Sparse polynomial space approach to dissipative quantum systems: application to the sub-ohmic spin-boson model.

PubMed

Alvermann, A; Fehske, H

2009-04-17

We propose a general numerical approach to open quantum systems with a coupling to bath degrees of freedom. The technique combines the methodology of polynomial expansions of spectral functions with the sparse grid concept from interpolation theory. Thereby we construct a Hilbert space of moderate dimension to represent the bath degrees of freedom, which allows us to perform highly accurate and efficient calculations of static, spectral, and dynamic quantities using standard exact diagonalization algorithms. The strength of the approach is demonstrated for the phase transition, critical behavior, and dissipative spin dynamics in the spin-boson model.

Exact solution of the XXX Gaudin model with generic open boundaries

NASA Astrophysics Data System (ADS)

Hao, Kun; Cao, Junpeng; Yang, Tao; Yang, Wen-Li

2015-03-01

The XXX Gaudin model with generic integrable open boundaries specified by the most general non-diagonal reflecting matrices is studied. Besides the inhomogeneous parameters, the associated Gaudin operators have six free parameters which break the U(1) -symmetry. With the help of the off-diagonal Bethe ansatz, we successfully obtained the eigenvalues of these Gaudin operators and the corresponding Bethe ansatz equations.

Reducing Memory Cost of Exact Diagonalization using Singular Value Decomposition

NASA Astrophysics Data System (ADS)

Weinstein, Marvin; Chandra, Ravi; Auerbach, Assa

2012-02-01

We present a modified Lanczos algorithm to diagonalize lattice Hamiltonians with dramatically reduced memory requirements. In contrast to variational approaches and most implementations of DMRG, Lanczos rotations towards the ground state do not involve incremental minimizations, (e.g. sweeping procedures) which may get stuck in false local minima. The lattice of size N is partitioned into two subclusters. At each iteration the rotating Lanczos vector is compressed into two sets of nsvd small subcluster vectors using singular value decomposition. For low entanglement entropy See, (satisfied by short range Hamiltonians), the truncation error is bounded by (-nsvd^1/See). Convergence is tested for the Heisenberg model on Kagom'e clusters of 24, 30 and 36 sites, with no lattice symmetries exploited, using less than 15GB of dynamical memory. Generalization of the Lanczos-SVD algorithm to multiple partitioning is discussed, and comparisons to other techniques are given. Reference: arXiv:1105.0007

An exact variational method to calculate rovibrational spectra of polyatomic molecules with large amplitude motion

NASA Astrophysics Data System (ADS)

Yu, Hua-Gen

2016-08-01

We report a new full-dimensional variational algorithm to calculate rovibrational spectra of polyatomic molecules using an exact quantum mechanical Hamiltonian. The rovibrational Hamiltonian of system is derived in a set of orthogonal polyspherical coordinates in the body-fixed frame. It is expressed in an explicitly Hermitian form. The Hamiltonian has a universal formulation regardless of the choice of orthogonal polyspherical coordinates and the number of atoms in molecule, which is suitable for developing a general program to study the spectra of many polyatomic systems. An efficient coupled-state approach is also proposed to solve the eigenvalue problem of the Hamiltonian using a multi-layer Lanczos iterative diagonalization approach via a set of direct product basis set in three coordinate groups: radial coordinates, angular variables, and overall rotational angles. A simple set of symmetric top rotational functions is used for the overall rotation whereas a potential-optimized discrete variable representation method is employed in radial coordinates. A set of contracted vibrationally diabatic basis functions is adopted in internal angular variables. Those diabatic functions are first computed using a neural network iterative diagonalization method based on a reduced-dimension Hamiltonian but only once. The final rovibrational energies are computed using a modified Lanczos method for a given total angular momentum J, which is usually fast. Two numerical applications to CH4 and H2CO are given, together with a comparison with previous results.

An exact variational method to calculate rovibrational spectra of polyatomic molecules with large amplitude motion

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

Yu, Hua-Gen, E-mail: hgy@bnl.gov

We report a new full-dimensional variational algorithm to calculate rovibrational spectra of polyatomic molecules using an exact quantum mechanical Hamiltonian. The rovibrational Hamiltonian of system is derived in a set of orthogonal polyspherical coordinates in the body-fixed frame. It is expressed in an explicitly Hermitian form. The Hamiltonian has a universal formulation regardless of the choice of orthogonal polyspherical coordinates and the number of atoms in molecule, which is suitable for developing a general program to study the spectra of many polyatomic systems. An efficient coupled-state approach is also proposed to solve the eigenvalue problem of the Hamiltonian using amore » multi-layer Lanczos iterative diagonalization approach via a set of direct product basis set in three coordinate groups: radial coordinates, angular variables, and overall rotational angles. A simple set of symmetric top rotational functions is used for the overall rotation whereas a potential-optimized discrete variable representation method is employed in radial coordinates. A set of contracted vibrationally diabatic basis functions is adopted in internal angular variables. Those diabatic functions are first computed using a neural network iterative diagonalization method based on a reduced-dimension Hamiltonian but only once. The final rovibrational energies are computed using a modified Lanczos method for a given total angular momentum J, which is usually fast. Two numerical applications to CH{sub 4} and H{sub 2}CO are given, together with a comparison with previous results.« less

sdg Interacting boson hamiltonian in the seniority scheme

NASA Astrophysics Data System (ADS)

Yoshinaga, N.

1989-03-01

The sdg interacting boson hamiltonian is derived in the seniority scheme. We use the method of Otsuka, Arima and Iachello in order to derive the boson hamiltonian from the fermion hamiltonian. To examine how good is the boson approximation in the zeroth-order, we carry out the exact shell model calculations in a single j-shell. It is found that almost all low-lying levels are reproduced quite well by diagonalizing the sdg interacting boson hamiltonian in the vibrational case. In the deformed case the introduction of g-bosons improves the reproduction of the spectra and of the binding energies which are obtained by diagonalizing the exact shell model hamiltonian. In particular the sdg interacting boson model reproduces well-developed rotational bands.

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.

Calculated momentum dependence of Zhang-Rice states in transition metal oxides.

PubMed

Yin, Quan; Gordienko, Alexey; Wan, Xiangang; Savrasov, Sergey Y

2008-02-15

Using a combination of local density functional theory and cluster exact diagonalization based dynamical mean field theory, we calculate many-body electronic structures of several Mott insulating oxides including undoped high T(c) materials. The dispersions of the lowest occupied electronic states are associated with the Zhang-Rice singlets in cuprates and with doublets, triplets, quadruplets, and quintets in more general cases. Our results agree with angle resolved photoemission experiments including the decrease of the spectral weight of the Zhang-Rice band as it approaches k=0.

Hubbard physics in the symmetric half-filled periodic anderson-hubbard model

NASA Astrophysics Data System (ADS)

Hagymási, I.; Itai, K.; Sólyom, J.

2013-05-01

Two very different methods — exact diagonalization on finite chains and a variational method — are used to study the possibility of a metal-insulator transition in the symmetric half-filled periodic Anderson-Hubbard model. With this aim we calculate the density of doubly occupied d sites ( gn d ) as a function of various parameters. In the absence of on-site Coulomb interaction ( U f ) between f electrons, the two methods yield similar results. The double occupancy of d levels remains always finite just as in the one-dimensional Hubbard model. Exact diagonalization on finite chains gives the same result for finite U f , while the Gutzwiller method leads to a Brinkman-Rice transition at a critical value ( U {/d c }), which depends on U f and V.

Exact finite volume expectation values of local operators in excited states

NASA Astrophysics Data System (ADS)

Pozsgay, B.; Szécsényi, I. M.; Takács, G.

2015-04-01

We present a conjecture for the exact expression of finite volume expectation values in excited states in integrable quantum field theories, which is an extension of an earlier conjecture to the case of general diagonal factorized scattering with bound states and a nontrivial bootstrap structure. The conjectured expression is a spectral expansion which uses the exact form factors and the excited state thermodynamic Bethe Ansatz as building blocks. The conjecture is proven for the case of the trace of the energy-moment tensor. Concerning its validity for more general operators, we provide numerical evidence using the truncated conformal space approach. It is found that the expansion fails to be well-defined for small values of the volume in cases when the singularity structure of the TBA equations undergoes a non-trivial rearrangement under some critical value of the volume. Despite these shortcomings, the conjectured expression is expected to be valid for all volumes for most of the excited states, and as an expansion above the critical volume for the rest.

Construction of exact constants of motion and effective models for many-body localized systems

NASA Astrophysics Data System (ADS)

Goihl, M.; Gluza, M.; Krumnow, C.; Eisert, J.

2018-04-01

One of the defining features of many-body localization is the presence of many quasilocal conserved quantities. These constants of motion constitute a cornerstone to an intuitive understanding of much of the phenomenology of many-body localized systems arising from effective Hamiltonians. They may be seen as local magnetization operators smeared out by a quasilocal unitary. However, accurately identifying such constants of motion remains a challenging problem. Current numerical constructions often capture the conserved operators only approximately, thus restricting a conclusive understanding of many-body localization. In this work, we use methods from the theory of quantum many-body systems out of equilibrium to establish an alternative approach for finding a complete set of exact constants of motion which are in addition guaranteed to represent Pauli-z operators. By this we are able to construct and investigate the proposed effective Hamiltonian using exact diagonalization. Hence, our work provides an important tool expected to further boost inquiries into the breakdown of transport due to quenched disorder.

Semiclassical description of resonance-assisted tunneling in one-dimensional integrable models

NASA Astrophysics Data System (ADS)

Le Deunff, Jérémy; Mouchet, Amaury; Schlagheck, Peter

2013-10-01

Resonance-assisted tunneling is investigated within the framework of one-dimensional integrable systems. We present a systematic recipe, based on Hamiltonian normal forms, to construct one-dimensional integrable models that exhibit resonance island chain structures with accurately controlled sizes and positions of the islands. Using complex classical trajectories that evolve along suitably defined paths in the complex time domain, we construct a semiclassical theory of the resonance-assisted tunneling process. This semiclassical approach yields a compact analytical expression for tunnelling-induced level splittings which is found to be in very good agreement with the exact splittings obtained through numerical diagonalization.

Comparative DMFT study of the eg-orbital Hubbard model in thin films

NASA Astrophysics Data System (ADS)

Rüegg, Andreas; Hung, Hsiang-Hsuan; Gull, Emanuel; Fiete, Gregory A.

2014-02-01

Heterostructures of transition-metal oxides have emerged as a new route to engineer electronic systems with desired functionalities. Motivated by these developments, we study a two-orbital Hubbard model in a thin-film geometry confined along the cubic [001] direction using the dynamical mean-field theory. We contrast the results of two approximate impurity solvers (exact diagonalization and one-crossing approximation) to the results of the numerically exact continuous-time quantum Monte Carlo solver. Consistent with earlier studies, we find that the one-crossing approximation performs well in the insulating regime, while the advantage of the exact-diagonalization-based solver is more pronounced in the metallic regime. We then investigate various aspects of strongly correlated eg-orbital systems in thin-film geometries. In particular, we show how the interfacial orbital polarization dies off quickly a few layers from the interface and how the film thickness affects the location of the interaction-driven Mott transition. In addition, we explore the changes in the electronic structure with varying carrier concentration and identify large variations of the orbital polarization in the strongly correlated regime.

Studying relaxation phenomena via effective master equations

NASA Astrophysics Data System (ADS)

Chan, David; Wan, Jones T. K.; Chu, L. L.; Yu, K. W.

