physics to dynamical mean-field theory at a tiny fraction of the cost but was inherently limited by the construction of a bath designed to reproduce ground-state, static properties. Here, we generalize the concept of quantum embedding to dynamic properties and demonstrate accurate bulk spectral functions at similarly small computational cost. The proposed spectral DMET utilizes the Schmidt decomposition of a response vector, mapping the bulk dynamic correlation functions to that of a quantum impurity cluster coupled to a set of frequency-dependent bath states. The resultant spectral functions are obtained on the real-frequency axis, without bath discretization error, and allows for the construction of arbitrary dynamic correlation functions. We demonstrate the method on the one- (1D) and two-dimensional (2D) Hubbard model, where we obtain zero temperature and thermodynamic limit spectral functions, and show the trivial extension to two-particle Green's functions. This advance therefore extends the scope and applicability of DMET in condensed-matter problems as a computationally tractable route to correlated spectral functions of extended systems and provides a competitive alternative to dynamical mean-field theory for dynamic quantities.

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.

Studying the validity of relativistic hydrodynamics with a new exact solution of the Boltzmann equation

NASA Astrophysics Data System (ADS)

Denicol, Gabriel; Heinz, Ulrich; Martinez, Mauricio; Noronha, Jorge; Strickland, Michael

2014-12-01

We present an exact solution to the Boltzmann equation which describes a system undergoing boost-invariant longitudinal and azimuthally symmetric radial expansion for arbitrary shear viscosity to entropy density ratio. This new solution is constructed by considering the conformal map between Minkowski space and the direct product of three-dimensional de Sitter space with a line. The resulting solution respects S O (3 )q⊗S O (1 ,1 )⊗Z2 symmetry. We compare the exact kinetic solution with exact solutions of the corresponding macroscopic equations that were obtained from the kinetic theory in ideal and second-order viscous hydrodynamic approximations. The macroscopic solutions are obtained in de Sitter space and are subject to the same symmetries used to obtain the exact kinetic solution.

Computing row and column counts for sparse QR and LU factorization

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

Gilbert, John R.; Li, Xiaoye S.; Ng, Esmond G.

2001-01-01

We present algorithms to determine the number of nonzeros in each row and column of the factors of a sparse matrix, for both the QR factorization and the LU factorization with partial pivoting. The algorithms use only the nonzero structure of the input matrix, and run in time nearly linear in the number of nonzeros in that matrix. They may be used to set up data structures or schedule parallel operations in advance of the numerical factorization. The row and column counts we compute are upper bounds on the actual counts. If the input matrix is strong Hall and theremore » is no coincidental numerical cancellation, the counts are exact for QR factorization and are the tightest bounds possible for LU factorization. These algorithms are based on our earlier work on computing row and column counts for sparse Cholesky factorization, plus an efficient method to compute the column elimination tree of a sparse matrix without explicitly forming the product of the matrix and its transpose.« less

Exact-Output Tracking Theory for Systems with Parameter Jumps

NASA Technical Reports Server (NTRS)

Devasia, Santosh; Paden, Brad; Rossi, Carlo

1996-01-01

In this paper we consider the exact output tracking problem for systems with parameter jumps. Necessary and sufficient conditions are derived for the elimination of switching-introduced output transient. Previous works have studied this problem by developing a regulator that maintains exact tracking through parameter jumps (switches). Such techniques are, however, only applicable to minimum-phase systems. In contrast, our approach is applicable to nonminimum-phase systems and obtains bounded but possibly non-causal solutions. If the reference trajectories are generated by an exo-system, then we develop an exact-tracking controller in a feedback form. As in standard regulator theory, we obtain a linear map from the states of the exo-system to the desired system state which is defined via a matrix differential equation. The constant solution of this differential equation provides asymptotic tracking, and coincides with the feedback law used in standard regulator theory. The obtained results are applied to a simple flexible manipulator with jumps in the pay-load mass.

Exact-Output Tracking Theory for Systems with Parameter Jumps

NASA Technical Reports Server (NTRS)

Devasia, Santosh; Paden, Brad; Rossi, Carlo

1997-01-01

We consider the exact output tracking problem for systems with parameter jumps. Necessary and sufficient conditions are derived for the elimination of switching-introduced output transient. Previous works have studied this problem by developing a regulator that maintains exact tracking through parameter jumps (switches). Such techniques are, however, only applicable to minimum-phase systems. In contrast, our approach is applicable to non-minimum-phase systems and it obtains bounded but possibly non-causal solutions. If the reference trajectories are generated by an exosystem, then we develop an exact-tracking controller in a feed-back form. As in standard regulator theory, we obtain a linear map from the states of the exosystem to the desired system state which is defined via a matrix differential equation. The constant solution of this differential equation provides asymptotic tracking, and coincides with the feedback law used in standard regulator theory. The obtained results are applied to a simple flexible manipulator with jumps in the pay-load mass.

Density-dependent resistance of the gypsy moth, Lymantria dispar, to its nucleopolyhedrovirus

Treesearch

James R. Reilly; Ann E. Hajek

2007-01-01

The processes controlling disease resistance can strongly influence the population dynamics of insect outbreaks. Evidence that disease resistance is density-dependent is accumulating, but the exact form of this relationship is highly variable from species to species.

Cross-section fluctuations in chaotic scattering systems.

PubMed

Ericson, Torleif E O; Dietz, Barbara; Richter, Achim

2016-10-01

Exact analytical expressions for the cross-section correlation functions of chaotic scattering systems have hitherto been derived only under special conditions. The objective of the present article is to provide expressions that are applicable beyond these restrictions. The derivation is based on a statistical model of Breit-Wigner type for chaotic scattering amplitudes which has been shown to describe the exact analytical results for the scattering (S)-matrix correlation functions accurately. Our results are given in the energy and in the time representations and apply in the whole range from isolated to overlapping resonances. The S-matrix contributions to the cross-section correlations are obtained in terms of explicit irreducible and reducible correlation functions. Consequently, the model can be used for a detailed exploration of the key features of the cross-section correlations and the underlying physical mechanisms. In the region of isolated resonances, the cross-section correlations contain a dominant contribution from the self-correlation term. For narrow states the self-correlations originate predominantly from widely spaced states with exceptionally large partial width. In the asymptotic region of well-overlapping resonances, the cross-section autocorrelation functions are given in terms of the S-matrix autocorrelation functions. For inelastic correlations, in particular, the Ericson fluctuations rapidly dominate in that region. Agreement with known analytical and experimental results is excellent.

Exact solution of corner-modified banded block-Toeplitz eigensystems

NASA Astrophysics Data System (ADS)

Cobanera, Emilio; Alase, Abhijeet; Ortiz, Gerardo; Viola, Lorenza

2017-05-01

Motivated by the challenge of seeking a rigorous foundation for the bulk-boundary correspondence for free fermions, we introduce an algorithm for determining exactly the spectrum and a generalized-eigenvector basis of a class of banded block quasi-Toeplitz matrices that we call corner-modified. Corner modifications of otherwise arbitrary banded block-Toeplitz matrices capture the effect of boundary conditions and the associated breakdown of translational invariance. Our algorithm leverages the interplay between a non-standard, projector-based method of kernel determination (physically, a bulk-boundary separation) and families of linear representations of the algebra of matrix Laurent polynomials. Thanks to the fact that these representations act on infinite-dimensional carrier spaces in which translation symmetry is restored, it becomes possible to determine the eigensystem of an auxiliary projected block-Laurent matrix. This results in an analytic eigenvector Ansatz, independent of the system size, which we prove is guaranteed to contain the full solution of the original finite-dimensional problem. The actual solution is then obtained by imposing compatibility with a boundary matrix, whose shape is also independent of system size. As an application, we show analytically that eigenvectors of short-ranged fermionic tight-binding models may display power-law corrections to exponential behavior, and demonstrate the phenomenon for the paradigmatic Majorana chain of Kitaev.

Nonlinear equation of the modes in circular slab waveguides and its application.

PubMed

Zhu, Jianxin; Zheng, Jia

2013-11-20

In this paper, circularly curved inhomogeneous waveguides are transformed into straight inhomogeneous waveguides first by a conformal mapping. Then, the differential transfer matrix method is introduced and adopted to deduce the exact dispersion relation for modes. This relation itself is complex and difficult to solve, but it can be approximated by a simpler nonlinear equation in practical applications, which is close to the exact relation and quite easy to analyze. Afterward, optimized asymptotic solutions are obtained and act as initial guesses for the following Newton's iteration. Finally, very accurate solutions are achieved in the numerical experiment.

Energy and contact of the one-dimensional Fermi polaron at zero and finite temperature.

PubMed

Doggen, E V H; Kinnunen, J J

2013-07-12

We use the T-matrix approach for studying highly polarized homogeneous Fermi gases in one dimension with repulsive or attractive contact interactions. Using this approach, we compute ground state energies and values for the contact parameter that show excellent agreement with exact and other numerical methods at zero temperature, even in the strongly interacting regime. Furthermore, we derive an exact expression for the value of the contact parameter in one dimension at zero temperature. The model is then extended and used for studying the temperature dependence of ground state energies and the contact parameter.

A Riemann solver for RANS

NASA Astrophysics Data System (ADS)

Chuvakhov, P. V.

2014-01-01

An exact expression for a system of both eigenvalues and right/left eigenvectors of a Jacobian matrix for a convective two-equation differential closure RANS operator split along a curvilinear coordinate is derived. It is shown by examples of numerical modeling of supersonic flows over a flat plate and a compression corner with separation that application of the exact system of eigenvalues and eigenvectors to the Roe approach for approximate solution of the Riemann problem gives rise to an increase in the convergence rate, better stability and higher accuracy of a steady-state solution in comparison with those in the case of an approximate system.

Effects of absorption on multiple scattering by random particulate media: exact results.

PubMed

Mishchenko, Michael I; Liu, Li; Hovenier, Joop W

2007-10-01

We employ the numerically exact superposition T-matrix method to perform extensive computations of elec nottromagnetic scattering by a volume of discrete random medium densely filled with increasingly absorbing as well as non-absorbing particles. Our numerical data demonstrate that increasing absorption diminishes and nearly extinguishes certain optical effects such as depolarization and coherent backscattering and increases the angular width of coherent backscattering patterns. This result corroborates the multiple-scattering origin of such effects and further demonstrates the heuristic value of the concept of multiple scattering even in application to densely packed particulate media.

Numerical Solution of the Electron Transport Equation in the Upper Atmosphere

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

Woods, Mark Christopher; Holmes, Mark; Sailor, William C

A new approach for solving the electron transport equation in the upper atmosphere is derived. The problem is a very stiff boundary value problem, and to obtain an accurate numerical solution, matrix factorizations are used to decouple the fast and slow modes. A stable finite difference method is applied to each mode. This solver is applied to a simplifieed problem for which an exact solution exists using various versions of the boundary conditions that might arise in a natural auroral display. The numerical and exact solutions are found to agree with each other to at least two significant digits.

Open Heisenberg chain under boundary fields: A magnonic logic gate

NASA Astrophysics Data System (ADS)

Landi, Gabriel T.; Karevski, Dragi

2015-05-01

We study the spin transport in the quantum Heisenberg spin chain subject to boundary magnetic fields and driven out of equilibrium by Lindblad dissipators. An exact solution is given in terms of matrix product states, which allows us to calculate exactly the spin current for any chain size. It is found that the system undergoes a discontinuous spin-valve-like quantum phase transition from ballistic to subdiffusive spin current, depending on the value of the boundary fields. Thus, the chain behaves as an extremely sensitive magnonic logic gate operating with the boundary fields as the base element.

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.

Multispecies reaction-diffusion systems

NASA Astrophysics Data System (ADS)

Aghamohammadi, A.; Fatollahi, A. H.; Khorrami, M.; Shariati, A.

2000-10-01

Multispecies reaction-diffusion systems, for which the time evolution equations of correlation functions become a closed set, are considered. A formal solution for the average densities is found. Some special interactions and the exact time dependence of the average densities in these cases are also studied. For the general case, the large-time behavior of the average densities has also been obtained.

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

Singleton, Jr., Robert; Israel, Daniel M.; Doebling, Scott William

For code verification, one compares the code output against known exact solutions. There are many standard test problems used in this capacity, such as the Noh and Sedov problems. ExactPack is a utility that integrates many of these exact solution codes into a common API (application program interface), and can be used as a stand-alone code or as a python package. ExactPack consists of python driver scripts that access a library of exact solutions written in Fortran or Python. The spatial profiles of the relevant physical quantities, such as the density, fluid velocity, sound speed, or internal energy, are returnedmore » at a time specified by the user. The solution profiles can be viewed and examined by a command line interface or a graphical user interface, and a number of analysis tools and unit tests are also provided. We have documented the physics of each problem in the solution library, and provided complete documentation on how to extend the library to include additional exact solutions. ExactPack’s code architecture makes it easy to extend the solution-code library to include additional exact solutions in a robust, reliable, and maintainable manner.« less

Quantum Engineering of Dynamical Gauge Fields on Optical Lattices

DTIC Science & Technology

2016-07-08

exact blocking formulas from the TRG formulation of the transfer matrix. The second is a worm algorithm. The particle number distributions obtained...a fact that can be explained by an approximate particle- hole symmetry. We have also developed a computer code suite for simulating the Abelian

Charge transfer excitations from exact and approximate ensemble Kohn-Sham theory

NASA Astrophysics Data System (ADS)

Gould, Tim; Kronik, Leeor; Pittalis, Stefano

2018-05-01

By studying the lowest excitations of an exactly solvable one-dimensional soft-Coulomb molecular model, we show that components of Kohn-Sham ensembles can be used to describe charge transfer processes. Furthermore, we compute the approximate excitation energies obtained by using the exact ensemble densities in the recently formulated ensemble Hartree-exchange theory [T. Gould and S. Pittalis, Phys. Rev. Lett. 119, 243001 (2017)]. Remarkably, our results show that triplet excitations are accurately reproduced across a dissociation curve in all cases tested, even in systems where ground state energies are poor due to strong static correlations. Singlet excitations exhibit larger deviations from exact results but are still reproduced semi-quantitatively.

Exact solution for the hydrogen atom confined by a dielectric continuum and the correct basis set to study many-electron atoms under similar confinements

NASA Astrophysics Data System (ADS)

Martínez-Sánchez, Michael-Adán; Aquino, Norberto; Vargas, Rubicelia; Garza, Jorge

2017-12-01

The Schrödinger equation associated to the hydrogen atom confined by a dielectric continuum is solved exactly and suggests the appropriate basis set to be used when an atom is immersed in a dielectric continuum. Exact results show that this kind of confinement spread the electron density, which is confirmed through the Shannon entropy. The basis set suggested by the exact results is similar to Slater type orbitals and it was applied on two-electron atoms, where the H- ion ejects one electron for moderate confinements for distances much larger than those commonly used to generate cavities in solvent models.