2000-04-01

The real-time dynamics of various relaxation phenomena can be conveniently formulated by a master equation with the enumeration of transition rates between given classes of conformations. To study the relaxation time towards equilibrium, it suffices to solve for the second largest eigenvalue of the resulting eigenvalue equation. Generally speaking, there is no analytic solution for the dynamic equation. Mean-field approaches generally yield misleading results while the presumably exact Monte-Carlo methods require prohibitive time steps in most real systems. In this work, we propose an exact decimation procedure for reducing the number of conformations significantly, while there is no loss of information, i.e., the reduced (or effective) equation is an exact transformed version of the original one. However, we have to pay the price: the initial Markovianity of the evolution equation is lost and the reduced equation contains memory terms in the transition rates. Since the transformed equation has significantly reduced number of degrees of freedom, the systems can readily be diagonalized by iterative means, to obtain the exact second largest eigenvalue and hence the relaxation time. The decimation method has been applied to various relaxation equations with generally desirable results. The advantages and limitations of the method will be discussed.

Morse oscillator propagator in the high temperature limit I: Theory

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

Toutounji, Mohamad, E-mail: Mtoutounji@uaeu.ac.ae

2017-02-15

In an earlier work of the author the time evolution of Morse oscillator was studied analytically and exactly at low temperatures whereupon optical correlation functions were calculated using Morse oscillator coherent states were employed. Morse oscillator propagator in the high temperature limit is derived and a closed form of its corresponding canonical partition function is obtained. Both diagonal and off-diagonal forms of Morse oscillator propagator are derived in the high temperature limit. Partition functions of diatomic molecules are calculated. - Highlights: • Derives the quantum propagator of Morse oscillator in the high temperature limit. • Uses the resulting diagonal propagatormore » to derive a closed form of Morse oscillator partition function. • Provides a more sophisticated formula of the quantum propagator to test the accuracy of the herein results.« less

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.

Line Interference Effects Using a Refined Robert-Bonamy Formalism: the Test Case of the Isotropic Raman Spectra of Autoperturbed N2

NASA Technical Reports Server (NTRS)

Boulet, Christian; Ma, Qiancheng; Thibault, Franck

2014-01-01

A symmetrized version of the recently developed refined Robert-Bonamy formalism [Q. Ma, C. Boulet, and R. H. Tipping, J. Chem. Phys. 139, 034305 (2013)] is proposed. This model takes into account line coupling effects and hence allows the calculation of the off-diagonal elements of the relaxation matrix, without neglecting the rotational structure of the perturbing molecule. The formalism is applied to the isotropic Raman spectra of autoperturbed N2 for which a benchmark quantum relaxation matrix has recently been proposed. The consequences of the classical path approximation are carefully analyzed. Methods correcting for effects of inelasticity are considered. While in the right direction, these corrections appear to be too crude to provide off diagonal elements which would yield, via the sum rule, diagonal elements in good agreement with the quantum results. In order to overcome this difficulty, a re-normalization procedure is applied, which ensures that the off-diagonal elements do lead to the exact quantum diagonal elements. The agreement between the (re-normalized) semi-classical and quantum relaxation matrices is excellent, at least for the Raman spectra of N2, opening the way to the analysis of more complex molecular systems.

Efficient implementation of one- and two-component analytical energy gradients in exact two-component theory

NASA Astrophysics Data System (ADS)

Franzke, Yannick J.; Middendorf, Nils; Weigend, Florian

2018-03-01

We present an efficient algorithm for one- and two-component analytical energy gradients with respect to nuclear displacements in the exact two-component decoupling approach to the one-electron Dirac equation (X2C). Our approach is a generalization of the spin-free ansatz by Cheng and Gauss [J. Chem. Phys. 135, 084114 (2011)], where the perturbed one-electron Hamiltonian is calculated by solving a first-order response equation. Computational costs are drastically reduced by applying the diagonal local approximation to the unitary decoupling transformation (DLU) [D. Peng and M. Reiher, J. Chem. Phys. 136, 244108 (2012)] to the X2C Hamiltonian. The introduced error is found to be almost negligible as the mean absolute error of the optimized structures amounts to only 0.01 pm. Our implementation in TURBOMOLE is also available within the finite nucleus model based on a Gaussian charge distribution. For a X2C/DLU gradient calculation, computational effort scales cubically with the molecular size, while storage increases quadratically. The efficiency is demonstrated in calculations of large silver clusters and organometallic iridium complexes.

Time-dependent Gutzwiller theory of magnetic excitations in the Hubbard model

NASA Astrophysics Data System (ADS)

Seibold, G.; Becca, F.; Rubin, P.; Lorenzana, J.

2004-04-01

We use a spin-rotational invariant Gutzwiller energy functional to compute random-phase-approximation-like (RPA) fluctuations on top of the Gutzwiller approximation (GA). The method can be viewed as an extension of the previously developed GA+RPA approach for the charge sector [G. Seibold and J. Lorenzana, Phys. Rev. Lett. 86, 2605 (2001)] with respect to the inclusion of the magnetic excitations. Unlike the charge case, no assumptions about the time evolution of the double occupancy are needed in this case. Interestingly, in a spin-rotational invariant system, we find the correct degeneracy between triplet excitations, showing the consistency of both computations. Since no restrictions are imposed on the symmetry of the underlying saddle-point solution, our approach is suitable for the evaluation of the magnetic susceptibility and dynamical structure factor in strongly correlated inhomogeneous systems. We present a detailed study of the quality of our approach by comparing with exact diagonalization results and show its much higher accuracy compared to the conventional Hartree-Fock+RPA theory. In infinite dimensions, where the GA becomes exact for the Gutzwiller variational energy, we evaluate ferromagnetic and antiferromagnetic instabilities from the transverse magnetic susceptibility. The resulting phase diagram is in complete agreement with previous variational computations.

Quantum Entanglement and the Topological Order of Fractional Hall States

NASA Astrophysics Data System (ADS)

Rezayi, Edward

2015-03-01

Fractional quantum Hall states or, more generally, topological phases of matter defy Landau classification based on order parameter and broken symmetry. Instead they have been characterized by their topological order. Quantum information concepts, such as quantum entanglement, appear to provide the most efficient method of detecting topological order solely from the knowledge of the ground state wave function. This talk will focus on real-space bi-partitioning of quantum Hall states and will present both exact diagonalization and quantum Monte Carlo studies of topological entanglement entropy in various geometries. Results on the torus for non-contractible cuts are quite rich and, through the use of minimum entropy states, yield the modular S-matrix and hence uniquely determine the topological order, as shown in recent literature. Concrete examples of minimum entropy states from known quantum Hall wave functions and their corresponding quantum numbers, used in exact diagonalizations, will be given. In collaboration with Clare Abreu and Raul Herrera. Supported by DOE Grant DE-SC0002140.

Polaron dynamics with a multitude of Davydov D{sub 2} trial states

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

Zhou, Nengji; Department of Physics, Hangzhou Normal University, Hangzhou 310046; Huang, Zhongkai

2015-07-07

We propose an extension to the Davydov D{sub 2} Ansatz in the dynamics study of the Holstein molecular crystal model with diagonal and off-diagonal exciton-phonon coupling using the Dirac-Frenkel time-dependent variational principle. The new trial state by the name of the “multi-D{sub 2} Ansatz” is a linear combination of Davydov D{sub 2} trial states, and its validity is carefully examined by quantifying how faithfully it follows the Schrödinger equation. Considerable improvements in accuracy have been demonstrated in comparison with the usual Davydov trial states, i.e., the single D{sub 1} and D{sub 2} Ansätze. With an increase in the number ofmore » the Davydov D{sub 2} trial states in the multi-D{sub 2} Ansatz, deviation from the exact Schrödinger dynamics is gradually diminished, leading to a numerically exact solution to the Schrödinger equation.« less

Detecting many-body-localization lengths with cold atoms

NASA Astrophysics Data System (ADS)

Guo, Xuefei; Li, Xiaopeng

2018-03-01

Considering ultracold atoms in optical lattices, we propose experimental protocols to study many-body-localization (MBL) length and criticality in quench dynamics. Through numerical simulations with exact diagonalization, we show that in the MBL phase the perturbed density profile following a local quench remains exponentially localized in postquench dynamics. The size of this density profile after long-time-dynamics defines a localization length, which tends to diverge at the MBL-to-ergodic transition as we increase the system size. The determined localization transition point agrees with previous exact diagonalization calculations using other diagnostics. Our numerical results provide evidence for violation of the Harris-Chayes bound for the MBL criticality. The critical exponent ν can be extracted from our proposed dynamical procedure, which can then be used directly in experiments to determine whether the Harris-Chayes-bound holds for the MBL transition. These proposed protocols to detect localization criticality are justified by benchmarking to the well-established results for the noninteracting three-dimensional Anderson localization.

Line interference effects using a refined Robert-Bonamy formalism: The test case of the isotropic Raman spectra of autoperturbed N{sub 2}

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

Boulet, Christian, E-mail: Christian.boulet@u-psud.fr; Ma, Qiancheng; Thibault, Franck

A symmetrized version of the recently developed refined Robert-Bonamy formalism [Q. Ma, C. Boulet, and R. H. Tipping, J. Chem. Phys. 139, 034305 (2013)] is proposed. This model takes into account line coupling effects and hence allows the calculation of the off-diagonal elements of the relaxation matrix, without neglecting the rotational structure of the perturbing molecule. The formalism is applied to the isotropic Raman spectra of autoperturbed N{sub 2} for which a benchmark quantum relaxation matrix has recently been proposed. The consequences of the classical path approximation are carefully analyzed. Methods correcting for effects of inelasticity are considered. While inmore » the right direction, these corrections appear to be too crude to provide off diagonal elements which would yield, via the sum rule, diagonal elements in good agreement with the quantum results. In order to overcome this difficulty, a re-normalization procedure is applied, which ensures that the off-diagonal elements do lead to the exact quantum diagonal elements. The agreement between the (re-normalized) semi-classical and quantum relaxation matrices is excellent, at least for the Raman spectra of N{sub 2}, opening the way to the analysis of more complex molecular systems.« less

Log-Linear Modeling of Agreement among Expert Exposure Assessors

PubMed Central

Hunt, Phillip R.; Friesen, Melissa C.; Sama, Susan; Ryan, Louise; Milton, Donald

2015-01-01

Background: Evaluation of expert assessment of exposure depends, in the absence of a validation measurement, upon measures of agreement among the expert raters. Agreement is typically measured using Cohen’s Kappa statistic, however, there are some well-known limitations to this approach. We demonstrate an alternate method that uses log-linear models designed to model agreement. These models contain parameters that distinguish between exact agreement (diagonals of agreement matrix) and non-exact associations (off-diagonals). In addition, they can incorporate covariates to examine whether agreement differs across strata. Methods: We applied these models to evaluate agreement among expert ratings of exposure to sensitizers (none, likely, high) in a study of occupational asthma. Results: Traditional analyses using weighted kappa suggested potential differences in agreement by blue/white collar jobs and office/non-office jobs, but not case/control status. However, the evaluation of the covariates and their interaction terms in log-linear models found no differences in agreement with these covariates and provided evidence that the differences observed using kappa were the result of marginal differences in the distribution of ratings rather than differences in agreement. Differences in agreement were predicted across the exposure scale, with the likely moderately exposed category more difficult for the experts to differentiate from the highly exposed category than from the unexposed category. Conclusions: The log-linear models provided valuable information about patterns of agreement and the structure of the data that were not revealed in analyses using kappa. The models’ lack of dependence on marginal distributions and the ease of evaluating covariates allow reliable detection of observational bias in exposure data. PMID:25748517

Relativistic energy-dispersion relations of 2D rectangular lattices

NASA Astrophysics Data System (ADS)

Ata, Engin; Demirhan, Doğan; Büyükkılıç, Fevzi

2017-04-01

An exactly solvable relativistic approach based on inseparable periodic well potentials is developed to obtain energy-dispersion relations of spin states of a single-electron in two-dimensional (2D) rectangular lattices. Commutation of axes transfer matrices is exploited to find energy dependencies of the wave vector components. From the trace of the lattice transfer matrix, energy-dispersion relations of conductance and valence states are obtained in transcendental form. Graphical solutions of relativistic and nonrelativistic transcendental energy-dispersion relations are plotted to compare how lattice parameters V0, core and interstitial size of the rectangular lattice affects to the energy-band structures in a situation core and interstitial diagonals are of equal slope.

Phase transition in one Josephson junction with a side-coupled magnetic impurity

NASA Astrophysics Data System (ADS)

Zhi, Li-Ming; Wang, Xiao-Qi; Jiang, Cui; Yi, Guang-Yu; Gong, Wei-Jiang

2018-04-01

This work focuses on one Josephson junction with a side-coupled magnetic impurity. And then, the Josephson phase transition is theoretically investigated, with the help of the exact diagonalization approach. It is found that even in the absence of intradot Coulomb interaction, the magnetic impurity can efficiently induce the phenomenon of Josephson phase transition, which is tightly related to the spin correlation manners (i.e., ferromagnetic or antiferromagnetic) between the impurity and the junction. Moreover, the impurity plays different roles when it couples to the dot and superconductor, respectively. This work can be helpful in describing the influence of one magnetic impurity on the supercurrent through the Josephson junction.

Large-scale exact diagonalizations reveal low-momentum scales of nuclei

NASA Astrophysics Data System (ADS)

Forssén, C.; Carlsson, B. D.; Johansson, H. T.; Sääf, D.; Bansal, A.; Hagen, G.; Papenbrock, T.

2018-03-01

Ab initio methods aim to solve the nuclear many-body problem with controlled approximations. Virtually exact numerical solutions for realistic interactions can only be obtained for certain special cases such as few-nucleon systems. Here we extend the reach of exact diagonalization methods to handle model spaces with dimension exceeding 1010 on a single compute node. This allows us to perform no-core shell model (NCSM) calculations for 6Li in model spaces up to Nmax=22 and to reveal the 4He+d halo structure of this nucleus. Still, the use of a finite harmonic-oscillator basis implies truncations in both infrared (IR) and ultraviolet (UV) length scales. These truncations impose finite-size corrections on observables computed in this basis. We perform IR extrapolations of energies and radii computed in the NCSM and with the coupled-cluster method at several fixed UV cutoffs. It is shown that this strategy enables information gain also from data that is not fully UV converged. IR extrapolations improve the accuracy of relevant bound-state observables for a range of UV cutoffs, thus making them profitable tools. We relate the momentum scale that governs the exponential IR convergence to the threshold energy for the first open decay channel. Using large-scale NCSM calculations we numerically verify this small-momentum scale of finite nuclei.

A numerical projection technique for large-scale eigenvalue problems

NASA Astrophysics Data System (ADS)

Gamillscheg, Ralf; Haase, Gundolf; von der Linden, Wolfgang

2011-10-01

We present a new numerical technique to solve large-scale eigenvalue problems. It is based on the projection technique, used in strongly correlated quantum many-body systems, where first an effective approximate model of smaller complexity is constructed by projecting out high energy degrees of freedom and in turn solving the resulting model by some standard eigenvalue solver. Here we introduce a generalization of this idea, where both steps are performed numerically and which in contrast to the standard projection technique converges in principle to the exact eigenvalues. This approach is not just applicable to eigenvalue problems encountered in many-body systems but also in other areas of research that result in large-scale eigenvalue problems for matrices which have, roughly speaking, mostly a pronounced dominant diagonal part. We will present detailed studies of the approach guided by two many-body models.

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.

Challenges in design of Kitaev materials: Magnetic interactions from competing energy scales

NASA Astrophysics Data System (ADS)

Winter, Stephen M.; Li, Ying; Jeschke, Harald O.; Valentí, Roser

2016-06-01

In this study, we reanalyze the magnetic interactions in the Kitaev spin-liquid candidate materials Na2IrO3,α -RuCl3 , and α -Li2IrO3 using nonperturbative exact diagonalization methods. These methods are more appropriate given the relatively itinerant nature of the systems suggested in previous works. We treat all interactions up to third neighbors on equal footing. The computed terms reveal significant long-range coupling, bond anisotropy, and/or off-diagonal couplings which we argue naturally explain the observed ordered phases in these systems. Given these observations, the potential for realizing the spin-liquid state in real materials is analyzed, and synthetic challenges are defined and explained.

Vaidya spacetime in the diagonal coordinates

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

Berezin, V. A., E-mail: berezin@inr.ac.ru; Dokuchaev, V. I., E-mail: dokuchaev@inr.ac.ru; Eroshenko, Yu. N., E-mail: eroshenko@inr.ac.ru

We have analyzed the transformation from initial coordinates (v, r) of the Vaidya metric with light coordinate v to the most physical diagonal coordinates (t, r). An exact solution has been obtained for the corresponding metric tensor in the case of a linear dependence of the mass function of the Vaidya metric on light coordinate v. In the diagonal coordinates, a narrow region (with a width proportional to the mass growth rate of a black hole) has been detected near the visibility horizon of the Vaidya accreting black hole, in which the metric differs qualitatively from the Schwarzschild metric andmore » cannot be represented as a small perturbation. It has been shown that, in this case, a single set of diagonal coordinates (t, r) is insufficient to cover the entire range of initial coordinates (v, r) outside the visibility horizon; at least three sets of diagonal coordinates are required, the domains of which are separated by singular surfaces on which the metric components have singularities (either g{sub 00} = 0 or g{sub 00} = ∞). The energy–momentum tensor diverges on these surfaces; however, the tidal forces turn out to be finite, which follows from an analysis of the deviation equations for geodesics. Therefore, these singular surfaces are exclusively coordinate singularities that can be referred to as false fire-walls because there are no physical singularities on them. We have also considered the transformation from the initial coordinates to other diagonal coordinates (η, y), in which the solution is obtained in explicit form, and there is no energy–momentum tensor divergence.« less

Two Universality Classes for the Many-Body Localization Transition

NASA Astrophysics Data System (ADS)

Khemani, Vedika; Sheng, D. N.; Huse, David A.

2017-08-01

We provide a systematic comparison of the many-body localization (MBL) transition in spin chains with nonrandom quasiperiodic versus random fields. We find evidence suggesting that these belong to two separate universality classes: the first dominated by "intrinsic" intrasample randomness, and the second dominated by external intersample quenched randomness. We show that the effects of intersample quenched randomness are strongly growing, but not yet dominant, at the system sizes probed by exact-diagonalization studies on random models. Thus, the observed finite-size critical scaling collapses in such studies appear to be in a preasymptotic regime near the nonrandom universality class, but showing signs of the initial crossover towards the external-randomness-dominated universality class. Our results provide an explanation for why exact-diagonalization studies on random models see an apparent scaling near the transition while also obtaining finite-size scaling exponents that strongly violate Harris-Chayes bounds that apply to disorder-driven transitions. We also show that the MBL phase is more stable for the quasiperiodic model as compared to the random one, and the transition in the quasiperiodic model suffers less from certain finite-size effects.

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.

Parallelized traveling cluster approximation to study numerically spin-fermion models on large lattices

NASA Astrophysics Data System (ADS)

Mukherjee, Anamitra; Patel, Niravkumar D.; Bishop, Chris; Dagotto, Elbio

2015-06-01

Lattice spin-fermion models are important to study correlated systems where quantum dynamics allows for a separation between slow and fast degrees of freedom. The fast degrees of freedom are treated quantum mechanically while the slow variables, generically referred to as the "spins," are treated classically. At present, exact diagonalization coupled with classical Monte Carlo (ED + MC) is extensively used to solve numerically a general class of lattice spin-fermion problems. In this common setup, the classical variables (spins) are treated via the standard MC method while the fermion problem is solved by exact diagonalization. The "traveling cluster approximation" (TCA) is a real space variant of the ED + MC method that allows to solve spin-fermion problems on lattice sizes with up to 103 sites. In this publication, we present a novel reorganization of the TCA algorithm in a manner that can be efficiently parallelized. This allows us to solve generic spin-fermion models easily on 104 lattice sites and with some effort on 105 lattice sites, representing the record lattice sizes studied for this family of models.

Spin-1/2 Heisenberg antiferromagnet on the pyrochlore lattice: An exact diagonalization study

NASA Astrophysics Data System (ADS)

Chandra, V. Ravi; Sahoo, Jyotisman

2018-04-01

We present exact diagonalization calculations for the spin-1/2 nearest-neighbor antiferromagnet on the pyrochlore lattice. We study a section of the lattice in the [111] direction and analyze the Hamiltonian of the breathing pyrochlore system with two coupling constants J1 and J2 for tetrahedra of different orientations and investigate the evolution of the system from the limit of disconnected tetrahedra (J2=0 ) to a correlated state at J1=J2 . We evaluate the low-energy spectrum, two and four spin correlations, and spin chirality correlations for a system size of up to 36 sites. The model shows a fast decay of spin correlations and we confirm the presence of several singlet excitations below the lowest magnetic excitation. We find chirality correlations near J1=J2 to be small at the length scales available at this system size. Evaluation of dimer-dimer correlations and analysis of the nature of the entanglement of the tetrahedral unit shows that the triplet sector of the tetrahedron contributes significantly to the ground-state entanglement at J1=J2 .

Light-Enhanced Spin Fluctuations and d -Wave Superconductivity at a Phase Boundary

NASA Astrophysics Data System (ADS)

Wang, Yao; Chen, Cheng-Chien; Moritz, B.; Devereaux, T. P.

2018-06-01

Time-domain techniques have shown the potential of photomanipulating existing orders and inducing new states of matter in strongly correlated materials. Using time-resolved exact diagonalization, we perform numerical studies of pump dynamics in a Mott-Peierls system with competing charge and spin density waves. A light-enhanced d -wave superconductivity is observed when the system resides near a quantum phase boundary. By examining the evolution of spin, charge, and superconducting susceptibilities, we show that a subdominant state in equilibrium can be stabilized by photomanipulating the charge order to allow superconductivity to appear and dominate. This work provides an interpretation of light-induced superconductivity from the perspective of order competition and offers a promising approach for designing novel emergent states out of equilibrium.

Strong spin-orbit effects in transition metal oxides with tetrahedral coordination

NASA Astrophysics Data System (ADS)

Forte, Filomena; Guerra, Delia; Autieri, Carmine; Romano, Alfonso; Noce, Canio; Avella, Adolfo

2018-05-01

To prove that spin-orbit coupling can play a relevant role in determining the magnetic structure of transition metal oxides with tetrahedral coordination, we investigate the d1 Mott insulator KOsO4, combining density functional theory calculations and the exact diagonalization approach. We find that the interplay between crystal field, strong spin-orbit coupling, electronic correlations and structural distortions brings the system towards an antiferromagnetic phase, characterized by a non-vanishing orbital angular momentum and anisotropy among the in-plane and the out-of-plane antiferromagnetic correlations. We also show that, due to the peculiar interplay between spin-orbit coupling, Hund's coupling and hopping connectivity the system is on the verge of developing short range ferromagnetic correlations marked by strong directionality.

Multiparticle instability in a spin-imbalanced Fermi gas

NASA Astrophysics Data System (ADS)

Whitehead, T. M.; Conduit, G. J.

2018-01-01

Weak attractive interactions in a spin-imbalanced Fermi gas induce a multiparticle instability, binding multiple fermions together. The maximum binding energy per particle is achieved when the ratio of the number of up- and down-spin particles in the instability is equal to the ratio of the up- and down-spin densities of states in momentum at the Fermi surfaces, to utilize the variational freedom of all available momentum states. We derive this result using an analytical approach, and verify it using exact diagonalization. The multiparticle instability extends the Cooper pairing instability of balanced Fermi gases to the imbalanced case, and could form the basis of a many-body state, analogously to the construction of the Bardeen-Cooper-Schrieffer theory of superconductivity out of Cooper pairs.

The diagonalization of cubic matrices

NASA Astrophysics Data System (ADS)

Cocolicchio, D.; Viggiano, M.