Comparison of Effective Medium Schemes For Seismic Velocities in Cracked Anisotropic Rock

NASA Astrophysics Data System (ADS)

Morshed, S.; Chesnokov, E.

2017-12-01

Understanding of elastic properties of reservoir rock is necessary for meaningful interpretation and analysis of seismic measurements. The elastic properties of a rock are controlled by the microstructural properties such as mineralogical composition, pore and crack distribution, texture and pore connectivity. However, seismic scale is much larger than microstructure scale. Understanding of macroscopic properties at relevant seismic scale (e.g. borehole sonic data) comes from effective medium theory (EMT). However, most of the effective medium theories fail at high crack density as the interactions of strain fields of the cracks can't be ignored. We compare major EMT schemes from low to high crack density. While at low crack density all method gives similar results, at high crack density they differ significantly. Then, we focus on generalized singular approximation (GSA) and effective field (EF) method as they allow cracks beyond the limit of dilute concentrations. Additionally, we use grain contact (GC) method to examine the stiffness constants of the rock matrix. We prepare simple models of a multiphase media containing low to high concentrations of isolated pores. Randomly oriented spherical pores and horizontally oriented ellipsoidal (aspect ratio =0.1) pores have been considered. For isolated spherical pores, all the three methods show exactly same or similar results. However, inclusion interactions are different in different directions in case of horizontal ellipsoidal pores and individual stiffness constants differ greatly from one method to another at different crack density. Stiffness constants remain consistent in GSA method whereas some components become unusual in EF method at a higher crack density (>0.15). Finally, we applied GSA method to interpret ultrasonic velocities of core samples. Mineralogical composition from X-ray diffraction (XRD) data and lab measured porosity data have been utilized. Both compressional and shear wave velocities from GSA method show good fit with the lab measured velocities.

Kohn-Sham approach to quantum electrodynamical density-functional theory: Exact time-dependent effective potentials in real space.

PubMed

Flick, Johannes; Ruggenthaler, Michael; Appel, Heiko; Rubio, Angel

2015-12-15

The density-functional approach to quantum electrodynamics extends traditional density-functional theory and opens the possibility to describe electron-photon interactions in terms of effective Kohn-Sham potentials. In this work, we numerically construct the exact electron-photon Kohn-Sham potentials for a prototype system that consists of a trapped electron coupled to a quantized electromagnetic mode in an optical high-Q cavity. Although the effective current that acts on the photons is known explicitly, the exact effective potential that describes the forces exerted by the photons on the electrons is obtained from a fixed-point inversion scheme. This procedure allows us to uncover important beyond-mean-field features of the effective potential that mark the breakdown of classical light-matter interactions. We observe peak and step structures in the effective potentials, which can be attributed solely to the quantum nature of light; i.e., they are real-space signatures of the photons. Our findings show how the ubiquitous dipole interaction with a classical electromagnetic field has to be modified in real space to take the quantum nature of the electromagnetic field fully into account.

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.

Exact statistical results for binary mixing and reaction in variable density turbulence

NASA Astrophysics Data System (ADS)

Ristorcelli, J. R.

2017-02-01

We report a number of rigorous statistical results on binary active scalar mixing in variable density turbulence. The study is motivated by mixing between pure fluids with very different densities and whose density intensity is of order unity. Our primary focus is the derivation of exact mathematical results for mixing in variable density turbulence and we do point out the potential fields of application of the results. A binary one step reaction is invoked to derive a metric to asses the state of mixing. The mean reaction rate in variable density turbulent mixing can be expressed, in closed form, using the first order Favre mean variables and the Reynolds averaged density variance, ⟨ρ2⟩ . We show that the normalized density variance, ⟨ρ2⟩ , reflects the reduction of the reaction due to mixing and is a mix metric. The result is mathematically rigorous. The result is the variable density analog, the normalized mass fraction variance ⟨c2⟩ used in constant density turbulent mixing. As a consequence, we demonstrate that use of the analogous normalized Favre variance of the mass fraction, c″ ⁣2˜ , as a mix metric is not theoretically justified in variable density turbulence. We additionally derive expressions relating various second order moments of the mass fraction, specific volume, and density fields. The central role of the density specific volume covariance ⟨ρ v ⟩ is highlighted; it is a key quantity with considerable dynamical significance linking various second order statistics. For laboratory experiments, we have developed exact relations between the Reynolds scalar variance ⟨c2⟩ its Favre analog c″ ⁣2˜ , and various second moments including ⟨ρ v ⟩ . For moment closure models that evolve ⟨ρ v ⟩ and not ⟨ρ2⟩ , we provide a novel expression for ⟨ρ2⟩ in terms of a rational function of ⟨ρ v ⟩ that avoids recourse to Taylor series methods (which do not converge for large density differences). We have derived analytic results relating several other second and third order moments and see coupling between odd and even order moments demonstrating a natural and inherent skewness in the mixing in variable density turbulence. The analytic results have applications in the areas of isothermal material mixing, isobaric thermal mixing, and simple chemical reaction (in progress variable formulation).

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

Inertially Stabilized Platforms for SATCOM On-The-Move Applications: A Hybrid Open/Closed-Loop Antenna Pointing Strategy

DTIC Science & Technology

2008-06-01

Photo courtesy of www.mathworks.com. Next, Equation (3.16) translates the aircraft disturbance rates through the de - sired local azimuth and elevation...Hessian matrix of the assumed quadratic cost function [34–36]. Equation (4.11) exactly de - termines the minimum of a quadratic function in a single...according to: Bkpk = −gk (4.21) Bk+1 = Bk +Qk (4.22) where Bk in some way approximates Gk from (4.12), and Qk is an update matrix de - pendent upon xk

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.

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

Simplified equation for Young's modulus of CNT reinforced concrete

NASA Astrophysics Data System (ADS)

Chandran, RameshBabu; Gifty Honeyta A, Maria

2017-12-01

This research investigation focuses on finite element modeling of carbon nanotube (CNT) reinforced concrete matrix for three grades of concrete namely M40, M60 and M120. Representative volume element (RVE) was adopted and one-eighth model depicting the CNT reinforced concrete matrix was simulated using FEA software ANSYS17.2. Adopting random orientation of CNTs, with nine fibre volume fractions from 0.1% to 0.9%, finite element modeling simulations replicated exactly the CNT reinforced concrete matrix. Upon evaluations of the model, the longitudinal and transverse Young's modulus of elasticity of the CNT reinforced concrete was arrived. The graphical plots between various fibre volume fractions and the concrete grade revealed simplified equation for estimating the young's modulus. It also exploited the fact that the concrete grade does not have significant impact in CNT reinforced concrete matrix.

Performance analysis of structured gradient algorithm. [for adaptive beamforming linear arrays

NASA Technical Reports Server (NTRS)

Godara, Lal C.

1990-01-01

The structured gradient algorithm uses a structured estimate of the array correlation matrix (ACM) to estimate the gradient required for the constrained least-mean-square (LMS) algorithm. This structure reflects the structure of the exact array correlation matrix for an equispaced linear array and is obtained by spatial averaging of the elements of the noisy correlation matrix. In its standard form the LMS algorithm does not exploit the structure of the array correlation matrix. The gradient is estimated by multiplying the array output with the receiver outputs. An analysis of the two algorithms is presented to show that the covariance of the gradient estimated by the structured method is less sensitive to the look direction signal than that estimated by the standard method. The effect of the number of elements on the signal sensitivity of the two algorithms is studied.

Inference for multivariate regression model based on multiply imputed synthetic data generated via posterior predictive sampling

NASA Astrophysics Data System (ADS)

Moura, Ricardo; Sinha, Bimal; Coelho, Carlos A.

2017-06-01

The recent popularity of the use of synthetic data as a Statistical Disclosure Control technique has enabled the development of several methods of generating and analyzing such data, but almost always relying in asymptotic distributions and in consequence being not adequate for small sample datasets. Thus, a likelihood-based exact inference procedure is derived for the matrix of regression coefficients of the multivariate regression model, for multiply imputed synthetic data generated via Posterior Predictive Sampling. Since it is based in exact distributions this procedure may even be used in small sample datasets. Simulation studies compare the results obtained from the proposed exact inferential procedure with the results obtained from an adaptation of Reiters combination rule to multiply imputed synthetic datasets and an application to the 2000 Current Population Survey is discussed.

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

Practical implementation of tetrahedral mesh reconstruction in emission tomography

PubMed Central

Boutchko, R.; Sitek, A.; Gullberg, G. T.

2014-01-01

This paper presents a practical implementation of image reconstruction on tetrahedral meshes optimized for emission computed tomography with parallel beam geometry. Tetrahedral mesh built on a point cloud is a convenient image representation method, intrinsically three-dimensional and with a multi-level resolution property. Image intensities are defined at the mesh nodes and linearly interpolated inside each tetrahedron. For the given mesh geometry, the intensities can be computed directly from tomographic projections using iterative reconstruction algorithms with a system matrix calculated using an exact analytical formula. The mesh geometry is optimized for a specific patient using a two stage process. First, a noisy image is reconstructed on a finely-spaced uniform cloud. Then, the geometry of the representation is adaptively transformed through boundary-preserving node motion and elimination. Nodes are removed in constant intensity regions, merged along the boundaries, and moved in the direction of the mean local intensity gradient in order to provide higher node density in the boundary regions. Attenuation correction and detector geometric response are included in the system matrix. Once the mesh geometry is optimized, it is used to generate the final system matrix for ML-EM reconstruction of node intensities and for visualization of the reconstructed images. In dynamic PET or SPECT imaging, the system matrix generation procedure is performed using a quasi-static sinogram, generated by summing projection data from multiple time frames. This system matrix is then used to reconstruct the individual time frame projections. Performance of the new method is evaluated by reconstructing simulated projections of the NCAT phantom and the method is then applied to dynamic SPECT phantom and patient studies and to a dynamic microPET rat study. Tetrahedral mesh-based images are compared to the standard voxel-based reconstruction for both high and low signal-to-noise ratio projection datasets. The results demonstrate that the reconstructed images represented as tetrahedral meshes based on point clouds offer image quality comparable to that achievable using a standard voxel grid while allowing substantial reduction in the number of unknown intensities to be reconstructed and reducing the noise. PMID:23588373

Practical implementation of tetrahedral mesh reconstruction in emission tomography

NASA Astrophysics Data System (ADS)

Boutchko, R.; Sitek, A.; Gullberg, G. T.

2013-05-01

This paper presents a practical implementation of image reconstruction on tetrahedral meshes optimized for emission computed tomography with parallel beam geometry. Tetrahedral mesh built on a point cloud is a convenient image representation method, intrinsically three-dimensional and with a multi-level resolution property. Image intensities are defined at the mesh nodes and linearly interpolated inside each tetrahedron. For the given mesh geometry, the intensities can be computed directly from tomographic projections using iterative reconstruction algorithms with a system matrix calculated using an exact analytical formula. The mesh geometry is optimized for a specific patient using a two stage process. First, a noisy image is reconstructed on a finely-spaced uniform cloud. Then, the geometry of the representation is adaptively transformed through boundary-preserving node motion and elimination. Nodes are removed in constant intensity regions, merged along the boundaries, and moved in the direction of the mean local intensity gradient in order to provide higher node density in the boundary regions. Attenuation correction and detector geometric response are included in the system matrix. Once the mesh geometry is optimized, it is used to generate the final system matrix for ML-EM reconstruction of node intensities and for visualization of the reconstructed images. In dynamic PET or SPECT imaging, the system matrix generation procedure is performed using a quasi-static sinogram, generated by summing projection data from multiple time frames. This system matrix is then used to reconstruct the individual time frame projections. Performance of the new method is evaluated by reconstructing simulated projections of the NCAT phantom and the method is then applied to dynamic SPECT phantom and patient studies and to a dynamic microPET rat study. Tetrahedral mesh-based images are compared to the standard voxel-based reconstruction for both high and low signal-to-noise ratio projection datasets. The results demonstrate that the reconstructed images represented as tetrahedral meshes based on point clouds offer image quality comparable to that achievable using a standard voxel grid while allowing substantial reduction in the number of unknown intensities to be reconstructed and reducing the noise.

A proposed method for enhanced eigen-pair extraction using finite element methods: Theory and application

NASA Technical Reports Server (NTRS)

Jara-Almonte, J.; Mitchell, L. D.

1988-01-01

The paper covers two distinct parts: theory and application. The goal of this work was the reduction of model size with an increase in eigenvalue/vector accuracy. This method is ideal for the condensation of large truss- or beam-type structures. The theoretical approach involves the conversion of a continuum transfer matrix beam element into an 'Exact' dynamic stiffness element. This formulation is implemented in a finite element environment. This results in the need to solve a transcendental eigenvalue problem. Once the eigenvalue is determined the eigenvectors can be reconstructed with any desired spatial precision. No discretization limitations are imposed on the reconstruction. The results of such a combined finite element and transfer matrix formulation is a much smaller FEM eigenvalue problem. This formulation has the ability to extract higher eigenvalues as easily and as accurately as lower eigenvalues. Moreover, one can extract many more eigenvalues/vectors from the model than the number of degrees of freedom in the FEM formulation. Typically, the number of eigenvalues accurately extractable via the 'Exact' element method are at least 8 times the number of degrees of freedom. In contrast, the FEM usually extracts one accurate (within 5 percent) eigenvalue for each 3-4 degrees of freedom. The 'Exact' element results in a 20-30 improvement in the number of accurately extractable eigenvalues and eigenvectors.

Exact Solutions for Wind-Driven Coastal Upwelling and Downwelling over Sloping Topography

NASA Astrophysics Data System (ADS)

Choboter, P.; Duke, D.; Horton, J.; Sinz, P.

2009-12-01

The dynamics of wind-driven coastal upwelling and downwelling are studied using a simplified dynamical model. Exact solutions are examined as a function of time and over a family of sloping topographies. Assumptions in the two-dimensional model include a frictionless ocean interior below the surface Ekman layer, and no alongshore dependence of the variables; however, dependence in the cross-shore and vertical directions is retained. Additionally, density and alongshore momentum are advected by the cross-shore velocity in order to maintain thermal wind. The time-dependent initial-value problem is solved with constant initial stratification and no initial alongshore flow. An alongshore pressure gradient is added to allow the cross-shore flow to be geostrophically balanced far from shore. Previously, this model has been used to study upwelling over flat-bottom and sloping topographies, but the novel feature in this work is the discovery of exact solutions for downwelling. These exact solutions are compared to numerical solutions from a primitive-equation ocean model, based on the Princeton Ocean Model, configured in a similar two-dimensional geometry. Many typical features of the evolution of density and velocity during downwelling are displayed by the analytical model.

Explorations in fuzzy physics and non-commutative geometry

NASA Astrophysics Data System (ADS)

Kurkcuoglu, Seckin

Fuzzy spaces arise as discrete approximations to continuum manifolds. They are usually obtained through quantizing coadjoint orbits of compact Lie groups and they can be described in terms of finite-dimensional matrix algebras, which for large matrix sizes approximate the algebra of functions of the limiting continuum manifold. Their ability to exactly preserve the symmetries of their parent manifolds is especially appealing for physical applications. Quantum Field Theories are built over them as finite-dimensional matrix models preserving almost all the symmetries of their respective continuum models. In this dissertation, we first focus our attention to the study of fuzzy supersymmetric spaces. In this regard, we obtain the fuzzy supersphere S2,2F through quantizing the supersphere, and demonstrate that it has exact supersymmetry. We derive a finite series formula for the *-product of functions over S2,2F and analyze the differential geometric information encoded in this formula. Subsequently, we show that quantum field theories on S2,2F are realized as finite-dimensional supermatrix models, and in particular we obtain the non-linear sigma model over the fuzzy supersphere by constructing the fuzzy supersymmetric extensions of a certain class of projectors. We show that this model too, is realized as a finite-dimensional supermatrix model with exact supersymmetry. Next, we show that fuzzy spaces have a generalized Hopf algebra structure. By focusing on the fuzzy sphere, we establish that there is a *-homomorphism from the group algebra SU(2)* of SU(2) to the fuzzy sphere. Using this and the canonical Hopf algebra structure of SU(2)* we show that both the fuzzy sphere and their direct sum are Hopf algebras. Using these results, we discuss processes in which a fuzzy sphere with angular momenta J splits into fuzzy spheres with angular momenta K and L. Finally, we study the formulation of Chern-Simons (CS) theory on an infinite strip of the non-commutative plane. We develop a finite-dimensional matrix model, whose large size limit approximates the CS theory on the infinite strip, and show that there are edge observables in this model obeying a finite-dimensional Lie algebra, that resembles the Kac-Moody algebra.

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

Curchod, Basile F. E.; Agostini, Federica, E-mail: agostini@mpi-halle.mpg.de; Gross, E. K. U.

Nonadiabatic quantum interferences emerge whenever nuclear wavefunctions in different electronic states meet and interact in a nonadiabatic region. In this work, we analyze how nonadiabatic quantum interferences translate in the context of the exact factorization of the molecular wavefunction. In particular, we focus our attention on the shape of the time-dependent potential energy surface—the exact surface on which the nuclear dynamics takes place. We use a one-dimensional exactly solvable model to reproduce different conditions for quantum interferences, whose characteristic features already appear in one-dimension. The time-dependent potential energy surface develops complex features when strong interferences are present, in clear contrastmore » to the observed behavior in simple nonadiabatic crossing cases. Nevertheless, independent classical trajectories propagated on the exact time-dependent potential energy surface reasonably conserve a distribution in configuration space that mimics one of the exact nuclear probability densities.« less

Approximations to the exact exchange potential: KLI versus semilocal

NASA Astrophysics Data System (ADS)

Tran, Fabien; Blaha, Peter; Betzinger, Markus; Blügel, Stefan

2016-10-01

In the search for an accurate and computationally efficient approximation to the exact exchange potential of Kohn-Sham density functional theory, we recently compared various semilocal exchange potentials to the exact one [F. Tran et al., Phys. Rev. B 91, 165121 (2015), 10.1103/PhysRevB.91.165121]. It was concluded that the Becke-Johnson (BJ) potential is a very good starting point, but requires the use of empirical parameters to obtain good agreement with the exact exchange potential. In this work, we extend the comparison by considering the Krieger-Li-Iafrate (KLI) approximation, which is a beyond-semilocal approximation. It is shown that overall the KLI- and BJ-based potentials are the most reliable approximations to the exact exchange potential, however, sizable differences, especially for the antiferromagnetic transition-metal oxides, can be obtained.

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…

Modeling L2,3-Edge X-ray Absorption Spectroscopy with Real-Time Exact Two-Component Relativistic Time-Dependent Density Functional Theory.

PubMed

Kasper, Joseph M; Lestrange, Patrick J; Stetina, Torin F; Li, Xiaosong

2018-04-10

X-ray absorption spectroscopy is a powerful technique to probe local electronic and nuclear structure. There has been extensive theoretical work modeling K-edge spectra from first principles. However, modeling L-edge spectra directly with density functional theory poses a unique challenge requiring further study. Spin-orbit coupling must be included in the model, and a noncollinear density functional theory is required. Using the real-time exact two-component method, we are able to variationally include one-electron spin-orbit coupling terms when calculating the absorption spectrum. The abilities of different basis sets and density functionals to model spectra for both closed- and open-shell systems are investigated using SiCl 4 and three transition metal complexes, TiCl 4 , CrO 2 Cl 2 , and [FeCl 6 ] 3- . Although we are working in the real-time framework, individual molecular orbital transitions can still be recovered by projecting the density onto the ground state molecular orbital space and separating contributions to the time evolving dipole moment.

In vitro development of preimplantation porcine embryos using alginate hydrogels as a three-dimensional extracellular matrix

USDA-ARS?s Scientific Manuscript database

Between day 10 and 12 of gestation, porcine embryos undergo a dramatic morphological change, known as elongation, with a corresponding increase in estrogen production for maternal recognition of pregnancy. Elongation deficiencies contribute to ~20% of embryonic loss, but exact mechanisms of elongati...

Spin-locking of half-integer quadrupolar nuclei in NMR of solids: The far off-resonance case.

PubMed

Odedra, Smita; Wimperis, Stephen

Spin-locking of spin I=3/2 and I=5/2 nuclei in the presence of large resonance offsets has been studied using both approximate and exact theoretical approaches and, in the case of I=3/2, experimentally. We show the variety of coherences and population states produced in a far off-resonance spin-locking NMR experiment (one consisting solely of a spin-locking pulse) and how these vary with the radiofrequency field strength and offset frequency. Under magic angle spinning (MAS) conditions and in the "adiabatic limit", these spin-locked states acquire a time dependence. We discuss the rotor-driven interconversion of the spin-locked states, using an exact density matrix approach to confirm the results of the approximate model. Using conventional and multiple-quantum filtered spin-locking 23 Na (I=3/2) NMR experiments under both static and MAS conditions, we confirm the results of the theoretical calculations, demonstrating the applicability of the approximate theoretical model to the far off-resonance case. This simplified model includes only the effects of the initial rapid dephasing of coherences that occurs at the start of the spin-locking period and its success in reproducing both experimental and exact simulation data indicates that it is this dephasing that is the dominant phenomenon in NMR spin-locking of quadrupolar nuclei, as we have previously found for the on-resonance and near-resonance cases. Potentially, far off-resonance spin-locking of quadrupolar nuclei could be of interest in experiments such as cross polarisation as a consequence of the spin-locking pulse being applied to a better defined initial state (the thermal equilibrium bulk magnetisation aligned along the z-axis) than can be created in a powdered solid with a selective radiofrequency pulse, where the effect of the pulse depends on the orientation of the individual crystallites. Copyright © 2016 Elsevier Inc. All rights reserved.

Excitation energies from particle-particle random phase approximation with accurate optimized effective potentials

NASA Astrophysics Data System (ADS)

Jin, Ye; Yang, Yang; Zhang, Du; Peng, Degao; Yang, Weitao

2017-10-01

The optimized effective potential (OEP) that gives accurate Kohn-Sham (KS) orbitals and orbital energies can be obtained from a given reference electron density. These OEP-KS orbitals and orbital energies are used here for calculating electronic excited states with the particle-particle random phase approximation (pp-RPA). Our calculations allow the examination of pp-RPA excitation energies with the exact KS density functional theory (DFT). Various input densities are investigated. Specifically, the excitation energies using the OEP with the electron densities from the coupled-cluster singles and doubles method display the lowest mean absolute error from the reference data for the low-lying excited states. This study probes into the theoretical limit of the pp-RPA excitation energies with the exact KS-DFT orbitals and orbital energies. We believe that higher-order correlation contributions beyond the pp-RPA bare Coulomb kernel are needed in order to achieve even higher accuracy in excitation energy calculations.

Size-dependent error of the density functional theory ionization potential in vacuum and solution

DOE PAGES

Sosa Vazquez, Xochitl A.; Isborn, Christine M.

2015-12-22

Density functional theory is often the method of choice for modeling the energetics of large molecules and including explicit solvation effects. It is preferable to use a method that treats systems of different sizes and with different amounts of explicit solvent on equal footing. However, recent work suggests that approximate density functional theory has a size-dependent error in the computation of the ionization potential. We here investigate the lack of size-intensivity of the ionization potential computed with approximate density functionals in vacuum and solution. We show that local and semi-local approximations to exchange do not yield a constant ionization potentialmore » for an increasing number of identical isolated molecules in vacuum. Instead, as the number of molecules increases, the total energy required to ionize the system decreases. Rather surprisingly, we find that this is still the case in solution, whether using a polarizable continuum model or with explicit solvent that breaks the degeneracy of each solute, and we find that explicit solvent in the calculation can exacerbate the size-dependent delocalization error. We demonstrate that increasing the amount of exact exchange changes the character of the polarization of the solvent molecules; for small amounts of exact exchange the solvent molecules contribute a fraction of their electron density to the ionized electron, but for larger amounts of exact exchange they properly polarize in response to the cationic solute. As a result, in vacuum and explicit solvent, the ionization potential can be made size-intensive by optimally tuning a long-range corrected hybrid functional.« less

Size-dependent error of the density functional theory ionization potential in vacuum and solution

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

Sosa Vazquez, Xochitl A.; Isborn, Christine M., E-mail: cisborn@ucmerced.edu

2015-12-28

Density functional theory is often the method of choice for modeling the energetics of large molecules and including explicit solvation effects. It is preferable to use a method that treats systems of different sizes and with different amounts of explicit solvent on equal footing. However, recent work suggests that approximate density functional theory has a size-dependent error in the computation of the ionization potential. We here investigate the lack of size-intensivity of the ionization potential computed with approximate density functionals in vacuum and solution. We show that local and semi-local approximations to exchange do not yield a constant ionization potentialmore » for an increasing number of identical isolated molecules in vacuum. Instead, as the number of molecules increases, the total energy required to ionize the system decreases. Rather surprisingly, we find that this is still the case in solution, whether using a polarizable continuum model or with explicit solvent that breaks the degeneracy of each solute, and we find that explicit solvent in the calculation can exacerbate the size-dependent delocalization error. We demonstrate that increasing the amount of exact exchange changes the character of the polarization of the solvent molecules; for small amounts of exact exchange the solvent molecules contribute a fraction of their electron density to the ionized electron, but for larger amounts of exact exchange they properly polarize in response to the cationic solute. In vacuum and explicit solvent, the ionization potential can be made size-intensive by optimally tuning a long-range corrected hybrid functional.« less

Matrix product operators, matrix product states, and ab initio density matrix renormalization group algorithms

NASA Astrophysics Data System (ADS)

Chan, Garnet Kin-Lic; Keselman, Anna; Nakatani, Naoki; Li, Zhendong; White, Steven R.

2016-07-01

Current descriptions of the ab initio density matrix renormalization group (DMRG) algorithm use two superficially different languages: an older language of the renormalization group and renormalized operators, and a more recent language of matrix product states and matrix product operators. The same algorithm can appear dramatically different when written in the two different vocabularies. In this work, we carefully describe the translation between the two languages in several contexts. First, we describe how to efficiently implement the ab initio DMRG sweep using a matrix product operator based code, and the equivalence to the original renormalized operator implementation. Next we describe how to implement the general matrix product operator/matrix product state algebra within a pure renormalized operator-based DMRG code. Finally, we discuss two improvements of the ab initio DMRG sweep algorithm motivated by matrix product operator language: Hamiltonian compression, and a sum over operators representation that allows for perfect computational parallelism. The connections and correspondences described here serve to link the future developments with the past and are important in the efficient implementation of continuing advances in ab initio DMRG and related algorithms.

Matrix product operators, matrix product states, and ab initio density matrix renormalization group algorithms.

PubMed

Chan, Garnet Kin-Lic; Keselman, Anna; Nakatani, Naoki; Li, Zhendong; White, Steven R

2016-07-07

Current descriptions of the ab initio density matrix renormalization group (DMRG) algorithm use two superficially different languages: an older language of the renormalization group and renormalized operators, and a more recent language of matrix product states and matrix product operators. The same algorithm can appear dramatically different when written in the two different vocabularies. In this work, we carefully describe the translation between the two languages in several contexts. First, we describe how to efficiently implement the ab initio DMRG sweep using a matrix product operator based code, and the equivalence to the original renormalized operator implementation. Next we describe how to implement the general matrix product operator/matrix product state algebra within a pure renormalized operator-based DMRG code. Finally, we discuss two improvements of the ab initio DMRG sweep algorithm motivated by matrix product operator language: Hamiltonian compression, and a sum over operators representation that allows for perfect computational parallelism. The connections and correspondences described here serve to link the future developments with the past and are important in the efficient implementation of continuing advances in ab initio DMRG and related algorithms.

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.

The use of an analytic Hamiltonian matrix for solving the hydrogenic atom

NASA Astrophysics Data System (ADS)

Bhatti, Mohammad

2001-10-01

The non-relativistic Hamiltonian corresponding to the Shrodinger equation is converted into analytic Hamiltonian matrix using the kth order B-splines functions. The Galerkin method is applied to the solution of the Shrodinger equation for bound states of hydrogen-like systems. The program Mathematica is used to create analytic matrix elements and exact integration is performed over the knot-sequence of B-splines and the resulting generalized eigenvalue problem is solved on a specified numerical grid. The complete basis set and the energy spectrum is obtained for the coulomb potential for hydrogenic systems with Z less than 100 with B-splines of order eight. Another application is given to test the Thomas-Reiche-Kuhn sum rule for the hydrogenic systems.

A note on the accuracy of KS-DFT densities

NASA Astrophysics Data System (ADS)

Ranasinghe, Duminda S.; Perera, Ajith; Bartlett, Rodney J.