2000-08-01

This paper is devoted to analysing the problem of the diagonalization of cubic matrices. We extend the familiar algebraic approach which is based on the Cardano formulae. We rewrite the complex roots of the associated resolvent secular equation in terms of transcendental functions and we derive the diagonalizing matrix.

Phase Space Approach to Dynamics of Interacting Fermions

NASA Astrophysics Data System (ADS)

Davidson, Shainen; Sels, Dries; Kasper, Valentin; Polkovnikov, Anatoli

Understanding the behavior of interacting fermions is of fundamental interest in many fields ranging from condensed matter to high energy physics. Developing numerically efficient and accurate simulation methods is an indispensable part of this. Already in equilibrium, fermions are notoriously hard to handle due to the sign problem. Out of equilibrium, an important outstanding problem is the efficient numerical simulation of the dynamics of these systems. In this work we develop a new semiclassical phase-space approach (a.k.a. the truncated Wigner approximation) for simulating the dynamics of interacting lattice fermions in arbitrary dimensions. We demonstrate the strength of the method by comparing the results to exact diagonalization (ED) on small 1D and 2D systems. We furthermore present results on Many-Body Localized (MBL) systems in 1D and 2D, and demonstrate how the method can be used to determine the MBL transition.

Gapless spin excitations in the S = 1 / 2 Kagome- and triangular-lattice Heisenberg antiferromagnets

NASA Astrophysics Data System (ADS)

Sakai, Tôru; Nakano, Hiroki

2018-05-01

The S = 1 / 2 kagome- and triangular-lattice Heisenberg antiferromagnets are investigated using the numerical exact diagonalization and the finite-size scaling analysis. The behaviour of the field derivative at zero magnetization is examined for both systems. The present result indicates that the spin excitation is gapless for each system.

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.

Hybrid Monte Carlo approach to the entanglement entropy of interacting fermions

NASA Astrophysics Data System (ADS)

Drut, Joaquín E.; Porter, William J.

2015-09-01

The Monte Carlo calculation of Rényi entanglement entropies Sn of interacting fermions suffers from a well-known signal-to-noise problem, even for a large number of situations in which the infamous sign problem is absent. A few methods have been proposed to overcome this issue, such as ensemble switching and the use of auxiliary partition-function ratios. Here, we present an approach that builds on the recently proposed free-fermion decomposition method; it incorporates entanglement in the probability measure in a natural way; it takes advantage of the hybrid Monte Carlo algorithm (an essential tool in lattice quantum chromodynamics and other gauge theories with dynamical fermions); and it does not suffer from noise problems. This method displays no sign problem for the same cases as other approaches and is therefore useful for a wide variety of systems. As a proof of principle, we calculate S2 for the one-dimensional, half-filled Hubbard model and compare with results from exact diagonalization and the free-fermion decomposition method.

Deforming black hole and cosmological solutions by quasiperiodic and/or pattern forming structures in modified and Einstein gravity

NASA Astrophysics Data System (ADS)

Bubuianu, Laurenţiu; Vacaru, Sergiu I.

2018-05-01

We elaborate on the anholonomic frame deformation method, AFDM, for constructing exact solutions with quasiperiodic structure in modified gravity theories, MGTs, and general relativity, GR. Such solutions are described by generic off-diagonal metrics, nonlinear and linear connections and (effective) matter sources with coefficients depending on all spacetime coordinates via corresponding classes of generation and integration functions and (effective) matter sources. There are studied effective free energy functionals and nonlinear evolution equations for generating off-diagonal quasiperiodic deformations of black hole and/or homogeneous cosmological metrics. The physical data for such functionals are stated by different values of constants and prescribed symmetries for defining quasiperiodic structures at cosmological scales, or astrophysical objects in nontrivial gravitational backgrounds some similar forms as in condensed matter physics. It is shown how quasiperiodic structures determined by general nonlinear, or additive, functionals for generating functions and (effective) sources may transform black hole like configurations into cosmological metrics and inversely. We speculate on possible implications of quasiperiodic solutions in dark energy and dark matter physics. Finally, it is concluded that geometric methods for constructing exact solutions consist an important alternative tool to numerical relativity for investigating nonlinear effects in astrophysics and cosmology.

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

Parallelized traveling cluster approximation to study numerically spin-fermion models on large lattices

DOE PAGES

Mukherjee, Anamitra; Patel, Niravkumar D.; Bishop, Chris; ...

2015-06-08

Lattice spin-fermion models are quite important to study correlated systems where quantum dynamics allows for a separation between slow and fast degrees of freedom. The fast degrees of freedom are treated quantum mechanically while the slow variables, generically referred to as the “spins,” are treated classically. At present, exact diagonalization coupled with classical Monte Carlo (ED + MC) is extensively used to solve numerically a general class of lattice spin-fermion problems. In this common setup, the classical variables (spins) are treated via the standard MC method while the fermion problem is solved by exact diagonalization. The “traveling cluster approximation” (TCA)more » is a real space variant of the ED + MC method that allows to solve spin-fermion problems on lattice sizes with up to 10 3 sites. In this paper, we present a novel reorganization of the TCA algorithm in a manner that can be efficiently parallelized. Finally, this allows us to solve generic spin-fermion models easily on 10 4 lattice sites and with some effort on 10 5 lattice sites, representing the record lattice sizes studied for this family of models.« less

Parallelized traveling cluster approximation to study numerically spin-fermion models on large lattices

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

Mukherjee, Anamitra; Patel, Niravkumar D.; Bishop, Chris

Lattice spin-fermion models are quite important to study correlated systems where quantum dynamics allows for a separation between slow and fast degrees of freedom. The fast degrees of freedom are treated quantum mechanically while the slow variables, generically referred to as the “spins,” are treated classically. At present, exact diagonalization coupled with classical Monte Carlo (ED + MC) is extensively used to solve numerically a general class of lattice spin-fermion problems. In this common setup, the classical variables (spins) are treated via the standard MC method while the fermion problem is solved by exact diagonalization. The “traveling cluster approximation” (TCA)more » is a real space variant of the ED + MC method that allows to solve spin-fermion problems on lattice sizes with up to 10 3 sites. In this paper, we present a novel reorganization of the TCA algorithm in a manner that can be efficiently parallelized. Finally, this allows us to solve generic spin-fermion models easily on 10 4 lattice sites and with some effort on 10 5 lattice sites, representing the record lattice sizes studied for this family of models.« less

Nonlocal Electrostatics in Spherical Geometries Using Eigenfunction Expansions of Boundary-Integral Operators.

PubMed

Bardhan, Jaydeep P; Knepley, Matthew G; Brune, Peter

2015-01-01

In this paper, we present an exact, infinite-series solution to Lorentz nonlocal continuum electrostatics for an arbitrary charge distribution in a spherical solute. Our approach relies on two key steps: (1) re-formulating the PDE problem using boundary-integral equations, and (2) diagonalizing the boundary-integral operators using the fact that their eigenfunctions are the surface spherical harmonics. To introduce this uncommon approach for calculations in separable geometries, we first re-derive Kirkwood's classic results for a protein surrounded concentrically by a pure-water ion-exclusion (Stern) layer and then a dilute electrolyte, which is modeled with the linearized Poisson-Boltzmann equation. The eigenfunction-expansion approach provides a computationally efficient way to test some implications of nonlocal models, including estimating the reasonable range of the nonlocal length-scale parameter λ. Our results suggest that nonlocal solvent response may help to reduce the need for very high dielectric constants in calculating pH-dependent protein behavior, though more sophisticated nonlocal models are needed to resolve this question in full. An open-source MATLAB implementation of our approach is freely available online.

Nonlocal Electrostatics in Spherical Geometries Using Eigenfunction Expansions of Boundary-Integral Operators

PubMed Central

Bardhan, Jaydeep P.; Knepley, Matthew G.; Brune, Peter

2015-01-01

In this paper, we present an exact, infinite-series solution to Lorentz nonlocal continuum electrostatics for an arbitrary charge distribution in a spherical solute. Our approach relies on two key steps: (1) re-formulating the PDE problem using boundary-integral equations, and (2) diagonalizing the boundary-integral operators using the fact that their eigenfunctions are the surface spherical harmonics. To introduce this uncommon approach for calculations in separable geometries, we first re-derive Kirkwood’s classic results for a protein surrounded concentrically by a pure-water ion-exclusion (Stern) layer and then a dilute electrolyte, which is modeled with the linearized Poisson–Boltzmann equation. The eigenfunction-expansion approach provides a computationally efficient way to test some implications of nonlocal models, including estimating the reasonable range of the nonlocal length-scale parameter λ. Our results suggest that nonlocal solvent response may help to reduce the need for very high dielectric constants in calculating pH-dependent protein behavior, though more sophisticated nonlocal models are needed to resolve this question in full. An open-source MATLAB implementation of our approach is freely available online. PMID:26273581

Finite temperature dynamics of a Holstein polaron: The thermo-field dynamics approach

NASA Astrophysics Data System (ADS)

Chen, Lipeng; Zhao, Yang

2017-12-01

Combining the multiple Davydov D2 Ansatz with the method of thermo-field dynamics, we study finite temperature dynamics of a Holstein polaron on a lattice. It has been demonstrated, using the hierarchy equations of motion method as a benchmark, that our approach provides an efficient, robust description of finite temperature dynamics of the Holstein polaron in the simultaneous presence of diagonal and off-diagonal exciton-phonon coupling. The method of thermo-field dynamics handles temperature effects in the Hilbert space with key numerical advantages over other treatments of finite-temperature dynamics based on quantum master equations in the Liouville space or wave function propagation with Monte Carlo importance sampling. While for weak to moderate diagonal coupling temperature increases inhibit polaron mobility, it is found that off-diagonal coupling induces phonon-assisted transport that dominates at high temperatures. Results on the mean square displacements show that band-like transport features dominate the diagonal coupling cases, and there exists a crossover from band-like to hopping transport with increasing temperature when including off-diagonal coupling. As a proof of concept, our theory provides a unified treatment of coherent and incoherent transport in molecular crystals and is applicable to any temperature.

Inelastic Transitions in Slow Collisions of Anti-Hydrogen with Hydrogen Atoms

NASA Astrophysics Data System (ADS)

Harrison, Robert; Krstic, Predrag

2007-06-01

We calculate excited adiabatic states and nonadiabatic coupling matrix elements of a quasimolecular system containing hydrogen and anti-hydrogen atoms, for a range of internuclear distances from 0.2 to 20 Bohrs. High accuracy is achieved by exact diagonalization of the molecular Hamiltionian in a large Gaussian basis. Nonadiabatic dynamics was calculated by solving MOCC equations. Positronium states are included in the consideration.

A Note on Parameters of Random Substitutions by γ-Diagonal Matrices

NASA Astrophysics Data System (ADS)

Kang, Ju-Sung

Random substitutions are very useful and practical method for privacy-preserving schemes. In this paper we obtain the exact relationship between the estimation errors and three parameters used in the random substitutions, namely the privacy assurance metric γ, the total number n of data records, and the size N of transition matrix. We also demonstrate some simulations concerning the theoretical result.

Iterating the Number of Intersection Points of the Diagonals of Irregular Convex Polygons, or C (n, 4) the Hard Way!

ERIC Educational Resources Information Center

Hathout, Leith

2007-01-01

Counting the number of internal intersection points made by the diagonals of irregular convex polygons where no three diagonals are concurrent is an interesting problem in discrete mathematics. This paper uses an iterative approach to develop a summation relation which tallies the total number of intersections, and shows that this total can be…

Large-deviation theory for diluted Wishart random matrices

NASA Astrophysics Data System (ADS)

Castillo, Isaac Pérez; Metz, Fernando L.