2017-11-01

The accuracy of the density of wave function methods and Kohn-Sham (KS) density functionals is studied using moments of the density, ⟨rn ⟩ =∫ ρ (r )rnd τ =∫0∞4 π r2ρ (r ) rnd r ,where n =-1 ,-2,0,1,2 ,and 3 provides information about the short- and long-range behavior of the density. Coupled cluster (CC) singles, doubles, and perturbative triples (CCSD(T)) is considered as the reference density. Three test sets are considered: boron through neon neutral atoms, two and four electron cations, and 3d transition metals. The total density and valence only density are distinguished by dropping appropriate core orbitals. Among density functionals tested, CAMQTP00 and ωB97x show the least deviation for boron through neon neutral atoms. They also show accurate eigenvalues for the HOMO indicating that they should have a more correct long-range behavior for the density. For transition metals, some density functional approximations outperform some wave function methods, suggesting that the KS determinant could be a better starting point for some kinds of correlated calculations. By using generalized many-body perturbation theory (MBPT), the convergence of second-, third-, and fourth-order KS-MBPT for the density is addressed as it converges to the infinite-order coupled cluster result. For the transition metal test set, the deviations in the KS density functional theory methods depend on the amount of exact exchange the functional uses. Functionals with exact exchange close to 25% show smaller deviations from the CCSD(T) density.

Ground State Resonance Structure of Some Typical High Explosives Calculated by Density Functional Theory

DTIC Science & Technology

2011-03-04

direct relationships between calculated quantities obtained by DFT and the “conveniently measurable” quantities α and rn...VCH Verlag, Weinheim, 2004). [11] A. D. Becke, “Density- funtional Thermochemistry. III. The Role of Exact Exchange”, J. Chem. Phys. 98, 5648-5652

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.

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.

Effective photon mass and exact translating quantum relativistic structures

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

Haas, Fernando, E-mail: fernando.haas@ufrgs.br; Manrique, Marcos Antonio Albarracin, E-mail: sagret10@hotmail.com

2016-04-15

Using a variation of the celebrated Volkov solution, the Klein-Gordon equation for a charged particle is reduced to a set of ordinary differential equations, exactly solvable in specific cases. The new quantum relativistic structures can reveal a localization in the radial direction perpendicular to the wave packet propagation, thanks to a non-vanishing scalar potential. The external electromagnetic field, the particle current density, and the charge density are determined. The stability analysis of the solutions is performed by means of numerical simulations. The results are useful for the description of a charged quantum test particle in the relativistic regime, provided spinmore » effects are not decisive.« less

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.

A new bidirectional generalization of (2+1)-dimensional matrix k-constrained Kadomtsev-Petviashvili hierarchy

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

Chvartatskyi, O. I., E-mail: alex.chvartatskyy@gmail.com; Sydorenko, Yu. M., E-mail: y-sydorenko@franko.lviv.ua

We introduce a new bidirectional generalization of (2+1)-dimensional k-constrained Kadomtsev-Petviashvili (KP) hierarchy ((2+1)-BDk-cKPH). This new hierarchy generalizes (2+1)-dimensional k-cKP hierarchy, (t{sub A}, τ{sub B}) and (γ{sub A}, σ{sub B}) matrix hierarchies. (2+1)-BDk-cKPH contains a new matrix (1+1)-k-constrained KP hierarchy. Some members of (2+1)-BDk-cKPH are also listed. In particular, it contains matrix generalizations of Davey-Stewartson (DS) systems, (2+1)-dimensional modified Korteweg-de Vries equation and the Nizhnik equation. (2+1)-BDk-cKPH also includes new matrix (2+1)-dimensional generalizations of the Yajima-Oikawa and Melnikov systems. Binary Darboux Transformation Dressing Method is also proposed for construction of exact solutions for equations from (2+1)-BDk-cKPH. As an example the exactmore » form of multi-soliton solutions for vector generalization of the DS system is given.« less

CPDES3: A preconditioned conjugate gradient solver for linear asymmetric matrix equations arising from coupled partial differential equations in three dimensions

NASA Astrophysics Data System (ADS)

Anderson, D. V.; Koniges, A. E.; Shumaker, D. E.

1988-11-01

Many physical problems require the solution of coupled partial differential equations on three-dimensional domains. When the time scales of interest dictate an implicit discretization of the equations a rather complicated global matrix system needs solution. The exact form of the matrix depends on the choice of spatial grids and on the finite element or finite difference approximations employed. CPDES3 allows each spatial operator to have 7, 15, 19, or 27 point stencils and allows for general couplings between all of the component PDE's and it automatically generates the matrix structures needed to perform the algorithm. The resulting sparse matrix equation is solved by either the preconditioned conjugate gradient (CG) method or by the preconditioned biconjugate gradient (BCG) algorithm. An arbitrary number of component equations are permitted only limited by available memory. In the sub-band representation used, we generate an algorithm that is written compactly in terms of indirect induces which is vectorizable on some of the newer scientific computers.

CPDES2: A preconditioned conjugate gradient solver for linear asymmetric matrix equations arising from coupled partial differential equations in two dimensions

NASA Astrophysics Data System (ADS)

Anderson, D. V.; Koniges, A. E.; Shumaker, D. E.

1988-11-01

Many physical problems require the solution of coupled partial differential equations on two-dimensional domains. When the time scales of interest dictate an implicit discretization of the equations a rather complicated global matrix system needs solution. The exact form of the matrix depends on the choice of spatial grids and on the finite element or finite difference approximations employed. CPDES2 allows each spatial operator to have 5 or 9 point stencils and allows for general couplings between all of the component PDE's and it automatically generates the matrix structures needed to perform the algorithm. The resulting sparse matrix equation is solved by either the preconditioned conjugate gradient (CG) method or by the preconditioned biconjugate gradient (BCG) algorithm. An arbitrary number of component equations are permitted only limited by available memory. In the sub-band representation used, we generate an algorithm that is written compactly in terms of indirect indices which is vectorizable on some of the newer scientific computers.

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.

High-dimensional statistical inference: From vector to matrix

NASA Astrophysics Data System (ADS)

Zhang, Anru

Statistical inference for sparse signals or low-rank matrices in high-dimensional settings is of significant interest in a range of contemporary applications. It has attracted significant recent attention in many fields including statistics, applied mathematics and electrical engineering. In this thesis, we consider several problems in including sparse signal recovery (compressed sensing under restricted isometry) and low-rank matrix recovery (matrix recovery via rank-one projections and structured matrix completion). The first part of the thesis discusses compressed sensing and affine rank minimization in both noiseless and noisy cases and establishes sharp restricted isometry conditions for sparse signal and low-rank matrix recovery. The analysis relies on a key technical tool which represents points in a polytope by convex combinations of sparse vectors. The technique is elementary while leads to sharp results. It is shown that, in compressed sensing, delta kA < 1/3, deltak A+ thetak,kA < 1, or deltatkA < √( t - 1)/t for any given constant t ≥ 4/3 guarantee the exact recovery of all k sparse signals in the noiseless case through the constrained ℓ1 minimization, and similarly in affine rank minimization delta rM < 1/3, deltar M + thetar, rM < 1, or deltatrM< √( t - 1)/t ensure the exact reconstruction of all matrices with rank at most r in the noiseless case via the constrained nuclear norm minimization. Moreover, for any epsilon > 0, delta kA < 1/3 + epsilon, deltak A + thetak,kA < 1 + epsilon, or deltatkA< √(t - 1) / t + epsilon are not sufficient to guarantee the exact recovery of all k-sparse signals for large k. Similar result also holds for matrix recovery. In addition, the conditions delta kA<1/3, deltak A+ thetak,kA<1, delta tkA < √(t - 1)/t and deltarM<1/3, delta rM+ thetar,rM<1, delta trM< √(t - 1)/ t are also shown to be sufficient respectively for stable recovery of approximately sparse signals and low-rank matrices in the noisy case. For the second part of the thesis, we introduce a rank-one projection model for low-rank matrix recovery and propose a constrained nuclear norm minimization method for stable recovery of low-rank matrices in the noisy case. The procedure is adaptive to the rank and robust against small perturbations. Both upper and lower bounds for the estimation accuracy under the Frobenius norm loss are obtained. The proposed estimator is shown to be rate-optimal under certain conditions. The estimator is easy to implement via convex programming and performs well numerically. The techniques and main results developed in the chapter also have implications to other related statistical problems. An application to estimation of spiked covariance matrices from one-dimensional random projections is considered. The results demonstrate that it is still possible to accurately estimate the covariance matrix of a high-dimensional distribution based only on one-dimensional projections. For the third part of the thesis, we consider another setting of low-rank matrix completion. Current literature on matrix completion focuses primarily on independent sampling models under which the individual observed entries are sampled independently. Motivated by applications in genomic data integration, we propose a new framework of structured matrix completion (SMC) to treat structured missingness by design. Specifically, our proposed method aims at efficient matrix recovery when a subset of the rows and columns of an approximately low-rank matrix are observed. We provide theoretical justification for the proposed SMC method and derive lower bound for the estimation errors, which together establish the optimal rate of recovery over certain classes of approximately low-rank matrices. Simulation studies show that the method performs well in finite sample under a variety of configurations. The method is applied to integrate several ovarian cancer genomic studies with different extent of genomic measurements, which enables us to construct more accurate prediction rules for ovarian cancer survival.

Accurate van der Waals coefficients from density functional theory

PubMed Central

Tao, Jianmin; Perdew, John P.; Ruzsinszky, Adrienn

2012-01-01

The van der Waals interaction is a weak, long-range correlation, arising from quantum electronic charge fluctuations. This interaction affects many properties of materials. A simple and yet accurate estimate of this effect will facilitate computer simulation of complex molecular materials and drug design. Here we develop a fast approach for accurate evaluation of dynamic multipole polarizabilities and van der Waals (vdW) coefficients of all orders from the electron density and static multipole polarizabilities of each atom or other spherical object, without empirical fitting. Our dynamic polarizabilities (dipole, quadrupole, octupole, etc.) are exact in the zero- and high-frequency limits, and exact at all frequencies for a metallic sphere of uniform density. Our theory predicts dynamic multipole polarizabilities in excellent agreement with more expensive many-body methods, and yields therefrom vdW coefficients C6, C8, C10 for atom pairs with a mean absolute relative error of only 3%. PMID:22205765

Violation of the continuity equation in the Krieger-Li-Iafrate approximation for current-density functional theory

NASA Astrophysics Data System (ADS)

Siegmund, Marc; Pankratov, Oleg

2011-01-01

We show that the exchange-correlation scalar and vector potentials obtained from the optimized effective potential (OEP) equations and from the Krieger-Li-Iafrate (KLI) approximation for the current-density functional theory (CDFT) change under a gauge transformation such that the energy functional remains invariant. This alone does not assure, however, the theory’s compliance with the continuity equation. Using the model of a quantum ring with a broken angular symmetry which is penetrated by a magnetic flux we demonstrate that the physical current density calculated with the exact-exchange CDFT in the KLI approximation violates the continuity condition. In contrast, the current found from a solution of the full OEP equations satisfies this condition. We argue that the continuity violation stems from the fact that the KLI potentials are not (in general) the exact functional derivatives of a gauge-invariant exchange-correlation functional.

Duality in left-right symmetric seesaw mechanism.

PubMed

Akhmedov, E Kh; Frigerio, M

2006-02-17

We consider type I + II seesaw mechanism, where the exchanges of both right-handed neutrinos and isotriplet Higgs bosons contribute to the neutrino mass. Working in the left-right symmetric framework and assuming the mass matrix of light neutrinos m(v) and the Dirac-type Yukawa couplings to be known, we find the triplet Yukawa coupling matrix f, which carries the information about the masses and mixing of the right-handed neutrinos. We show that in this case there exists a duality: for any solution f, there is a dual solution [symbol: see text] = m(v)/nu(L) - f, where nu(L) is the vacuum expectation value of the triplet Higgs boson. Thus, unlike in pure type I (II) seesaw, there is no unique allowed structure for the matrix f. For n lepton generations the number of solutions is 2(n). We develop an exact analytic method of solving the seesaw nonlinear matrix equation for f.

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.

Envelope and phase distribution of a resonance transmission through a complex environment

NASA Astrophysics Data System (ADS)

Savin, Dmitry V.

2018-06-01

A transmission amplitude is considered for quantum or wave transport mediated by a single resonance coupled to the background of many chaotic states. Such a model provides a useful approach to quantify fluctuations in an established signal induced by a complex environment. Applying random matrix theory to the problem, we derive an exact result for the joint distribution of the transmission intensity (envelope) and the transmission phase at arbitrary coupling to the background with finite absorption. The intensity and phase are distributed within a certain region, revealing essential correlations even at strong absorption. In the latter limit, we obtain a simple asymptotic expression that provides a uniformly good approximation of the exact distribution within its whole support, thus going beyond the Rician distribution often used for such purposes. Exact results are also derived for the marginal distribution of the phase, including its limiting forms at weak and strong absorption.

Spinon excitation spectra of the J1-J2 chain from analytical calculations in the dimer basis and exact diagonalization

NASA Astrophysics Data System (ADS)

Lavarélo, Arthur; Roux, Guillaume

2014-10-01

The excitation spectrum of the frustrated spin-1/2 Heisenberg chain is reexamined using variational and exact diagonalization calculations. We show that the overlap matrix of the short-range resonating valence bond states basis can be inverted which yields tractable equations for single and two spinons excitations. Older results are recovered and new ones, such as the bond-state dispersion relation and its size with momentum at the Majumdar-Ghosh point are found. In particular, this approach yields a gap opening at J 2 = 0.25 J 1 and an onset of incommensurability in the dispersion relation at J 2 = 9/17 J 1 as in [S. Brehmer et al., J. Phys.: Condens. Matter 10, 1103 (1998)]. These analytical results provide a good support for the understanding of exact diagonalization spectra, assuming an independent spinons picture.

How to formulate and solve "optimal stand density over time" problems for even-aged stands using dynamic programming.

Treesearch

Chung M. Chen; Dietmar W. Rose; Rolfe A. Leary

1980-01-01

Describes how dynamic programming can be used to solve optimal stand density problems when yields are given by prior simulation or by a new stand growth equation that is a function of the decision variable. Formulations of the latter type allow use of a calculus-based search procedure; they determine exact optimal residual density at each stage.

The coprime quantum chain

NASA Astrophysics Data System (ADS)

Mussardo, G.; Giudici, G.; Viti, J.

2017-03-01

In this paper we introduce and study the coprime quantum chain, i.e. a strongly correlated quantum system defined in terms of the integer eigenvalues n i of the occupation number operators at each site of a chain of length M. The n i ’s take value in the interval [2,q] and may be regarded as S z eigenvalues in the spin representation j  =  (q  -  2)/2. The distinctive interaction of the model is based on the coprimality matrix \\boldsymbolΦ : for the ferromagnetic case, this matrix assigns lower energy to configurations where occupation numbers n i and n i+1 of neighbouring sites share a common divisor, while for the anti-ferromagnetic case it assigns a lower energy to configurations where n i and n i+1 are coprime. The coprime chain, both in the ferro and anti-ferromagnetic cases, may present an exponential number of ground states whose values can be exactly computed by means of graph theoretical tools. In the ferromagnetic case there are generally also frustration phenomena. A fine tuning of local operators may lift the exponential ground state degeneracy and, according to which operators are switched on, the system may be driven into different classes of universality, among which the Ising or Potts universality class. The paper also contains an appendix by Don Zagier on the exact eigenvalues and eigenvectors of the coprimality matrix in the limit q\\to ∞ .