2018-03-01

Wishart random matrices with a sparse or diluted structure are ubiquitous in the processing of large datasets, with applications in physics, biology, and economy. In this work, we develop a theory for the eigenvalue fluctuations of diluted Wishart random matrices based on the replica approach of disordered systems. We derive an analytical expression for the cumulant generating function of the number of eigenvalues IN(x ) smaller than x ∈R+ , from which all cumulants of IN(x ) and the rate function Ψx(k ) controlling its large-deviation probability Prob[IN(x ) =k N ] ≍e-N Ψx(k ) follow. Explicit results for the mean value and the variance of IN(x ) , its rate function, and its third cumulant are discussed and thoroughly compared to numerical diagonalization, showing very good agreement. The present work establishes the theoretical framework put forward in a recent letter [Phys. Rev. Lett. 117, 104101 (2016), 10.1103/PhysRevLett.117.104101] as an exact and compelling approach to deal with eigenvalue fluctuations of sparse random matrices.

Multiorbital kinetic effects on charge ordering of frustrated electrons on the triangular lattice

NASA Astrophysics Data System (ADS)

Février, C.; Fratini, S.; Ralko, A.

2015-06-01

The role of the multiorbital effects on the emergence of frustrated electronic orders on the triangular lattice at half filling is investigated through an extended spinless fermion Hubbard model. By using two complementary approaches, unrestricted Hartree-Fock and exact diagonalizations, we unravel a very rich phase diagram controlled by the strength of both local and off-site Coulomb interactions and by the interorbital hopping anisotropy ratio t'/t . Three robust unconventional electronic phases, a pinball liquid, an inverse pinball liquid, and a large-unit-cell √{12 }×√{12 } droplet phase, are found to be generic in the triangular geometry, being controlled by the band structure parameters. The latter are also stabilized in the isotropic limit of our microscopic model, which recovers the standard SU(2) spinful extended single-band Hubbard model.

An exact variational method to calculate vibrational energies of five atom molecules beyond the normal mode approach

DOE PAGES

Yu, Hua-Gen

2002-01-01

We present a full dimensional variational algorithm to calculate vibrational energies of penta-atomic molecules. The quantum mechanical Hamiltonian of the system for J=0 is derived in a set of orthogonal polyspherical coordinates in the body-fixed frame without any dynamical approximation. Moreover, the vibrational Hamiltonian has been obtained in an explicitly Hermitian form. Variational calculations are performed in a direct product discrete variable representation basis set. The sine functions are used for the radial coordinates, whereas the Legendre polynomials are employed for the polar angles. For the azimuthal angles, the symmetrically adapted Fourier–Chebyshev basis functions are utilized. The eigenvalue problem ismore » solved by a Lanczos iterative diagonalization algorithm. The preliminary application to methane is given. Ultimately, we made a comparison with previous results.« less

Spectral function of a hole in the t - J model

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

Liu, Z.; Manousakis, E.

1991-08-01

We give numerical solutions, on finite but large-size square lattices, of the equation for the single-hole Green's function obtained by the self-consistent approach of Schmitt-Rink {ital et} {ital al}. and Kane {ital et} {ital al}. The spectral function of the hole in a quantum antiferromagnet shows that most features describing the hole motion are in close agreement with the results of the exact diagonalization on the 4{sup 2} lattice in the region of {ital J}/{ital t}{le}0.2. Our results obtained on sufficiently large-size lattices suggest that certain important features of the spectral function survive in the thermodynamic limit while others changemore » due to finite-size effects. We find that the leading nonzero vertex correction is given by a two-loop diagram, which has a small contribution.« less

Quantum criticality and first-order transitions in the extended periodic Anderson model

NASA Astrophysics Data System (ADS)

Hagymási, I.; Itai, K.; Sólyom, J.

2013-03-01

We investigate the behavior of the periodic Anderson model in the presence of d-f Coulomb interaction (Udf) using mean-field theory, variational calculation, and exact diagonalization of finite chains. The variational approach based on the Gutzwiller trial wave function gives a critical value of Udf and two quantum critical points (QCPs), where the valence susceptibility diverges. We derive the critical exponent for the valence susceptibility and investigate how the position of the QCP depends on the other parameters of the Hamiltonian. For larger values of Udf, the Kondo regime is bounded by two first-order transitions. These first-order transitions merge into a triple point at a certain value of Udf. For even larger Udf valence skipping occurs. Although the other methods do not give a critical point, they support this scenario.

Hidden symmetries for ellipsoid-solitonic deformations of Kerr-Sen black holes and quantum anomalies

NASA Astrophysics Data System (ADS)

Vacaru, Sergiu I.

2013-02-01

We prove the existence of hidden symmetries in the general relativity theory defined by exact solutions with generic off-diagonal metrics, nonholonomic (non-integrable) constraints, and deformations of the frame and linear connection structure. A special role in characterization of such spacetimes is played by the corresponding nonholonomic generalizations of Stackel-Killing and Killing-Yano tensors. There are constructed new classes of black hole solutions and we study hidden symmetries for ellipsoidal and/or solitonic deformations of "prime" Kerr-Sen black holes into "target" off-diagonal metrics. In general, the classical conserved quantities (integrable and not-integrable) do not transfer to the quantized systems and produce quantum gravitational anomalies. We prove that such anomalies can be eliminated via corresponding nonholonomic deformations of fundamental geometric objects (connections and corresponding Riemannian and Ricci tensors) and by frame transforms.

Density-Functional Theory description of transport in the single-electron transistor

NASA Astrophysics Data System (ADS)

Zawadzki, Krissia; Oliveira, Luiz N.

The Kondo effect governs the low-temperature transport properties of the single electron transistor (SET), a quantum dot bridging two electron gases. In the weak coupling limit, for odd dot occupation, the gate-potential profile of the conductance approaches a step, known as the Kondo plateau. The plateau and other SET properties being well understood on the basis of the Anderson model, more realistic (i. e., DFT) descriptions of the device are now desired. This poses a challenge, since the SET is strongly correlated. DFT computations that reproduce the conductance plateau have been reported, e. g., by, which rely on the exact functional provided by the Bethe-Ansatz solution for the Anderson model. Here, sticking to DFT tradition, we employ a functional derived from a homogeneous system: the parametrization of the Lieb-Wu solution for the Hubbard model due to. Our computations reproduce the plateau and yield other results in accurate agreement with the exact diagonalization of the Anderson Hamiltonian. The prospects for extensions to realistic descriptions of two-dimensional nanostructured devices will be discussed. Luiz N. Oliveira thanks CNPq (312658/2013-3) and Krissia Zawadzki thanks CNPq (140703/2014-4) for financial support.

Theoretical study of the dependence of single impurity Anderson model on various parameters within distributional exact diagonalization method

NASA Astrophysics Data System (ADS)

Syaina, L. P.; Majidi, M. A.

2018-04-01

Single impurity Anderson model describes a system consisting of non-interacting conduction electrons coupled with a localized orbital having strongly interacting electrons at a particular site. This model has been proven successful to explain the phenomenon of metal-insulator transition through Anderson localization. Despite the well-understood behaviors of the model, little has been explored theoretically on how the model properties gradually evolve as functions of hybridization parameter, interaction energy, impurity concentration, and temperature. Here, we propose to do a theoretical study on those aspects of a single impurity Anderson model using the distributional exact diagonalization method. We solve the model Hamiltonian by randomly generating sampling distribution of some conducting electron energy levels with various number of occupying electrons. The resulting eigenvalues and eigenstates are then used to define the local single-particle Green function for each sampled electron energy distribution using Lehmann representation. Later, we extract the corresponding self-energy of each distribution, then average over all the distributions and construct the local Green function of the system to calculate the density of states. We repeat this procedure for various values of those controllable parameters, and discuss our results in connection with the criteria of the occurrence of metal-insulator transition in this system.

Multi-subject Manifold Alignment of Functional Network Structures via Joint Diagonalization.

PubMed

Nenning, Karl-Heinz; Kollndorfer, Kathrin; Schöpf, Veronika; Prayer, Daniela; Langs, Georg

2015-01-01

Functional magnetic resonance imaging group studies rely on the ability to establish correspondence across individuals. This enables location specific comparison of functional brain characteristics. Registration is often based on morphology and does not take variability of functional localization into account. This can lead to a loss of specificity, or confounds when studying diseases. In this paper we propose multi-subject functional registration by manifold alignment via coupled joint diagonalization. The functional network structure of each subject is encoded in a diffusion map, where functional relationships are decoupled from spatial position. Two-step manifold alignment estimates initial correspondences between functionally equivalent regions. Then, coupled joint diagonalization establishes common eigenbases across all individuals, and refines the functional correspondences. We evaluate our approach on fMRI data acquired during a language paradigm. Experiments demonstrate the benefits in matching accuracy achieved by coupled joint diagonalization compared to previously proposed functional alignment approaches, or alignment based on structural correspondences.

An integrated chronic disease management model: a diagonal approach to health system strengthening in South Africa.

PubMed

Mahomed, Ozayr Haroon; Asmall, Shaidah; Freeman, Melvyn

2014-11-01

The integrated chronic disease management model provides a systematic framework for creating a fundamental change in the orientation of the health system. This model adopts a diagonal approach to health system strengthening by establishing a service-linked base to training, supervision, and the opportunity to try out, assess, and implement integrated interventions.

Can nonstandard interactions jeopardize the hierarchy sensitivity of DUNE?

NASA Astrophysics Data System (ADS)

Deepthi, K. N.; Goswami, Srubabati; Nath, Newton

2017-10-01

We study the effect of nonstandard interactions (NSIs) on the propagation of neutrinos through the Earth's matter and how it affects the hierarchy sensitivity of the DUNE experiment. We emphasize the special case when the diagonal NSI parameter ɛe e=-1 , nullifying the standard matter effect. We show that if, in addition, C P violation is maximal then this gives rise to an exact intrinsic hierarchy degeneracy in the appearance channel, irrespective of the baseline and energy. Introduction of the off diagonal NSI parameter, ɛe τ, shifts the position of this degeneracy to a different ɛe e. Moreover the unknown magnitude and phases of the off diagonal NSI parameters can give rise to additional degeneracies. Overall, given the current model independent limits on NSI parameters, the hierarchy sensitivity of DUNE can get seriously impacted. However, a more precise knowledge of the NSI parameters, especially ɛe e, can give rise to an improved sensitivity. Alternatively, if a NSI exists in nature, and still DUNE shows hierarchy sensitivity, certain ranges of the NSI parameters can be excluded. Additionally, we briefly discuss the implications of ɛe e=-1 (in the Earth) on the Mikheyev-Smirnov-Wolfenstein effect in the Sun.

Experiments in Quantum Coherence and Computation With Single Cooper-Pair Electronics

DTIC Science & Technology

2006-01-22

through the cavity. In the absence of damping, exact diagonalization of the Jaynes - Cumming Hamiltonian yields the excited eigenstates (dressed states...neglecting rapidly oscillating terms and omitting damping for the moment, Eq. (16) reduces to the Jaynes - Cummings Hamiltonian (1) with V=EJ /" and cou...is therefore little entanglement between the field and qubit in this situation and the rotation fidelity is high. To model the effect of the drive on

Graduate Student Support for Quantum Computing With Superconducting Charge States

DTIC Science & Technology

2005-08-31

cavity resonance frequency ωr, the atomic transition frequency Ω, and the strength of the atom- photon coupling g appearing in the Jaynes - Cummings ...the atom through the cavity. In the absence of damping, exact diagonalization of the Jaynes - Cumming Hamiltonian yields the excited eigen- states...cillating terms and omitting damping for the moment, 5 Eq. (16) reduces to the Jaynes - Cummings Hamiltonian (1) with Ω = EJ/~ and the vacuum Rabi frequency

Time-dependent generalized Gibbs ensembles in open quantum systems

NASA Astrophysics Data System (ADS)

Lange, Florian; Lenarčič, Zala; Rosch, Achim

2018-04-01

Generalized Gibbs ensembles have been used as powerful tools to describe the steady state of integrable many-particle quantum systems after a sudden change of the Hamiltonian. Here, we demonstrate numerically that they can be used for a much broader class of problems. We consider integrable systems in the presence of weak perturbations which break both integrability and drive the system to a state far from equilibrium. Under these conditions, we show that the steady state and the time evolution on long timescales can be accurately described by a (truncated) generalized Gibbs ensemble with time-dependent Lagrange parameters, determined from simple rate equations. We compare the numerically exact time evolutions of density matrices for small systems with a theory based on block-diagonal density matrices (diagonal ensemble) and a time-dependent generalized Gibbs ensemble containing only a small number of approximately conserved quantities, using the one-dimensional Heisenberg model with perturbations described by Lindblad operators as an example.