Inclusion-Based Effective Medium Models for the Permeability of a 3D Fractured Rock Mass

NASA Astrophysics Data System (ADS)

Ebigbo, A.; Lang, P. S.; Paluszny, A.; Zimmerman, R. W.

2015-12-01

Following the work of Saevik et al. (Transp. Porous Media, 2013; Geophys. Prosp., 2014), we investigate the ability of classical inclusion-based effective medium theories to predict the macroscopic permeability of a fractured rock mass. The fractures are assumed to be thin, oblate spheroids, and are treated as porous media in their own right, with permeability kf, and are embedded in a homogeneous matrix having permeability km. At very low fracture densities, the effective permeability is given exactly by a well-known expression that goes back at least as far as Fricke (Phys. Rev., 1924). For non-trivial fracture densities, an effective medium approximation must be employed. We have investigated several such approximations: Maxwell's method, the differential method, and the symmetric and asymmetric versions of the self-consistent approximation. The predictions of the various approximate models are tested against the results of explicit numerical simulations, averaged over numerous statistical realizations for each set of parameters. Each of the various effective medium approximations satisfies the Hashin-Shtrikman (H-S) bounds. Unfortunately, these bounds are much too far apart to provide quantitatively useful estimates of keff. For the case of zero matrix permeability, the well-known approximation of Snow, which is based on network considerations rather than a continuum approach, is shown to essentially coincide with the upper H-S bound, thereby proving that the commonly made assumption that Snow's equation is an "upper bound" is indeed correct. This problem is actually characterized by two small parameters, the aspect ratio of the spheroidal fractures, α, and the permeability ratio, κ = km/kf. Two different regimes can be identified, corresponding to α < κ and κ < α, and expressions for each of the effective medium approximations are developed in both regimes. In both regimes, the symmetric version of the self-consistent approximation is the most accurate.

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.

Computational Modeling of Micro-Crack Induced Attenuation in CFRP Composites

NASA Technical Reports Server (NTRS)

Roberts, R. A.; Leckey, C. A. C.

2012-01-01

A computational study is performed to determine the contribution to ultrasound attenuation in carbon fiber reinforced polymer composite laminates of linear elastic scattering by matrix micro-cracking. Multiple scattering approximations are benchmarked against exact computational approaches. Results support linear scattering as the source of observed increased attenuation in the presence of micro-cracking.

Engineering applications of heuristic multilevel optimization methods

NASA Technical Reports Server (NTRS)

Barthelemy, Jean-Francois M.

1988-01-01

Some engineering applications of heuristic multilevel optimization methods are presented and the discussion focuses on the dependency matrix that indicates the relationship between problem functions and variables. Coordination of the subproblem optimizations is shown to be typically achieved through the use of exact or approximate sensitivity analysis. Areas for further development are identified.

Engineering applications of heuristic multilevel optimization methods

NASA Technical Reports Server (NTRS)

Barthelemy, Jean-Francois M.

1989-01-01

Some engineering applications of heuristic multilevel optimization methods are presented and the discussion focuses on the dependency matrix that indicates the relationship between problem functions and variables. Coordination of the subproblem optimizations is shown to be typically achieved through the use of exact or approximate sensitivity analysis. Areas for further development are identified.

Mathematical Analysis of a Multiple-Look Concept Identification Model.

ERIC Educational Resources Information Center

Cotton, John W.

The behavior of focus samples central to the multiple-look model of Trabasso and Bower is examined by three methods. First, exact probabilities of success conditional upon a certain brief history of stimulation are determined. Second, possible states of the organism during the experiment are defined and a transition matrix for those states…

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

Density-based empirical likelihood procedures for testing symmetry of data distributions and K-sample comparisons.

PubMed

Vexler, Albert; Tanajian, Hovig; Hutson, Alan D

In practice, parametric likelihood-ratio techniques are powerful statistical tools. In this article, we propose and examine novel and simple distribution-free test statistics that efficiently approximate parametric likelihood ratios to analyze and compare distributions of K groups of observations. Using the density-based empirical likelihood methodology, we develop a Stata package that applies to a test for symmetry of data distributions and compares K -sample distributions. Recognizing that recent statistical software packages do not sufficiently address K -sample nonparametric comparisons of data distributions, we propose a new Stata command, vxdbel, to execute exact density-based empirical likelihood-ratio tests using K samples. To calculate p -values of the proposed tests, we use the following methods: 1) a classical technique based on Monte Carlo p -value evaluations; 2) an interpolation technique based on tabulated critical values; and 3) a new hybrid technique that combines methods 1 and 2. The third, cutting-edge method is shown to be very efficient in the context of exact-test p -value computations. This Bayesian-type method considers tabulated critical values as prior information and Monte Carlo generations of test statistic values as data used to depict the likelihood function. In this case, a nonparametric Bayesian method is proposed to compute critical values of exact tests.

Theoretical and material studies on thin-film electroluminescent devices

NASA Technical Reports Server (NTRS)

Summers, C. J.; Brennan, K. F.

1986-01-01

A theoretical study of resonant tunneling in multilayered heterostructures is presented based on an exact solution of the Schroedinger equation under the application of a constant electric field. By use of the transfer matrix approach, the transmissivity of the structure is determined as a function of the incident electron energy. The approach presented is easily extended to many layer structures where it is more accurate than other existing transfer matrix or WKB models. The transmission resonances are compared to the bound state energies calculated for a finite square well under bias using either an asymmetric square well model or the exact solution of an infinite square well under the application of an electric field. The results show good agreement with other existing models as well as with the bound state energies. The calculations were then applied to a new superlattice structure, the variablly spaced superlattice energy filter, (VSSEP) which is designed such that under bias the spatial quantization levels fully align. Based on these calculations, a new class of resonant tunneling superlattice devices can be designed.

Exact numerical calculation of fixation probability and time on graphs.

PubMed

Hindersin, Laura; Möller, Marius; Traulsen, Arne; Bauer, Benedikt

2016-12-01

The Moran process on graphs is a popular model to study the dynamics of evolution in a spatially structured population. Exact analytical solutions for the fixation probability and time of a new mutant have been found for only a few classes of graphs so far. Simulations are time-expensive and many realizations are necessary, as the variance of the fixation times is high. We present an algorithm that numerically computes these quantities for arbitrary small graphs by an approach based on the transition matrix. The advantage over simulations is that the calculation has to be executed only once. Building the transition matrix is automated by our algorithm. This enables a fast and interactive study of different graph structures and their effect on fixation probability and time. We provide a fast implementation in C with this note (Hindersin et al., 2016). Our code is very flexible, as it can handle two different update mechanisms (Birth-death or death-Birth), as well as arbitrary directed or undirected graphs. Copyright © 2016 Elsevier Ireland Ltd. All rights reserved.

Matrix product state description of Halperin states

NASA Astrophysics Data System (ADS)

Crépel, V.; Estienne, B.; Bernevig, B. A.; Lecheminant, P.; Regnault, N.

2018-04-01

Many fractional quantum Hall states can be expressed as a correlator of a given conformal field theory used to describe their edge physics. As a consequence, these states admit an economical representation as an exact matrix product state (MPS) that was extensively studied for the systems without any spin or any other internal degrees of freedom. In that case, the correlators are built from a single electronic operator, which is primary with respect to the underlying conformal field theory. We generalize this construction to the archetype of Abelian multicomponent fractional quantum Hall wave functions, the Halperin states. These can be written as conformal blocks involving multiple electronic operators and we explicitly derive their exact MPS representation. In particular, we deal with the caveat of the full wave-function symmetry and show that any additional SU(2) symmetry is preserved by the natural MPS truncation scheme provided by the conformal dimension. We use our method to characterize the topological order of the Halperin states by extracting the topological entanglement entropy. We also evaluate their bulk correlation lengths, which are compared to plasma analogy arguments.

Exact sampling of graphs with prescribed degree correlations

NASA Astrophysics Data System (ADS)

Bassler, Kevin E.; Del Genio, Charo I.; Erdős, Péter L.; Miklós, István; Toroczkai, Zoltán

2015-08-01

Many real-world networks exhibit correlations between the node degrees. For instance, in social networks nodes tend to connect to nodes of similar degree and conversely, in biological and technological networks, high-degree nodes tend to be linked with low-degree nodes. Degree correlations also affect the dynamics of processes supported by a network structure, such as the spread of opinions or epidemics. The proper modelling of these systems, i.e., without uncontrolled biases, requires the sampling of networks with a specified set of constraints. We present a solution to the sampling problem when the constraints imposed are the degree correlations. In particular, we develop an exact method to construct and sample graphs with a specified joint-degree matrix, which is a matrix providing the number of edges between all the sets of nodes of a given degree, for all degrees, thus completely specifying all pairwise degree correlations, and additionally, the degree sequence itself. Our algorithm always produces independent samples without backtracking. The complexity of the graph construction algorithm is {O}({NM}) where N is the number of nodes and M is the number of edges.

On prototypical wave transmission across a junction of waveguides with honeycomb structure

NASA Astrophysics Data System (ADS)

Sharma, Basant Lal

2018-02-01

An exact expression for the scattering matrix associated with a junction generated by partial unzipping along the zigzag direction of armchair tubes is presented. The assumed simple, but representative, model, for scalar wave transmission can be interpreted in terms of the transport of the out-of-plane phonons in the ribbon-side vis-a-vis the radial phonons in the tubular-side of junction, based on the nearest-neighbor interactions between lattice sites. The exact solution for the `bondlength' in `broken' versus intact bonds can be constructed via a standard application of the Wiener-Hopf technique. The amplitude distribution of outgoing phonons, far away from the junction on either side of it, is obtained in closed form by the mode-matching method; eventually, this leads to the provision of the scattering matrix. As the main result of the paper, a succinct and closed form expression for the accompanying reflection and transmission coefficients is provided along with a detailed derivation using the Chebyshev polynomials. Applications of the analysis presented in this paper include linear wave transmission in nanotubes, nanoribbons, and monolayers of honeycomb lattices containing carbon-like units.

How perfect can a gluon plasma be in perturbative QCD?

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

Chen, Jiunn-Wei; Deng Jian; Dong Hui

2011-02-01

The shear viscosity to entropy density ratio, {eta}/s, characterizes how perfect a fluid is. We calculate the leading order {eta}/s of a gluon plasma in perturbation using the kinetic theory. The leading order contribution only involves the elastic gg{r_reversible}gg (22) process and the inelastic gg{r_reversible}ggg (23) process. The hard-thermal-loop (HTL) treatment is used for the 22 matrix element, while the exact matrix element in vacuum is supplemented by the gluon Debye mass insertion for the 23 process. Also, the asymptotic mass is used for the external gluons in the kinetic theory. The errors from not implementing HTL and the Landau-Pomeranchuk-Migdalmore » effect in the 23 process, and from the uncalculated higher order corrections, are estimated. Our result smoothly connects the two different approximations used by Arnold, Moore, and Yaffe (AMY) and Xu and Greiner (XG). At small {alpha}{sub s} ({alpha}{sub s}<<1), our result is closer to AMY's collinear result while at larger {alpha}{sub s} the finite angle noncollinear configurations become more important and our result is closer to XG's soft bremsstrahlung result. In the region where perturbation is reliable ({alpha}{sub s} < or approx. 0.1), we find no indication that the proposed perfect fluid limit {eta}/s{approx_equal}1/(4{pi}) can be achieved by perturbative QCD alone. Whether this can be achieve for {alpha}{sub s} > or approx. 0.1 is still an open question.« 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.

Individual complex Dirac eigenvalue distributions from random matrix theory and comparison to quenched lattice QCD with a quark chemical potential.

PubMed

Akemann, G; Bloch, J; Shifrin, L; Wettig, T

2008-01-25

We analyze how individual eigenvalues of the QCD Dirac operator at nonzero quark chemical potential are distributed in the complex plane. Exact and approximate analytical results for both quenched and unquenched distributions are derived from non-Hermitian random matrix theory. When comparing these to quenched lattice QCD spectra close to the origin, excellent agreement is found for zero and nonzero topology at several values of the quark chemical potential. Our analytical results are also applicable to other physical systems in the same symmetry class.

The application of trigonal curve to the Mikhailov-Shabat-Sokolov flows

NASA Astrophysics Data System (ADS)

He, Guoliang; Geng, Xianguo; Wu, Lihua

2016-08-01

Resorting to the characteristic polynomial of Lax matrix for the Mikhailov-Shabat-Sokolov hierarchy associated with a {3 × 3} matrix spectral problem, we introduce a trigonal curve, from which we deduce the associated Baker-Akhiezer function, meromorphic functions and Dubrovin-type equations. The straightening out of the Mikhailov-Shabat-Sokolov flows is exactly given through the Abel map. On the basis of these results and the theory of trigonal curve, we obtain the explicit theta function representations of the Baker-Akhiezer function, the meromorphic functions, and in particular, that of solutions for the entire Mikhailov-Shabat-Sokolov hierarchy.

An iterative solver for the 3D Helmholtz equation

NASA Astrophysics Data System (ADS)

Belonosov, Mikhail; Dmitriev, Maxim; Kostin, Victor; Neklyudov, Dmitry; Tcheverda, Vladimir

2017-09-01

We develop a frequency-domain iterative solver for numerical simulation of acoustic waves in 3D heterogeneous media. It is based on the application of a unique preconditioner to the Helmholtz equation that ensures convergence for Krylov subspace iteration methods. Effective inversion of the preconditioner involves the Fast Fourier Transform (FFT) and numerical solution of a series of boundary value problems for ordinary differential equations. Matrix-by-vector multiplication for iterative inversion of the preconditioned matrix involves inversion of the preconditioner and pointwise multiplication of grid functions. Our solver has been verified by benchmarking against exact solutions and a time-domain solver.

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.

SILICON AND BONE HEALTH

PubMed Central

JUGDAOHSINGH, R.

2009-01-01

Low bone mass (osteoporosis) is a silent epidemic of the 21st century, which presently in the UK results in over 200,000 fractures annually at a cost of over one billion pounds. Figures are set to increase worldwide. Understanding the factors which affect bone metabolism is thus of primary importance in order to establish preventative measures or treatments for this condition. Nutrition is an important determinant of bone health, but the effects of the individual nutrients and minerals, other than calcium, is little understood. Accumulating evidence over the last 30 years strongly suggest that dietary silicon is beneficial to bone and connective tissue health and we recently reported strong positive associations between dietary Si intake and bone mineral density in US and UK cohorts. The exact biological role(s) of silicon in bone health is still not clear, although a number of possible mechanisms have been suggested, including the synthesis of collagen and/or its stabilization, and matrix mineralization. This review gives an overview of this naturally occurring dietary element, its metabolism and the evidence of its potential role in bone health. PMID:17435952

Boson peak and Ioffe-Regel criterion in amorphous siliconlike materials: The effect of bond directionality.

PubMed

Beltukov, Y M; Fusco, C; Parshin, D A; Tanguy, A

2016-02-01

The vibrational properties of model amorphous materials are studied by combining complete analysis of the vibration modes, dynamical structure factor, and energy diffusivity with exact diagonalization of the dynamical matrix and the kernel polynomial method, which allows a study of very large system sizes. Different materials are studied that differ only by the bending rigidity of the interactions in a Stillinger-Weber modelization used to describe amorphous silicon. The local bending rigidity can thus be used as a control parameter, to tune the sound velocity together with local bonds directionality. It is shown that for all the systems studied, the upper limit of the Boson peak corresponds to the Ioffe-Regel criterion for transverse waves, as well as to a minimum of the diffusivity. The Boson peak is followed by a diffusivity's increase supported by longitudinal phonons. The Ioffe-Regel criterion for transverse waves corresponds to a common characteristic mean-free path of 5-7 Å (which is slightly bigger for longitudinal phonons), while the fine structure of the vibrational density of states is shown to be sensitive to the local bending rigidity.

Direct Simulation of Multiple Scattering by Discrete Random Media Illuminated by Gaussian Beams

NASA Technical Reports Server (NTRS)

Mackowski, Daniel W.; Mishchenko, Michael I.

2011-01-01

The conventional orientation-averaging procedure developed in the framework of the superposition T-matrix approach is generalized to include the case of illumination by a Gaussian beam (GB). The resulting computer code is parallelized and used to perform extensive numerically exact calculations of electromagnetic scattering by volumes of discrete random medium consisting of monodisperse spherical particles. The size parameters of the scattering volumes are 40, 50, and 60, while their packing density is fixed at 5%. We demonstrate that all scattering patterns observed in the far-field zone of a random multisphere target and their evolution with decreasing width of the incident GB can be interpreted in terms of idealized theoretical concepts such as forward-scattering interference, coherent backscattering (CB), and diffuse multiple scattering. It is shown that the increasing violation of electromagnetic reciprocity with decreasing GB width suppresses and eventually eradicates all observable manifestations of CB. This result supplements the previous demonstration of the effects of broken reciprocity in the case of magneto-optically active particles subjected to an external magnetic field.

Role of the pair potential for the saturation of generalized Pauli constraints

NASA Astrophysics Data System (ADS)

Legeza, Örs; Schilling, Christian

2018-05-01

The dependence of the (quasi-)saturation of the generalized Pauli constraints on the pair potential is studied for ground states of few-fermion systems. For this, we consider spinless fermions in one dimension which are harmonically confined and interact by pair potentials of the form | xi-xj|s with -1 ≤s ≤5 . We use the density matrix renormalization group approach and large orbital basis to achieve the convergence on more than ten digits of both the variational energy and the natural occupation numbers. Our results confirm that the conflict between energy minimization and fermionic exchange symmetry results in a universal and nontrivial quasisaturation of the generalized Pauli constraints (quasipinning), implying tremendous structural simplifications of the fermionic ground state for all s . Those numerically exact results are complemented by an analytical study based on a self-consistent perturbation theory which we develop for this purpose. The respective results for the weak-coupling regime eventually elucidate the singular behavior found for the specific values s =2 ,4 ,..., resulting in an extremely strong quasipinning.

Exploring the nonequilibrium dynamics of ultracold quantum gases by using numerical tools

NASA Astrophysics Data System (ADS)

Heidrich-Meisner, Fabian

Numerical tools such as exact diagonalization or the density matrix renormalization group method have been vital for the study of the nonequilibrium dynamics of strongly correlated many-body systems. Moreover, they provided unique insight for the interpretation of quantum gas experiments, whenever a direct comparison with theory is possible. By considering the example of the experiment by Ronzheimer et al., in which both an interaction quench and the release of bosons from a trap into an empty optical lattice (sudden expansion) was realized, I discuss several nonequilibrium effects of strongly interacting quantum gases. These include the thermalization of a closed quantum system and its connection to the eigenstate thermalization hypothesis, nonequilibrium mass transport, dynamical fermionization, and transient phenomena such as quantum distillation or dynamical quasicondensation. I highlight the role of integrability in giving rise to ballistic transport in strongly interacting 1D systems and in determining the asymptotic state after a quantum quench. The talk concludes with a perspective on open questions concerning 2D systems and the numerical simulation of their nonequilibrium dynamics. Supported by Deutsche Forschungsgemeinschaft (DFG) via FOR 801.

Cavity-coupled double-quantum dot at finite bias: Analogy with lasers and beyond

NASA Astrophysics Data System (ADS)

Kulkarni, Manas; Cotlet, Ovidiu; Türeci, Hakan E.

2014-09-01

We present a theoretical and experimental study of photonic and electronic transport properties of a voltage biased InAs semiconductor double quantum dot (DQD) that is dipole coupled to a superconducting transmission line resonator. We obtain the master equation for the reduced density matrix of the coupled system of cavity photons and DQD electrons accounting systematically for both the presence of phonons and the effect of leads at finite voltage bias. We subsequently derive analytical expressions for transmission, phase response, photon number, and the nonequilibrium steady-state electron current. We show that the coupled system under finite bias realizes an unconventional version of a single-atom laser and analyze the spectrum and the statistics of the photon flux leaving the cavity. In the transmission mode, the system behaves as a saturable single-atom amplifier for the incoming photon flux. Finally, we show that the back action of the photon emission on the steady-state current can be substantial. Our analytical results are compared to exact master equation results establishing regimes of validity of various analytical models. We compare our findings to available experimental measurements.

Non-renewal statistics for electron transport in a molecular junction with electron-vibration interaction

NASA Astrophysics Data System (ADS)

Kosov, Daniel S.

2017-09-01

Quantum transport of electrons through a molecule is a series of individual electron tunneling events separated by stochastic waiting time intervals. We study the emergence of temporal correlations between successive waiting times for the electron transport in a vibrating molecular junction. Using the master equation approach, we compute the joint probability distribution for waiting times of two successive tunneling events. We show that the probability distribution is completely reset after each tunneling event if molecular vibrations are thermally equilibrated. If we treat vibrational dynamics exactly without imposing the equilibration constraint, the statistics of electron tunneling events become non-renewal. Non-renewal statistics between two waiting times τ1 and τ2 means that the density matrix of the molecule is not fully renewed after time τ1 and the probability of observing waiting time τ2 for the second electron transfer depends on the previous electron waiting time τ1. The strong electron-vibration coupling is required for the emergence of the non-renewal statistics. We show that in the Franck-Condon blockade regime, extremely rare tunneling events become positively correlated.

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

Exact solutions to Brans-Dicke cosmologies in flat Friedmann universes.

NASA Technical Reports Server (NTRS)

Morganstern, R. E.

1971-01-01

The Brans-Dicke cosmological equations for flat Friedmann-type expanding universes are solved parametrically for time, density, expansion parameter, and scalar field. These results reduce to a previously obtained exact solution to the radiation cosmology. Although the scalar field may be undetectable at the present epoch, it is felt that, if it exists, it must play an important role as one approaches the initial singularity of the cosmology.

Non-additive non-interacting kinetic energy of rare gas dimers

NASA Astrophysics Data System (ADS)

Jiang, Kaili; Nafziger, Jonathan; Wasserman, Adam

2018-03-01

Approximations of the non-additive non-interacting kinetic energy (NAKE) as an explicit functional of the density are the basis of several electronic structure methods that provide improved computational efficiency over standard Kohn-Sham calculations. However, within most fragment-based formalisms, there is no unique exact NAKE, making it difficult to develop general, robust approximations for it. When adjustments are made to the embedding formalisms to guarantee uniqueness, approximate functionals may be more meaningfully compared to the exact unique NAKE. We use numerically accurate inversions to study the exact NAKE of several rare-gas dimers within partition density functional theory, a method that provides the uniqueness for the exact NAKE. We find that the NAKE decreases nearly exponentially with atomic separation for the rare-gas dimers. We compute the logarithmic derivative of the NAKE with respect to the bond length for our numerically accurate inversions as well as for several approximate NAKE functionals. We show that standard approximate NAKE functionals do not reproduce the correct behavior for this logarithmic derivative and propose two new NAKE functionals that do. The first of these is based on a re-parametrization of a conjoint Perdew-Burke-Ernzerhof (PBE) functional. The second is a simple, physically motivated non-decomposable NAKE functional that matches the asymptotic decay constant without fitting.

Theoretical models of non-Maxwellian equilibria for one-dimensional collisionless plasmas

NASA Astrophysics Data System (ADS)

Allanson, O.; Neukirch, T.; Wilson, F.; Troscheit, S.

2016-12-01

It is ideal to use exact equilibrium solutions of the steady state Vlasov-Maxwell system to intialise collsionless simulations. However, exact equilibrium distribution functions (DFs) for a given macroscopic configuration are typically unknown, and it is common to resort to using `flow-shifted' Maxwellian DFs in their stead. These DFs may be consistent with a macrosopic system with the target number density and current density, but could well have inaccurate higher order moments. We present recent theoretical work on the `inverse problem in Vlasov-Maxwell equilibria', namely calculating an exact solution of the Vlasov equation for a specific given magnetic field. In particular, we focus on one-dimensional geometries in Cartesian (current sheets) coordinates.1. From 1D fields to Vlasov equilibria: Theory and application of Hermite Polynomials: (O. Allanson, T. Neukirch, S. Troscheit and F. Wilson, Journal of Plasma Physics, 82, 905820306 (2016) [28 pages, Open Access] )2. An exact collisionless equilibrium for the Force-Free Harris Sheet with low plasma beta: (O. Allanson, T. Neukirch, F. Wilson and S. Troscheit, Physics of Plasmas, 22, 102116 (2015) [11 pages, Open Access])3. Neutral and non-neutral collisionless plasma equilibria for twisted flux tubes: The Gold-Hoyle model in a background field (O. Allanson, F. Wilson and T. Neukirch, (2016)) (accepted, Physics of Plasmas)

Exact simulation of polarized light reflectance by particle deposits

NASA Astrophysics Data System (ADS)

Ramezan Pour, B.; Mackowski, D. W.

2015-12-01

The use of polarimetric light reflection measurements as a means of identifying the physical and chemical characteristics of particulate materials obviously relies on an accurate model of predicting the effects of particle size, shape, concentration, and refractive index on polarized reflection. The research examines two methods for prediction of reflection from plane parallel layers of wavelength—sized particles. The first method is based on an exact superposition solution to Maxwell's time harmonic wave equations for a deposit of spherical particles that are exposed to a plane incident wave. We use a FORTRAN-90 implementation of this solution (the Multiple Sphere T Matrix (MSTM) code), coupled with parallel computational platforms, to directly simulate the reflection from particle layers. The second method examined is based upon the vector radiative transport equation (RTE). Mie theory is used in our RTE model to predict the extinction coefficient, albedo, and scattering phase function of the particles, and the solution of the RTE is obtained from adding—doubling method applied to a plane—parallel configuration. Our results show that the MSTM and RTE predictions of the Mueller matrix elements converge when particle volume fraction in the particle layer decreases below around five percent. At higher volume fractions the RTE can yield results that, depending on the particle size and refractive index, significantly depart from the exact predictions. The particle regimes which lead to dependent scattering effects, and the application of methods to correct the vector RTE for particle interaction, will be discussed.

Spectral density of mixtures of random density matrices for qubits

NASA Astrophysics Data System (ADS)

Zhang, Lin; Wang, Jiamei; Chen, Zhihua

2018-06-01

We derive the spectral density of the equiprobable mixture of two random density matrices of a two-level quantum system. We also work out the spectral density of mixture under the so-called quantum addition rule. We use the spectral densities to calculate the average entropy of mixtures of random density matrices, and show that the average entropy of the arithmetic-mean-state of n qubit density matrices randomly chosen from the Hilbert-Schmidt ensemble is never decreasing with the number n. We also get the exact value of the average squared fidelity. Some conjectures and open problems related to von Neumann entropy are also proposed.

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.

Spin-adapted matrix product states and operators

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

Matrix product states (MPSs) and matrix product operators (MPOs) allow an alternative formulation of the density matrix renormalization group algorithm introduced by White. Here, we describe how non-abelian spin symmetry can be exploited in MPSs and MPOs by virtue of the Wigner–Eckart theorem at the example of the spin-adapted quantum chemical Hamiltonian operator.

Delayed coherent quantum feedback from a scattering theory and a matrix product state perspective

NASA Astrophysics Data System (ADS)

Guimond, P.-O.; Pletyukhov, M.; Pichler, H.; Zoller, P.

2017-12-01

We study the scattering of photons propagating in a semi-infinite waveguide terminated by a mirror and interacting with a quantum emitter. This paradigm constitutes an example of coherent quantum feedback, where light emitted towards the mirror gets redirected back to the emitter. We derive an analytical solution for the scattering of two-photon states, which is based on an exact resummation of the perturbative expansion of the scattering matrix, in a regime where the time delay of the coherent feedback is comparable to the timescale of the quantum emitter’s dynamics. We compare the results with numerical simulations based on matrix product state techniques simulating the full dynamics of the system, and extend the study to the scattering of coherent states beyond the low-power limit.

Trial densities for the extended Thomas-Fermi model

NASA Astrophysics Data System (ADS)

Yu, An; Jimin, Hu

1996-02-01

A new and simplified form of nuclear densities is proposed for the extended Thomas-Fermi method (ETF) and applied to calculate the ground-state properties of several spherical nuclei, with results comparable or even better than other conventional density profiles. With the expectation value method (EVM) for microscopic corrections we checked our new densities for spherical nuclei. The binding energies of ground states almost reproduce the Hartree-Fock (HF) calculations exactly. Further applications to nuclei far away from the β-stability line are discussed.

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.

Theory and analysis of statistical discriminant techniques as applied to remote sensing data

NASA Technical Reports Server (NTRS)

Odell, P. L.

1973-01-01

Classification of remote earth resources sensing data according to normed exponential density statistics is reported. The use of density models appropriate for several physical situations provides an exact solution for the probabilities of classifications associated with the Bayes discriminant procedure even when the covariance matrices are unequal.