The relation between the quantum discord and quantum teleportation: The physical interpretation of the transition point between different quantum discord decay regimes

NASA Astrophysics Data System (ADS)

Roszak, K.; Cywiński, Ł.

2015-10-01

We study quantum teleportation via Bell-diagonal mixed states of two qubits in the context of the intrinsic properties of the quantum discord. We show that when the quantum-correlated state of the two qubits is used for quantum teleportation, the character of the teleportation efficiency changes substantially depending on the Bell-diagonal-state parameters, which can be seen when the worst-case-scenario or best-case-scenario fidelity is studied. Depending on the parameter range, one of two types of single-qubit states is hardest/easiest to teleport. The transition between these two parameter ranges coincides exactly with the transition between the range of classical correlation decay and quantum correlation decay characteristic for the evolution of the quantum discord. The correspondence provides a physical interpretation for the prominent feature of the decay of the quantum discord.

Crossover from Super- to Subdiffusive Motion and Memory Effects in Crystalline Organic Semiconductors

NASA Astrophysics Data System (ADS)

De Filippis, G.; Cataudella, V.; Mishchenko, A. S.; Nagaosa, N.; Fierro, A.; de Candia, A.

2015-02-01

The transport properties at finite temperature of crystalline organic semiconductors are investigated, within the Su-Schrieffer-Heeger model, by combining an exact diagonalization technique, Monte Carlo approaches, and a maximum entropy method. The temperature-dependent mobility data measured in single crystals of rubrene are successfully reproduced: a crossover from super- to subdiffusive motion occurs in the range 150 ≤T ≤200 K , where the mean free path becomes of the order of the lattice parameter and strong memory effects start to appear. We provide an effective model, which can successfully explain features of the absorption spectra at low frequencies. The observed response to slowly varying electric field is interpreted by means of a simple model where the interaction between the charge carrier and lattice polarization modes is simulated by a harmonic interaction between a fictitious particle and an electron embedded in a viscous fluid.

Crossover from super- to subdiffusive motion and memory effects in crystalline organic semiconductors.

PubMed

De Filippis, G; Cataudella, V; Mishchenko, A S; Nagaosa, N; Fierro, A; de Candia, A

2015-02-27

The transport properties at finite temperature of crystalline organic semiconductors are investigated, within the Su-Schrieffer-Heeger model, by combining an exact diagonalization technique, Monte Carlo approaches, and a maximum entropy method. The temperature-dependent mobility data measured in single crystals of rubrene are successfully reproduced: a crossover from super- to subdiffusive motion occurs in the range 150≤T≤200  K, where the mean free path becomes of the order of the lattice parameter and strong memory effects start to appear. We provide an effective model, which can successfully explain features of the absorption spectra at low frequencies. The observed response to slowly varying electric field is interpreted by means of a simple model where the interaction between the charge carrier and lattice polarization modes is simulated by a harmonic interaction between a fictitious particle and an electron embedded in a viscous fluid.

Nonholonomic relativistic diffusion and exact solutions for stochastic Einstein spaces

NASA Astrophysics Data System (ADS)

Vacaru, S. I.

2012-03-01

We develop an approach to the theory of nonholonomic relativistic stochastic processes in curved spaces. The Itô and Stratonovich calculus are formulated for spaces with conventional horizontal (holonomic) and vertical (nonholonomic) splitting defined by nonlinear connection structures. Geometric models of the relativistic diffusion theory are elaborated for nonholonomic (pseudo) Riemannian manifolds and phase velocity spaces. Applying the anholonomic deformation method, the field equations in Einstein's gravity and various modifications are formally integrated in general forms, with generic off-diagonal metrics depending on some classes of generating and integration functions. Choosing random generating functions we can construct various classes of stochastic Einstein manifolds. We show how stochastic gravitational interactions with mixed holonomic/nonholonomic and random variables can be modelled in explicit form and study their main geometric and stochastic properties. Finally, the conditions when non-random classical gravitational processes transform into stochastic ones and inversely are analyzed.

Electronic excitations in γ -Li2IrO3

NASA Astrophysics Data System (ADS)

Li, Ying; Winter, Stephen M.; Jeschke, Harald O.; Valentí, Roser

2017-01-01

We investigate the electronic properties of the three-dimensional stripyhoneycomb γ -Li2IrO3 via relativistic density functional theory calculations as well as exact diagonalization of finite clusters and explore the details of the optical conductivity. Our analysis of this quantity reveals the microscopic origin of the experimentally observed (i) optical transitions and (ii) anisotropic behavior along the various polarization directions. In particular, we find that the optical excitations are overall dominated by transitions between jeff=1 /2 and 3/2 states and the weight of transitions between jeff=1 /2 states at low frequencies can be correlated to deviations from a pure Kitaev description. We furthermore reanalyze within this approach the electronic excitations in the known two-dimensional honeycomb systems α -Li2IrO3 and Na2IrO3 and discuss the results in comparison to γ -Li2IrO3 .

Using nonequilibrium dynamics to probe competing orders in a Mott-Peierls system

DOE PAGES

Wang, Y.; Moritz, B.; Chen, C. -C.; ...

2016-02-24

Competition between ordered phases, and their associated phase transitions, are significant in the study of strongly correlated systems. Here, we examine one aspect, the nonequilibrium dynamics of a photoexcited Mott-Peierls system, using an effective Peierls-Hubbard model and exact diagonalization. Near a transition where spin and charge become strongly intertwined, we observe antiphase dynamics and a coupling-strength-dependent suppression or enhancement in the static structure factors. The renormalized bosonic excitations coupled to a particular photoexcited electron can be extracted, which provides an approach for characterizing the underlying bosonic modes. The results from this analysis for different electronic momenta show an uneven softeningmore » due to a stronger coupling near k F. As a result, this behavior reflects the strong link between the fermionic momenta, the coupling vertices, and ultimately, the bosonic susceptibilities when multiple phases compete for the ground state of the system.« less

A tensor network approach to many-body localization

NASA Astrophysics Data System (ADS)

Yu, Xiongjie; Pekker, David; Clark, Bryan

Understanding the many-body localized phase requires access to eigenstates in the middle of the many-body spectrum. While exact-diagonalization is able to access these eigenstates, it is restricted to systems sizes of about 22 spins. To overcome this limitation, we develop tensor network algorithms which increase the accessible system size by an order of magnitude. We describe both our new algorithms as well as the additional physics about MBL we can extract from them. For example, we demonstrate the power of these methods by verifying the breakdown of the Eigenstate Thermalization Hypothesis (ETH) in the many-body localized phase of the random field Heisenberg model, and show the saturation of entanglement in the MBL phase and generate eigenstates that differ by local excitations. Work was supported by AFOSR FA9550-10-1-0524 and FA9550-12-1-0057, the Kaufmann foundation, and SciDAC FG02-12ER46875.

Exact decoupling of the Dirac Hamiltonian. II. The generalized Douglas-Kroll-Hess transformation up to arbitrary order.

PubMed

Reiher, Markus; Wolf, Alexander

2004-12-08

In order to achieve exact decoupling of the Dirac Hamiltonian within a unitary transformation scheme, we have discussed in part I of this series that either a purely numerical iterative technique (the Barysz-Sadlej-Snijders method) or a stepwise analytic approach (the Douglas-Kroll-Hess method) are possible. For the evaluation of Douglas-Kroll-Hess Hamiltonians up to a pre-defined order it was shown that a symbolic scheme has to be employed. In this work, an algorithm for this analytic derivation of Douglas-Kroll-Hess Hamiltonians up to any arbitrary order in the external potential is presented. We discuss how an estimate for the necessary order for exact decoupling (within machine precision) for a given system can be determined from the convergence behavior of the Douglas-Kroll-Hess expansion prior to a quantum chemical calculation. Once this maximum order has been accomplished, the spectrum of the positive-energy part of the decoupled Hamiltonian, e.g., for electronic bound states, cannot be distinguished from the corresponding part of the spectrum of the Dirac operator. An efficient scalar-relativistic implementation of the symbolic operations for the evaluation of the positive-energy part of the block-diagonal Hamiltonian is presented, and its accuracy is tested for ground-state energies of one-electron ions over the whole periodic table. Furthermore, the first many-electron calculations employing sixth up to fourteenth order DKH Hamiltonians are presented. (c) 2004 American Institute of Physics.

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.

Periodic Anderson model with correlated conduction electrons: Variational and exact diagonalization study

NASA Astrophysics Data System (ADS)

Hagymási, I.; Itai, K.; Sólyom, J.

2012-06-01

We investigate an extended version of the periodic Anderson model (the so-called periodic Anderson-Hubbard model) with the aim to understand the role of interaction between conduction electrons in the formation of the heavy-fermion and mixed-valence states. Two methods are used: (i) variational calculation with the Gutzwiller wave function optimizing numerically the ground-state energy and (ii) exact diagonalization of the Hamiltonian for short chains. The f-level occupancy and the renormalization factor of the quasiparticles are calculated as a function of the energy of the f orbital for a wide range of the interaction parameters. The results obtained by the two methods are in reasonably good agreement for the periodic Anderson model. The agreement is maintained even when the interaction between band electrons, Ud, is taken into account, except for the half-filled case. This discrepancy can be explained by the difference between the physics of the one- and higher-dimensional models. We find that this interaction shifts and widens the energy range of the bare f level, where heavy-fermion behavior can be observed. For large-enough Ud this range may lie even above the bare conduction band. The Gutzwiller method indicates a robust transition from Kondo insulator to Mott insulator in the half-filled model, while Ud enhances the quasiparticle mass when the filling is close to half filling.

Exchange potential from the common energy denominator approximation for the Kohn-Sham Green's function: Application to (hyper)polarizabilities of molecular chains

NASA Astrophysics Data System (ADS)

Grüning, M.; Gritsenko, O. V.; Baerends, E. J.

2002-04-01

An approximate Kohn-Sham (KS) exchange potential vxσCEDA is developed, based on the common energy denominator approximation (CEDA) for the static orbital Green's function, which preserves the essential structure of the density response function. vxσCEDA is an explicit functional of the occupied KS orbitals, which has the Slater vSσ and response vrespσCEDA potentials as its components. The latter exhibits the characteristic step structure with "diagonal" contributions from the orbital densities |ψiσ|2, as well as "off-diagonal" ones from the occupied-occupied orbital products ψiσψj(≠1)σ*. Comparison of the results of atomic and molecular ground-state CEDA calculations with those of the Krieger-Li-Iafrate (KLI), exact exchange (EXX), and Hartree-Fock (HF) methods show, that both KLI and CEDA potentials can be considered as very good analytical "closure approximations" to the exact KS exchange potential. The total CEDA and KLI energies nearly coincide with the EXX ones and the corresponding orbital energies ɛiσ are rather close to each other for the light atoms and small molecules considered. The CEDA, KLI, EXX-ɛiσ values provide the qualitatively correct order of ionizations and they give an estimate of VIPs comparable to that of the HF Koopmans' theorem. However, the additional off-diagonal orbital structure of vxσCEDA appears to be essential for the calculated response properties of molecular chains. KLI already considerably improves the calculated (hyper)polarizabilities of the prototype hydrogen chains Hn over local density approximation (LDA) and standard generalized gradient approximations (GGAs), while the CEDA results are definitely an improvement over the KLI ones. The reasons of this success are the specific orbital structures of the CEDA and KLI response potentials, which produce in an external field an ultranonlocal field-counteracting exchange potential.

A new fast direct solver for the boundary element method

NASA Astrophysics Data System (ADS)

Huang, S.; Liu, Y. J.

2017-09-01

A new fast direct linear equation solver for the boundary element method (BEM) is presented in this paper. The idea of the new fast direct solver stems from the concept of the hierarchical off-diagonal low-rank matrix. The hierarchical off-diagonal low-rank matrix can be decomposed into the multiplication of several diagonal block matrices. The inverse of the hierarchical off-diagonal low-rank matrix can be calculated efficiently with the Sherman-Morrison-Woodbury formula. In this paper, a more general and efficient approach to approximate the coefficient matrix of the BEM with the hierarchical off-diagonal low-rank matrix is proposed. Compared to the current fast direct solver based on the hierarchical off-diagonal low-rank matrix, the proposed method is suitable for solving general 3-D boundary element models. Several numerical examples of 3-D potential problems with the total number of unknowns up to above 200,000 are presented. The results show that the new fast direct solver can be applied to solve large 3-D BEM models accurately and with better efficiency compared with the conventional BEM.

Deterministic alternatives to the full configuration interaction quantum Monte Carlo method for strongly correlated systems

NASA Astrophysics Data System (ADS)

Tubman, Norm; Whaley, Birgitta

The development of exponential scaling methods has seen great progress in tackling larger systems than previously thought possible. One such technique, full configuration interaction quantum Monte Carlo, allows exact diagonalization through stochastically sampling of determinants. The method derives its utility from the information in the matrix elements of the Hamiltonian, together with a stochastic projected wave function, which are used to explore the important parts of Hilbert space. However, a stochastic representation of the wave function is not required to search Hilbert space efficiently and new deterministic approaches have recently been shown to efficiently find the important parts of determinant space. We shall discuss the technique of Adaptive Sampling Configuration Interaction (ASCI) and the related heat-bath Configuration Interaction approach for ground state and excited state simulations. We will present several applications for strongly correlated Hamiltonians. This work was supported through the Scientific Discovery through Advanced Computing (SciDAC) program funded by the U.S. Department of Energy, Office of Science, Advanced Scientific Computing Research and Basic Energy Sciences.

Bethe states of the trigonometric SU(3) spin chain with generic open boundaries

NASA Astrophysics Data System (ADS)

Sun, Pei; Xin, Zhirong; Qiao, Yi; Wen, Fakai; Hao, Kun; Cao, Junpeng; Li, Guang-Liang; Yang, Tao; Yang, Wen-Li; Shi, Kangjie

2018-06-01

By combining the algebraic Bethe ansatz and the off-diagonal Bethe ansatz, we investigate the trigonometric SU (3) model with generic open boundaries. The eigenvalues of the transfer matrix are given in terms of an inhomogeneous T - Q relation, and the corresponding eigenstates are expressed in terms of nested Bethe-type eigenstates which have well-defined homogeneous limit. This exact solution provides a basis for further analyzing the thermodynamic properties and correlation functions of the anisotropic models associated with higher rank algebras.

Exchange interactions in a dinuclear manganese (II) complex with cyanopyridine-N-oxide bridging ligands

NASA Astrophysics Data System (ADS)

Markosyan, A. S.; Gaidukova, I. Yu.; Ruchkin, A. V.; Anokhin, A. O.; Irkhin, V. Yu.; Ryazanov, M. V.; Kuz'mina, N. P.; Nikiforov, V. N.

2014-01-01

The magnetic properties of dinuclear manganese(II) complex [Mn(hfa)2cpo]2 (where hfa is hexafluoroacetylacetonate anion and cpo is 4-cyanopyridine-N-oxide) are presented. The non-monotonous dependence of magnetic susceptibility is explained in terms of the hierarchy of exchange parameters by using exact diagonalization. The thermodynamic behavior of pure cpo and [Mn(hfa)2(cpo)]2 is simulated numerically by an extrapolation to spin S=5/2. The Mn-Mn exchange integral is evaluated.

Frustrated honeycomb-lattice bilayer quantum antiferromagnet in a magnetic field

NASA Astrophysics Data System (ADS)

Krokhmalskii, Taras; Baliha, Vasyl; Derzhko, Oleg; Schulenburg, Jörg; Richter, Johannes

2018-05-01

Frustrated bilayer quantum magnets have attracted attention as flat-band spin systems with unconventional thermodynamic properties. We study the low-temperature properties of a frustrated honeycomb-lattice bilayer spin-1/2 isotropic (XXX) Heisenberg antiferromagnet in a magnetic field by means of an effective low-energy theory using exact diagonalizations and quantum Monte Carlo simulations. Our main focus is on the magnetization curve and the temperature dependence of the specific heat indicating a finite-temperature phase transition in high magnetic fields.

High-Tc superconductivity: The t-J-V model and its applications

NASA Astrophysics Data System (ADS)

Roy, K.; Pal, P.; Nath, S.; Ghosh, N. K.

2017-05-01

We present numerical results of the t-J-V model in an 8-site tilted square cluster using exact diagonalization (ED) method with periodic boundary conditions. Effective hopping amplitude initially increases with inter-site Coulomb repulsion (V), but decreases at larger V's. The hole-hole correlation decreases with inter-site distances at smaller V. With the increase of Coulomb repulsion, the system becomes ordered. The specific heat curves confirm the non-Fermi liquid behavior of the system under t-J-V model.

Spectral function of few electrons in quantum wires and carbon nanotubes as a signature of Wigner localization

NASA Astrophysics Data System (ADS)

Secchi, Andrea; Rontani, Massimo

2012-03-01

We demonstrate that the profile of the space-resolved spectral function at finite temperature provides a signature of Wigner localization for electrons in quantum wires and semiconducting carbon nanotubes. Our numerical evidence is based on the exact diagonalization of the microscopic Hamiltonian of few particles interacting in gate-defined quantum dots. The minimal temperature required to suppress residual exchange effects in the spectral function image of (nanotubes) quantum wires lies in the (sub)kelvin range.

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.

Fractional charge revealed in computer simulations of resonant tunneling in the fractional quantum Hall regime.

PubMed

Tsiper, E V

2006-08-18

The concept of fractional charge is central to the theory of the fractional quantum Hall effect. Here I use exact diagonalization as well as configuration space renormalization to study finite clusters which are large enough to contain two independent edges. I analyze the conditions of resonant tunneling between the two edges. The "computer experiment" reveals a periodic sequence of resonant tunneling events consistent with the experimentally observed fractional quantization of electric charge in units of e/3 and e/5.

Ground state transitions in vertically coupled N-layer single electron quantum dots

NASA Astrophysics Data System (ADS)

Xie, Wenfang; Wang, Anmei

2003-12-01

A method is proposed to exactly diagonalize the Hamiltonian of a N-layer quantum dot containing a single electron in each dot in arbitrary magnetic fields. For N=4, the energy spectra of the dot are calculated as a function of the applied magnetic field. We find discontinuous ground-state energy transitions induced by an external magnetic field in the case of strong coupling. However, in the case of weak coupling, such a transition does not occur and the angular momentum remains zero.

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.

Comparison of νμ->νe Oscillation calculations with matter effects

NASA Astrophysics Data System (ADS)

Gordon, Michael; Toki, Walter

2013-04-01

An introduction to neutrino oscillations in vacuum is presented, followed by a survey of various techniques for obtaining either exact or approximate expressions for νμ->νe oscillations in matter. The method devised by Mann, Kafka, Schneps, and Altinok produces an exact expression for the oscillation by determining explicitely the evolution operator. The method used by Freund yields an approximate oscillation probability by diagonalizing the Hamiltonian, finding the eigenvalues and eigenvectors, and then using those to find modified mixing angles with the matter effect taken into account. The method developed by Arafune, Koike, and Sato uses an alternate method to find an approximation of the evolution operator. These methods are compared to each other using parameters from both the T2K and LBNE experiments.

Implementation of the diagonalization-free algorithm in the self-consistent field procedure within the four-component relativistic scheme.

PubMed

Hrdá, Marcela; Kulich, Tomáš; Repiský, Michal; Noga, Jozef; Malkina, Olga L; Malkin, Vladimir G

2014-09-05

A recently developed Thouless-expansion-based diagonalization-free approach for improving the efficiency of self-consistent field (SCF) methods (Noga and Šimunek, J. Chem. Theory Comput. 2010, 6, 2706) has been adapted to the four-component relativistic scheme and implemented within the program package ReSpect. In addition to the implementation, the method has been thoroughly analyzed, particularly with respect to cases for which it is difficult or computationally expensive to find a good initial guess. Based on this analysis, several modifications of the original algorithm, refining its stability and efficiency, are proposed. To demonstrate the robustness and efficiency of the improved algorithm, we present the results of four-component diagonalization-free SCF calculations on several heavy-metal complexes, the largest of which contains more than 80 atoms (about 6000 4-spinor basis functions). The diagonalization-free procedure is about twice as fast as the corresponding diagonalization. Copyright © 2014 Wiley Periodicals, Inc.

Use of a Diagonal Approach to Health System Strengthening and Measles Elimination after a Large Nationwide Outbreak in Mongolia.

PubMed

Hagan, José E; Greiner, Ashley; Luvsansharav, Ulzii-Orshikh; Lake, Jason; Lee, Christopher; Pastore, Roberta; Takashima, Yoshihiro; Sarankhuu, Amarzaya; Demberelsuren, Sodbayar; Smith, Rachel; Park, Benjamin; Goodson, James L

2017-12-01

Measles is a highly transmissible infectious disease that causes serious illness and death worldwide. Efforts to eliminate measles through achieving high immunization coverage, well-performing surveillance systems, and rapid and effective outbreak response mechanisms while strategically engaging and strengthening health systems have been termed a diagonal approach. In March 2015, a large nationwide measles epidemic occurred in Mongolia, 1 year after verification of measles elimination in this country. A multidisciplinary team conducted an outbreak investigation that included a broad health system assessment, organized around the Global Health Security Agenda framework of Prevent-Detect-Respond, to provide recommendations for evidence-based interventions to interrupt the epidemic and strengthen the overall health system to prevent future outbreaks of measles and other epidemic-prone infectious threats. This investigation demonstrated the value of evaluating elements of the broader health system in investigating measles outbreaks and the need for using a diagonal approach to achieving sustainable measles elimination.

Exponential-fitted methods for integrating stiff systems of ordinary differential equations: Applications to homogeneous gas-phase chemical kinetics

NASA Technical Reports Server (NTRS)

Pratt, D. T.

1984-01-01

Conventional algorithms for the numerical integration of ordinary differential equations (ODEs) are based on the use of polynomial functions as interpolants. However, the exact solutions of stiff ODEs behave like decaying exponential functions, which are poorly approximated by polynomials. An obvious choice of interpolant are the exponential functions themselves, or their low-order diagonal Pade (rational function) approximants. A number of explicit, A-stable, integration algorithms were derived from the use of a three-parameter exponential function as interpolant, and their relationship to low-order, polynomial-based and rational-function-based implicit and explicit methods were shown by examining their low-order diagonal Pade approximants. A robust implicit formula was derived by exponential fitting the trapezoidal rule. Application of these algorithms to integration of the ODEs governing homogenous, gas-phase chemical kinetics was demonstrated in a developmental code CREK1D, which compares favorably with the Gear-Hindmarsh code LSODE in spite of the use of a primitive stepsize control strategy.