Accurate and Efficient Approximation to the Optimized Effective Potential for Exchange

NASA Astrophysics Data System (ADS)

Ryabinkin, Ilya G.; Kananenka, Alexei A.; Staroverov, Viktor N.

2013-07-01

We devise an efficient practical method for computing the Kohn-Sham exchange-correlation potential corresponding to a Hartree-Fock electron density. This potential is almost indistinguishable from the exact-exchange optimized effective potential (OEP) and, when used as an approximation to the OEP, is vastly better than all existing models. Using our method one can obtain unambiguous, nearly exact OEPs for any reasonable finite one-electron basis set at the same low cost as the Krieger-Li-Iafrate and Becke-Johnson potentials. For all practical purposes, this solves the long-standing problem of black-box construction of OEPs in exact-exchange calculations.

Role of exact exchange in thermally-assisted-occupation density functional theory: A proposal of new hybrid schemes.

PubMed

Chai, Jeng-Da

2017-01-28

We propose hybrid schemes incorporating exact exchange into thermally assisted-occupation-density functional theory (TAO-DFT) [J.-D. Chai, J. Chem. Phys. 136, 154104 (2012)] for an improved description of nonlocal exchange effects. With a few simple modifications, global and range-separated hybrid functionals in Kohn-Sham density functional theory (KS-DFT) can be combined seamlessly with TAO-DFT. In comparison with global hybrid functionals in KS-DFT, the resulting global hybrid functionals in TAO-DFT yield promising performance for systems with strong static correlation effects (e.g., the dissociation of H 2 and N 2 , twisted ethylene, and electronic properties of linear acenes), while maintaining similar performance for systems without strong static correlation effects. Besides, a reasonably accurate description of noncovalent interactions can be efficiently achieved through the inclusion of dispersion corrections in hybrid TAO-DFT. Relative to semilocal density functionals in TAO-DFT, global hybrid functionals in TAO-DFT are generally superior in performance for a wide range of applications, such as thermochemistry, kinetics, reaction energies, and optimized geometries.

Solution of the determinantal assignment problem using the Grassmann matrices

NASA Astrophysics Data System (ADS)

Karcanias, Nicos; Leventides, John

2016-02-01

The paper provides a direct solution to the determinantal assignment problem (DAP) which unifies all frequency assignment problems of the linear control theory. The current approach is based on the solvability of the exterior equation ? where ? is an n -dimensional vector space over ? which is an integral part of the solution of DAP. New criteria for existence of solution and their computation based on the properties of structured matrices are referred to as Grassmann matrices. The solvability of this exterior equation is referred to as decomposability of ?, and it is in turn characterised by the set of quadratic Plücker relations (QPRs) describing the Grassmann variety of the corresponding projective space. Alternative new tests for decomposability of the multi-vector ? are given in terms of the rank properties of the Grassmann matrix, ? of the vector ?, which is constructed by the coordinates of ?. It is shown that the exterior equation is solvable (? is decomposable), if and only if ? where ?; the solution space for a decomposable ?, is the space ?. This provides an alternative linear algebra characterisation of the decomposability problem and of the Grassmann variety to that defined by the QPRs. Further properties of the Grassmann matrices are explored by defining the Hodge-Grassmann matrix as the dual of the Grassmann matrix. The connections of the Hodge-Grassmann matrix to the solution of exterior equations are examined, and an alternative new characterisation of decomposability is given in terms of the dimension of its image space. The framework based on the Grassmann matrices provides the means for the development of a new computational method for the solutions of the exact DAP (when such solutions exist), as well as computing approximate solutions, when exact solutions do not exist.

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.

On mini-superspace limit of boundary three-point function in Liouville field theory

NASA Astrophysics Data System (ADS)

Apresyan, Elena; Sarkissian, Gor

2017-12-01

We study the mini-superspace semiclassical limit of the boundary three-point function in the Liouville field theory. We compute also matrix elements for the Morse potential quantum mechanics. An exact agreement between the former and the latter is found. We show that both of them are given by the generalized hypergeometric functions.

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

Sinitsyn, N. A.

We consider nonadiabatic transitions in explicitly time-dependent systems with Hamiltonians of the form Hˆ(t)=Aˆ+Bˆt+Cˆ/t, where t is time and Aˆ,Bˆ,Cˆ are Hermitian N × N matrices. We show that in any model of this type, scattering matrix elements satisfy nontrivial exact constraints that follow from the absence of the Stokes phenomenon for solutions with specific conditions at t→–∞. This allows one to continue such solutions analytically to t→+∞, and connect their asymptotic behavior at t→–∞ and t→+∞. This property becomes particularly useful when a model shows additional discrete symmetries. Specifically, we derive a number of simple exact constraints and explicitmore » expressions for scattering probabilities in such systems.« less

Power Spectrum of Long Eigenlevel Sequences in Quantum Chaotic Systems.

PubMed

Riser, Roman; Osipov, Vladimir Al; Kanzieper, Eugene

2017-05-19

We present a nonperturbative analysis of the power spectrum of energy level fluctuations in fully chaotic quantum structures. Focusing on systems with broken time-reversal symmetry, we employ a finite-N random matrix theory to derive an exact multidimensional integral representation of the power spectrum. The N→∞ limit of the exact solution furnishes the main result of this study-a universal, parameter-free prediction for the power spectrum expressed in terms of a fifth Painlevé transcendent. Extensive numerics lends further support to our theory which, as discussed at length, invalidates a traditional assumption that the power spectrum is merely determined by the spectral form factor of a quantum system.

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).

Hybrid reconstruction of quantum density matrix: when low-rank meets sparsity

NASA Astrophysics Data System (ADS)

Li, Kezhi; Zheng, Kai; Yang, Jingbei; Cong, Shuang; Liu, Xiaomei; Li, Zhaokai

2017-12-01

Both the mathematical theory and experiments have verified that the quantum state tomography based on compressive sensing is an efficient framework for the reconstruction of quantum density states. In recent physical experiments, we found that many unknown density matrices in which people are interested in are low-rank as well as sparse. Bearing this information in mind, in this paper we propose a reconstruction algorithm that combines the low-rank and the sparsity property of density matrices and further theoretically prove that the solution of the optimization function can be, and only be, the true density matrix satisfying the model with overwhelming probability, as long as a necessary number of measurements are allowed. The solver leverages the fixed-point equation technique in which a step-by-step strategy is developed by utilizing an extended soft threshold operator that copes with complex values. Numerical experiments of the density matrix estimation for real nuclear magnetic resonance devices reveal that the proposed method achieves a better accuracy compared to some existing methods. We believe that the proposed method could be leveraged as a generalized approach and widely implemented in the quantum state estimation.

Exact exchange potential evaluated from occupied Kohn-Sham and Hartree-Fock solutions

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

Cinal, M.; Holas, A.

2011-06-15

The reported algorithm determines the exact exchange potential v{sub x} in an iterative way using energy shifts (ESs) and orbital shifts (OSs) obtained with finite-difference formulas from the solutions (occupied orbitals and their energies) of the Hartree-Fock-like equation and the Kohn-Sham-like equation, the former used for the initial approximation to v{sub x} and the latter for increments of ES and OS due to subsequent changes of v{sub x}. Thus, the need for solution of the differential equations for OSs, used by Kuemmel and Perdew [Phys. Rev. Lett. 90, 043004 (2003)], is bypassed. The iterated exchange potential, expressed in terms ofmore » ESs and OSs, is improved by modifying ESs at odd iteration steps and OSs at even steps. The modification formulas are related to the optimized-effective-potential equation (satisfied at convergence) written as the condition of vanishing density shift (DS). They are obtained, respectively, by enforcing its satisfaction through corrections to approximate OSs and by determining the optimal ESs that minimize the DS norm. The proposed method, successfully tested for several closed-(sub)shell atoms, from Be to Kr, within the density functional theory exchange-only approximation, proves highly efficient. The calculations using the pseudospectral method for representing orbitals give iterative sequences of approximate exchange potentials (starting with the Krieger-Li-Iafrate approximation) that rapidly approach the exact v{sub x} so that, for Ne, Ar, and Zn, the corresponding DS norm becomes less than 10{sup -6} after 13, 13, and 9 iteration steps for a given electron density. In self-consistent density calculations, orbital energies of 10{sup -4} hartree accuracy are obtained for these atoms after, respectively, 9, 12, and 12 density iteration steps, each involving just two steps of v{sub x} iteration, while the accuracy limit of 10{sup -6} to 10{sup -7} hartree is reached after 20 density iterations.« less

Exact exchange potential evaluated from occupied Kohn-Sham and Hartree-Fock solutions

NASA Astrophysics Data System (ADS)

Cinal, M.; Holas, A.

2011-06-01

The reported algorithm determines the exact exchange potential vx in an iterative way using energy shifts (ESs) and orbital shifts (OSs) obtained with finite-difference formulas from the solutions (occupied orbitals and their energies) of the Hartree-Fock-like equation and the Kohn-Sham-like equation, the former used for the initial approximation to vx and the latter for increments of ES and OS due to subsequent changes of vx. Thus, the need for solution of the differential equations for OSs, used by Kümmel and Perdew [Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.90.043004 90, 043004 (2003)], is bypassed. The iterated exchange potential, expressed in terms of ESs and OSs, is improved by modifying ESs at odd iteration steps and OSs at even steps. The modification formulas are related to the optimized-effective-potential equation (satisfied at convergence) written as the condition of vanishing density shift (DS). They are obtained, respectively, by enforcing its satisfaction through corrections to approximate OSs and by determining the optimal ESs that minimize the DS norm. The proposed method, successfully tested for several closed-(sub)shell atoms, from Be to Kr, within the density functional theory exchange-only approximation, proves highly efficient. The calculations using the pseudospectral method for representing orbitals give iterative sequences of approximate exchange potentials (starting with the Krieger-Li-Iafrate approximation) that rapidly approach the exact vx so that, for Ne, Ar, and Zn, the corresponding DS norm becomes less than 10-6 after 13, 13, and 9 iteration steps for a given electron density. In self-consistent density calculations, orbital energies of 10-4 hartree accuracy are obtained for these atoms after, respectively, 9, 12, and 12 density iteration steps, each involving just two steps of vx iteration, while the accuracy limit of 10-6 to 10-7 hartree is reached after 20 density iterations.

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

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.

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.

Anomalous transport in turbulent plasmas and continuous time random walks

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

Balescu, R.

1995-05-01

The possibility of a model of anomalous transport problems in a turbulent plasma by a purely stochastic process is investigated. The theory of continuous time random walks (CTRW`s) is briefly reviewed. It is shown that a particular class, called the standard long tail CTRW`s is of special interest for the description of subdiffusive transport. Its evolution is described by a non-Markovian diffusion equation that is constructed in such a way as to yield exact values for all the moments of the density profile. The concept of a CTRW model is compared to an exact solution of a simple test problem:more » transport of charged particles in a fluctuating magnetic field in the limit of infinite perpendicular correlation length. Although the well-known behavior of the mean square displacement proportional to {ital t}{sup 1/2} is easily recovered, the exact density profile cannot be modeled by a CTRW. However, the quasilinear approximation of the kinetic equation has the form of a non-Markovian diffusion equation and can thus be generated by a CTRW.« less

Formally exact integral equation theory of the exchange-only potential in density functional theory: Refined closure approximation

NASA Astrophysics Data System (ADS)

March, N. H.; Nagy, Á.

A fonnally exact integral equation theory for the exchange-only potential Vx(r) in density functional theory was recently set up by Howard and March [I.A. Howard, N.H. March, J. Chem. Phys. 119 (2003) 5789]. It involved a `closure' function P(r) satisfying the exact sum rule ∫ P(r) dr = 0. The simplest choice P(r) = 0 recovers then the approximation proposed by Della Sala and Görling [F. Della Sala, A. Görling, J. Chem. Phys. 115 (2001) 5718] and by Gritsenko and Baerends [O.V. Gritsenko, E.J. Baerends, Phys. Rev. A 64 (2001) 042506]. Here, refined choices of P(r) are proposed, the most direct being based on the KLI (Krieger-Li-Iafrate) approximation. A further choice given some attention is where P(r) involves frontier orbital properties. In particular, the introduction of the LUMO (lowest unoccupied molecular) orbital, along with the energy separation between HOMO (highest occupied molecular orbital) and LUMO levels, should prove a significant step beyond current approximations to the optimized potential method, all of which involve only single-particle occupied orbitals.

Semilocal density functional obeying a strongly tightened bound for exchange

PubMed Central

Sun, Jianwei; Perdew, John P.; Ruzsinszky, Adrienn

2015-01-01

Because of its useful accuracy and efficiency, density functional theory (DFT) is one of the most widely used electronic structure theories in physics, materials science, and chemistry. Only the exchange-correlation energy is unknown, and needs to be approximated in practice. Exact constraints provide useful information about this functional. The local spin-density approximation (LSDA) was the first constraint-based density functional. The Lieb–Oxford lower bound on the exchange-correlation energy for any density is another constraint that plays an important role in the development of generalized gradient approximations (GGAs) and meta-GGAs. Recently, a strongly and optimally tightened lower bound on the exchange energy was proved for one- and two-electron densities, and conjectured for all densities. In this article, we present a realistic “meta-GGA made very simple” (MGGA-MVS) for exchange that respects this optimal bound, which no previous beyond-LSDA approximation satisfies. This constraint might have been expected to worsen predicted thermochemical properties, but in fact they are improved over those of the Perdew–Burke–Ernzerhof GGA, which has nearly the same correlation part. MVS exchange is however radically different from that of other GGAs and meta-GGAs. Its exchange enhancement factor has a very strong dependence upon the orbital kinetic energy density, which permits accurate energies even with the drastically tightened bound. When this nonempirical MVS meta-GGA is hybridized with 25% of exact exchange, the resulting global hybrid gives excellent predictions for atomization energies, reaction barriers, and weak interactions of molecules. PMID:25561554

Semilocal density functional obeying a strongly tightened bound for exchange.

PubMed

Sun, Jianwei; Perdew, John P; Ruzsinszky, Adrienn

2015-01-20

Because of its useful accuracy and efficiency, density functional theory (DFT) is one of the most widely used electronic structure theories in physics, materials science, and chemistry. Only the exchange-correlation energy is unknown, and needs to be approximated in practice. Exact constraints provide useful information about this functional. The local spin-density approximation (LSDA) was the first constraint-based density functional. The Lieb-Oxford lower bound on the exchange-correlation energy for any density is another constraint that plays an important role in the development of generalized gradient approximations (GGAs) and meta-GGAs. Recently, a strongly and optimally tightened lower bound on the exchange energy was proved for one- and two-electron densities, and conjectured for all densities. In this article, we present a realistic "meta-GGA made very simple" (MGGA-MVS) for exchange that respects this optimal bound, which no previous beyond-LSDA approximation satisfies. This constraint might have been expected to worsen predicted thermochemical properties, but in fact they are improved over those of the Perdew-Burke-Ernzerhof GGA, which has nearly the same correlation part. MVS exchange is however radically different from that of other GGAs and meta-GGAs. Its exchange enhancement factor has a very strong dependence upon the orbital kinetic energy density, which permits accurate energies even with the drastically tightened bound. When this nonempirical MVS meta-GGA is hybridized with 25% of exact exchange, the resulting global hybrid gives excellent predictions for atomization energies, reaction barriers, and weak interactions of molecules.

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.

Green's function enriched Poisson solver for electrostatics in many-particle systems

NASA Astrophysics Data System (ADS)

Sutmann, Godehard

2016-06-01

A highly accurate method is presented for the construction of the charge density for the solution of the Poisson equation in particle simulations. The method is based on an operator adjusted source term which can be shown to produce exact results up to numerical precision in the case of a large support of the charge distribution, therefore compensating the discretization error of finite difference schemes. This is achieved by balancing an exact representation of the known Green's function of regularized electrostatic problem with a discretized representation of the Laplace operator. It is shown that the exact calculation of the potential is possible independent of the order of the finite difference scheme but the computational efficiency for higher order methods is found to be superior due to a faster convergence to the exact result as a function of the charge support.

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.

Exact Solution of a Two-Species Quantum Dimer Model for Pseudogap Metals

NASA Astrophysics Data System (ADS)

Feldmeier, Johannes; Huber, Sebastian; Punk, Matthias

2018-05-01

We present an exact ground state solution of a quantum dimer model introduced by Punk, Allais, and Sachdev [Quantum dimer model for the pseudogap metal, Proc. Natl. Acad. Sci. U.S.A. 112, 9552 (2015)., 10.1073/pnas.1512206112], which features ordinary bosonic spin-singlet dimers as well as fermionic dimers that can be viewed as bound states of spinons and holons in a hole-doped resonating valence bond liquid. Interestingly, this model captures several essential properties of the metallic pseudogap phase in high-Tc cuprate superconductors. We identify a line in parameter space where the exact ground state wave functions can be constructed at an arbitrary density of fermionic dimers. At this exactly solvable line the ground state has a huge degeneracy, which can be interpreted as a flat band of fermionic excitations. Perturbing around the exactly solvable line, this degeneracy is lifted and the ground state is a fractionalized Fermi liquid with a small pocket Fermi surface in the low doping limit.

Exact representation of the asymptotic drift speed and diffusion matrix for a class of velocity-jump processes

NASA Astrophysics Data System (ADS)

Mascia, Corrado

2016-01-01

This paper examines a class of linear hyperbolic systems which generalizes the Goldstein-Kac model to an arbitrary finite number of speeds vi with transition rates μij. Under the basic assumptions that the transition matrix is symmetric and irreducible, and the differences vi -vj generate all the space, the system exhibits a large-time behavior described by a parabolic advection-diffusion equation. The main contribution is to determine explicit formulas for the asymptotic drift speed and diffusion matrix in term of the kinetic parameters vi and μij, establishing a complete connection between microscopic and macroscopic coefficients. It is shown that the drift speed is the arithmetic mean of the velocities vi. The diffusion matrix has a more complicate representation, based on the graph with vertices the velocities vi and arcs weighted by the transition rates μij. The approach is based on an exhaustive analysis of the dispersion relation and on the application of a variant of the Kirchoff's matrix tree Theorem from graph theory.

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.

The exact solution of the monoenergetic transport equation for critical cylinders

NASA Technical Reports Server (NTRS)

Westfall, R. M.; Metcalf, D. R.

1972-01-01

An analytic solution for the critical, monoenergetic, bare, infinite cylinder is presented. The solution is obtained by modifying a previous development based on a neutron density transform and Case's singular eigenfunction method. Numerical results for critical radii and the neutron density as a function of position are included and compared with the results of other methods.

Numerical study of incommensurate and decoupled phases of spin-1/2 chains with isotropic exchange J 1, J 2 between first and second neighbors

NASA Astrophysics Data System (ADS)

Soos, Zoltán G.; Parvej, Aslam; Kumar, Manoranjan

2016-05-01

The spin-1/2 chain with isotropic exchange J 1, J 2  >  0 between first and second neighbors is frustrated for either sign of J 1 and has a singlet ground state (GS) for J 1/J 2  ⩾  -4. Its rich quantum phase diagram supports gapless, gapped, commensurate (C), incommensurate (IC) and other phases. Critical points J 1/J 2 are evaluated using exact diagonalization and density matrix renormalization group calculations. The wave vector q G of spin correlations is related to GS degeneracy and obtained as the peak of the spin structure factor S(q). Variable q G indicates IC phases in two J 1/J 2 intervals, [-4, -  1.24] and [0.44, 2], and a C-IC point at J 1/J 2  =  2. The decoupled C phase in [-1.24, 0.44] has constant q G  =  π/2, nondegenerate GS, and a lowest triplet state with broken spin density on sublattices of odd and even numbered sites. The lowest triplet and singlet excitations, E m and E σ , are degenerate in finite systems at specific frustration J 1/J 2. Level crossing extrapolates in the thermodynamic limit to the same critical points as q G. The S(q) peak diverges at q G  =  π in the gapless phase with J 1/J 2  >  4.148 and quasi-long-range order (QLRO(π)). S(q) diverges at  ±π/2 in the decoupled phase with QLRO(π/2), but is finite in gapped phases with finite-range correlations. Numerical results and field theory agree at small J 2/J 1 but disagree for the decoupled phase with weak exchange J 1 between sublattices. Two related models are summarized: one has an exact gapless decoupled phase with QLRO(π/2) and no IC phases; the other has a single IC phase without a decoupled phase in between.

Adhesion of Mineral and Soot Aerosols can Strongly Affect their Scattering and Absorption Properties

NASA Technical Reports Server (NTRS)

Mishchenko, Michael I.; Dlugach, Jana M.

2012-01-01

We use the numerically exact superposition T-matrix method to compute the optical cross sections and the Stokes scattering matrix for polydisperse mineral aerosols (modeled as homogeneous spheres) covered with a large number of much smaller soot particles. These results are compared with the Lorenz-Mie results for a uniform external mixture of mineral and soot aerosols. We show that the effect of soot particles adhering to large mineral particles can be to change the extinction and scattering cross sections and the asymmetry parameter quite substantially. The effect on the phase function and degree of linear polarization can be equally significant.

Capacity of a quantum memory channel correlated by matrix product states

NASA Astrophysics Data System (ADS)

Mulherkar, Jaideep; Sunitha, V.

2018-04-01

We study the capacity of a quantum channel where channel acts like controlled phase gate with the control being provided by a one-dimensional quantum spin chain environment. Due to the correlations in the spin chain, we get a quantum channel with memory. We derive formulas for the quantum capacity of this channel when the spin state is a matrix product state. Particularly, we derive exact formulas for the capacity of the quantum memory channel when the environment state is the ground state of the AKLT model and the Majumdar-Ghosh model. We find that the behavior of the capacity for the range of the parameters is analytic.

Exact solution of some linear matrix equations using algebraic methods

NASA Technical Reports Server (NTRS)

Djaferis, T. E.; Mitter, S. K.

1977-01-01

A study is done of solution methods for Linear Matrix Equations including Lyapunov's equation, using methods of modern algebra. The emphasis is on the use of finite algebraic procedures which are easily implemented on a digital computer and which lead to an explicit solution to the problem. The action f sub BA is introduced a Basic Lemma is proven. The equation PA + BP = -C as well as the Lyapunov equation are analyzed. Algorithms are given for the solution of the Lyapunov and comment is given on its arithmetic complexity. The equation P - A'PA = Q is studied and numerical examples are given.

Rapid motif compliance scoring with match weight sets.

PubMed

Venezia, D; O'Hara, P J

1993-02-01

Most current implementations of motif matching in biological sequences have sacrificed the generality of weight matrix scoring for shorter runtimes. The program MOTIF incorporates a weight matrix and a rapid, backtracking tree-search algorithm to score motif compliance with greatly enhanced performance while placing no constraints on the motif. In addition, any positions within a motif can be marked as 'inviolate', thereby requiring an exact match. MOTIF allows a choice of regular expression formats and can use both motif and sequence libraries as either targets or queries. Nucleic acid sequences can optionally be translated by MOTIF in any frame(s) and used against peptide motifs.

Manipulator control by exact linearization

NASA Technical Reports Server (NTRS)

Kruetz, K.

1987-01-01

Comments on the application to rigid link manipulators of geometric control theory, resolved acceleration control, operational space control, and nonlinear decoupling theory are given, and the essential unity of these techniques for externally linearizing and decoupling end effector dynamics is discussed. Exploiting the fact that the mass matrix of a rigid link manipulator is positive definite, a consequence of rigid link manipulators belonging to the class of natural physical systems, it is shown that a necessary and sufficient condition for a locally externally linearizing and output decoupling feedback law to exist is that the end effector Jacobian matrix be nonsingular. Furthermore, this linearizing feedback is easy to produce.

An improved exceedance theory for combined random stresses

NASA Technical Reports Server (NTRS)

Lester, H. C.

1974-01-01

An extension is presented of Rice's classic solution for the exceedances of a constant level by a single random process to its counterpart for an n-dimensional vector process. An interaction boundary, analogous to the constant level considered by Rice for the one-dimensional case, is assumed in the form of a hypersurface. The theory for the numbers of boundary exceedances is developed by using a joint statistical approach which fully accounts for all cross-correlation effects. An exact expression is derived for the n-dimensional exceedance density function, which is valid for an arbitrary interaction boundary. For application to biaxial states of combined random stress, the general theory is reduced to the two-dimensional case. An elliptical stress interaction boundary is assumed and the exact expression for the density function is presented. The equations are expressed in a format which facilitates calculating the exceedances by numerically evaluating a line integral. The behavior of the density function for the two-dimensional case is briefly discussed.

Chiral density wave versus pion condensation at finite density and zero temperature

NASA Astrophysics Data System (ADS)

Andersen, Jens O.; Kneschke, Patrick

2018-04-01

The quark-meson model is often used as a low-energy effective model for QCD to study the chiral transition at finite temperature T , baryon chemical potential μB , and isospin chemical potential μI . We determine the parameters of the model by matching the meson and quark masses, as well as the pion decay constant to their physical values using the on shell (OS) and modified minimal subtraction (MS ¯ ) schemes. In this paper, the existence of different phases at zero temperature is studied. In particular, we investigate the competition between an inhomogeneous chiral condensate and a homogeneous pion condensate. For the inhomogeneity, we use a chiral-density wave ansatz. For a sigma mass of 600 MeV, we find that an inhomogeneous chiral condensate exists only for pion masses below approximately 37 MeV. We also show that due to our parameter fixing, the onset of pion condensation takes place exactly at μIc=1/2 mπ in accordance with exact results.

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.

MOVES-Matrix and distributed computing for microscale line source dispersion analysis.

PubMed

Liu, Haobing; Xu, Xiaodan; Rodgers, Michael O; Xu, Yanzhi Ann; Guensler, Randall L

2017-07-01

MOVES and AERMOD are the U.S. Environmental Protection Agency's recommended models for use in project-level transportation conformity and hot-spot analysis. However, the structure and algorithms involved in running MOVES make analyses cumbersome and time-consuming. Likewise, the modeling setup process, including extensive data requirements and required input formats, in AERMOD lead to a high potential for analysis error in dispersion modeling. This study presents a distributed computing method for line source dispersion modeling that integrates MOVES-Matrix, a high-performance emission modeling tool, with the microscale dispersion models CALINE4 and AERMOD. MOVES-Matrix was prepared by iteratively running MOVES across all possible iterations of vehicle source-type, fuel, operating conditions, and environmental parameters to create a huge multi-dimensional emission rate lookup matrix. AERMOD and CALINE4 are connected with MOVES-Matrix in a distributed computing cluster using a series of Python scripts. This streamlined system built on MOVES-Matrix generates exactly the same emission rates and concentration results as using MOVES with AERMOD and CALINE4, but the approach is more than 200 times faster than using the MOVES graphical user interface. Because AERMOD requires detailed meteorological input, which is difficult to obtain, this study also recommends using CALINE4 as a screening tool for identifying the potential area that may exceed air quality standards before using AERMOD (and identifying areas that are exceedingly unlikely to exceed air quality standards). CALINE4 worst case method yields consistently higher concentration results than AERMOD for all comparisons in this paper, as expected given the nature of the meteorological data employed. The paper demonstrates a distributed computing method for line source dispersion modeling that integrates MOVES-Matrix with the CALINE4 and AERMOD. This streamlined system generates exactly the same emission rates and concentration results as traditional way to use MOVES with AERMOD and CALINE4, which are regulatory models approved by the U.S. EPA for conformity analysis, but the approach is more than 200 times faster than implementing the MOVES model. We highlighted the potentially significant benefit of using CALINE4 as screening tool for identifying potential area that may exceeds air quality standards before using AERMOD, which requires much more meteorology input than CALINE4.

Systematics in lensing reconstruction: dark matter rings in the sky?

NASA Astrophysics Data System (ADS)

Ponente, P. P.; Diego, J. M.

2011-11-01

Context. Non-parametric lensing methods are a useful way of reconstructing the lensing mass of a cluster without making assumptions about the way the mass is distributed in the cluster. These methods are particularly powerful in the case of galaxy clusters with a large number of constraints. The advantage of not assuming implicitly that the luminous matter follows the dark matter is particularly interesting in those cases where the cluster is in a non-relaxed dynamical state. On the other hand, non-parametric methods have several limitations that should be taken into account carefully. Aims: We explore some of these limitations and focus on their implications for the possible ring of dark matter around the galaxy cluster CL0024+17. Methods: We project three background galaxies through a mock cluster of known radial profile density and obtain a map for the arcs (θ map). We also calculate the shear field associated with the mock cluster across the whole field of view (3.3 arcmin). Combining the positions of the arcs and the two-direction shear, we perform an inversion of the lens equation using two separate methods, the biconjugate gradient, and the quadratic programming (QADP) to reconstruct the convergence map of the mock cluster. Results: We explore the space of the solutions of the convergence map and compare the radial density profiles to the density profile of the mock cluster. When the inversion matrix algorithms are forced to find the exact solution, we encounter systematic effects resembling ring structures, that clearly depart from the original convergence map. Conclusions: Overfitting lensing data with a non-parametric method can produce ring-like structures similar to the alleged one in CL0024.