On the consistency of the Oppenheimer-Snyder solution for a dust star. Reply to Marshall's criticism

NASA Astrophysics Data System (ADS)

Zakir, Zahid

2018-02-01

The recent alternative to the Oppenheimer-Snyder (OS) solution for a dust star proposed by Marshall in the paper "Gravitational collapse without black holes" (Astrophys. Space Sci. 342:329, 2012) is analyzed. It is shown that this proposal leads to a non-diagonal metric, with which the Einstein equations become practically unsolvable. Any ansatz proposed as their exact solution turns out to be arbitrary and may be unlimited number of the such solutions. This is due to the fact that an auxiliary function y(R,r), introduced by OS as t=M(y), is unambiguously fixed by the diagonality condition and the matching on the surface, and thus in the non-diagonal case it remains arbitrary. It is also shown that the OS solution, as a description in terms of the Schwarzschild coordinates, leads to a frozen star (or frozar) picture not only for the surface, asymptotically freezing outside the gravitational radius, but for interior layers too which also freeze near their own asymptotes. At most of the inner region these asymptotes are located almost equidistantly and only for layers initially close to the surface they become denser. The reason for the such densifying is not "a gravitational repulsion", but their later freezing and higher spatial contractions, while they remain be uniform and free falling in the comoving frames.

Unveiling magnetic interactions of ruthenium trichloride via constraining direction of orbital moments: Potential routes to realize a quantum spin liquid

NASA Astrophysics Data System (ADS)

Hou, Y. S.; Xiang, H. J.; Gong, X. G.

2017-08-01

Recent experiments reveal that the honeycomb ruthenium trichloride α -RuC l3 is a prime candidate of the Kitaev quantum spin liquid (QSL). However, there is no theoretical model which can properly describe its experimental dynamical response due to the lack of a full understanding of its magnetic interactions. Here, we propose a general scheme to calculate the magnetic interactions in systems (e.g., α -RuC l3 ) with nonnegligible orbital moments by constraining the directions of orbital moments. With this scheme, we put forward a minimal J1-K1-Γ1-J3-K3 model for α -RuC l3 and find that: (I) The third nearest neighbor (NN) antiferromagnetic Heisenberg interaction J3 stabilizes the zigzag antiferromagnetic order; (II) The NN symmetric off-diagonal exchange Γ1 plays a pivotal role in determining the preferred direction of magnetic moments and generating the spin wave gap. An exact diagonalization study on this model shows that the Kitaev QSL can be realized by suppressing the NN symmetric off-diagonal exchange Γ1 and the third NN Heisenberg interaction J3. Thus, we not only propose a powerful general scheme for investigating the intriguing magnetism of Jeff=1 /2 magnets, but also point out future directions for realizing the Kitaev QSL in the honeycomb ruthenium trichloride α -RuC l3 .

Overlaps with arbitrary two-site states in the XXZ spin chain

NASA Astrophysics Data System (ADS)

Pozsgay, B.

2018-05-01

We present a conjectured exact formula for overlaps between the Bethe states of the spin-1/2 XXZ chain and generic two-site states. The result takes the same form as in the previously known cases: it involves the same ratio of two Gaudin-like determinants, and a product of single-particle overlap functions, which can be fixed using a combination of the quench action and quantum transfer matrix methods. Our conjecture is confirmed by numerical data from exact diagonalization. For one-site states, the formula is found to be correct even in chains with odd length. It is also pointed out that the ratio of the Gaudin-like determinants plays a crucial role in the overlap sum rule: it guarantees that in the thermodynamic limit there remains no term in the quench action.

Trial wave functions for a composite Fermi liquid on a torus

NASA Astrophysics Data System (ADS)

Fremling, M.; Moran, N.; Slingerland, J. K.; Simon, S. H.

2018-01-01

We study the two-dimensional electron gas in a magnetic field at filling fraction ν =1/2 . At this filling the system is in a gapless state which can be interpreted as a Fermi liquid of composite fermions. We construct trial wave functions for the system on a torus, based on this idea, and numerically compare these to exact wave functions for small systems found by exact diagonalization. We find that the trial wave functions give an excellent description of the ground state of the system, as well as its charged excitations, in all momentum sectors. We analyze the dispersion of the composite fermions and the Berry phase associated with dragging a single fermion around the Fermi surface and comment on the implications of our results for the current debate on whether composite fermions are Dirac fermions.

Goldstone and Higgs modes of photons inside a cavity

NASA Astrophysics Data System (ADS)

Yi-Xiang, Yu; Ye, Jinwu; Liu, Wu-Ming

2013-12-01

Goldstone and Higgs modes have been detected in various condensed matter, cold atom and particle physics experiments. Here, we demonstrate that the two modes can also be observed in optical systems with only a few (artificial) atoms inside a cavity. We establish this connection by studying the U(1)/Z2 Dicke model where N qubits (atoms) coupled to a single photon mode. We determine the Goldstone and Higgs modes inside the super-radiant phase and their corresponding spectral weights by performing both 1/J = 2/N expansion and exact diagonalization (ED) study at a finite N. We find nearly perfect agreements between the results achieved by the two approaches when N gets down even to N = 2. The quantum finite size effects at a few qubits make the two modes quite robust against an effectively small counterrotating wave term. We present a few schemes to reduce the critical coupling strength, so the two modes can be observed in several current available experimental systems by just conventional optical measurements.

A Deconstruction Lattice Description of the D1/D5 Brane World-Volume Gauge Theory

DOE PAGES

Giedt, Joel

2011-01-01

I genermore » alize the deconstruction lattice formulation of Endres and Kaplan to two-dimensional super-QCD with eight supercharges, denoted by (4,4), and bifundamental matter. I specialize to a particularly interesting (4,4) gauge theory, with gauge group U ( N c ) × U ( N f ) , and U ( N f ) being weakly gauged. It describes the infrared limit of the D1/D5 brane system, which has been studied extensively as an example of the AdS 3 /CFT 2 correspondence. The construction here preserves two supercharges exactly and has a lattice structure quite similar to that which has previously appeared in the deconstruction approach, that is, site, link, and diagonal fields with both the Bose and Fermi statistics. I remark on possible applications of the lattice theory that would test the AdS 3 /CFT 2 correspondence, particularly one that would exploit the recent worldsheet instanton analysis of Chen and Tong.« less

Discrete disorder models for many-body localization

NASA Astrophysics Data System (ADS)

Janarek, Jakub; Delande, Dominique; Zakrzewski, Jakub

2018-04-01

Using exact diagonalization technique, we investigate the many-body localization phenomenon in the 1D Heisenberg chain comparing several disorder models. In particular we consider a family of discrete distributions of disorder strengths and compare the results with the standard uniform distribution. Both statistical properties of energy levels and the long time nonergodic behavior are discussed. The results for different discrete distributions are essentially identical to those obtained for the continuous distribution, provided the disorder strength is rescaled by the standard deviation of the random distribution. Only for the binary distribution significant deviations are observed.

Quantum dimer model for the pseudogap metal

PubMed Central

Punk, Matthias; Allais, Andrea; Sachdev, Subir

2015-01-01

We propose a quantum dimer model for the metallic state of the hole-doped cuprates at low hole density, p. The Hilbert space is spanned by spinless, neutral, bosonic dimers and spin S=1/2, charge +e fermionic dimers. The model realizes a “fractionalized Fermi liquid” with no symmetry breaking and small hole pocket Fermi surfaces enclosing a total area determined by p. Exact diagonalization, on lattices of sizes up to 8×8, shows anisotropic quasiparticle residue around the pocket Fermi surfaces. We discuss the relationship to experiments. PMID:26195771

A fully redundant double difference algorithm for obtaining minimum variance estimates from GPS observations

NASA Technical Reports Server (NTRS)

Melbourne, William G.

1986-01-01

In double differencing a regression system obtained from concurrent Global Positioning System (GPS) observation sequences, one either undersamples the system to avoid introducing colored measurement statistics, or one fully samples the system incurring the resulting non-diagonal covariance matrix for the differenced measurement errors. A suboptimal estimation result will be obtained in the undersampling case and will also be obtained in the fully sampled case unless the color noise statistics are taken into account. The latter approach requires a least squares weighting matrix derived from inversion of a non-diagonal covariance matrix for the differenced measurement errors instead of inversion of the customary diagonal one associated with white noise processes. Presented is the so-called fully redundant double differencing algorithm for generating a weighted double differenced regression system that yields equivalent estimation results, but features for certain cases a diagonal weighting matrix even though the differenced measurement error statistics are highly colored.

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

Pratapa, Phanisri P.; Suryanarayana, Phanish; Pask, John E.

We present the Clenshaw–Curtis Spectral Quadrature (SQ) method for real-space O(N) Density Functional Theory (DFT) calculations. In this approach, all quantities of interest are expressed as bilinear forms or sums over bilinear forms, which are then approximated by spatially localized Clenshaw–Curtis quadrature rules. This technique is identically applicable to both insulating and metallic systems, and in conjunction with local reformulation of the electrostatics, enables the O(N) evaluation of the electronic density, energy, and atomic forces. The SQ approach also permits infinite-cell calculations without recourse to Brillouin zone integration or large supercells. We employ a finite difference representation in order tomore » exploit the locality of electronic interactions in real space, enable systematic convergence, and facilitate large-scale parallel implementation. In particular, we derive expressions for the electronic density, total energy, and atomic forces that can be evaluated in O(N) operations. We demonstrate the systematic convergence of energies and forces with respect to quadrature order as well as truncation radius to the exact diagonalization result. In addition, we show convergence with respect to mesh size to established O(N 3) planewave results. In conclusion, we establish the efficiency of the proposed approach for high temperature calculations and discuss its particular suitability for large-scale parallel computation.« less

Spectral Quadrature method for accurate O ( N ) electronic structure calculations of metals and insulators

DOE PAGES

Pratapa, Phanisri P.; Suryanarayana, Phanish; Pask, John E.

2015-12-02

We present the Clenshaw–Curtis Spectral Quadrature (SQ) method for real-space O(N) Density Functional Theory (DFT) calculations. In this approach, all quantities of interest are expressed as bilinear forms or sums over bilinear forms, which are then approximated by spatially localized Clenshaw–Curtis quadrature rules. This technique is identically applicable to both insulating and metallic systems, and in conjunction with local reformulation of the electrostatics, enables the O(N) evaluation of the electronic density, energy, and atomic forces. The SQ approach also permits infinite-cell calculations without recourse to Brillouin zone integration or large supercells. We employ a finite difference representation in order tomore » exploit the locality of electronic interactions in real space, enable systematic convergence, and facilitate large-scale parallel implementation. In particular, we derive expressions for the electronic density, total energy, and atomic forces that can be evaluated in O(N) operations. We demonstrate the systematic convergence of energies and forces with respect to quadrature order as well as truncation radius to the exact diagonalization result. In addition, we show convergence with respect to mesh size to established O(N 3) planewave results. In conclusion, we establish the efficiency of the proposed approach for high temperature calculations and discuss its particular suitability for large-scale parallel computation.« less

Semi-implicit iterative methods for low Mach number turbulent reacting flows: Operator splitting versus approximate factorization

NASA Astrophysics Data System (ADS)

MacArt, Jonathan F.; Mueller, Michael E.

2016-12-01

Two formally second-order accurate, semi-implicit, iterative methods for the solution of scalar transport-reaction equations are developed for Direct Numerical Simulation (DNS) of low Mach number turbulent reacting flows. The first is a monolithic scheme based on a linearly implicit midpoint method utilizing an approximately factorized exact Jacobian of the transport and reaction operators. The second is an operator splitting scheme based on the Strang splitting approach. The accuracy properties of these schemes, as well as their stability, cost, and the effect of chemical mechanism size on relative performance, are assessed in two one-dimensional test configurations comprising an unsteady premixed flame and an unsteady nonpremixed ignition, which have substantially different Damköhler numbers and relative stiffness of transport to chemistry. All schemes demonstrate their formal order of accuracy in the fully-coupled convergence tests. Compared to a (non-)factorized scheme with a diagonal approximation to the chemical Jacobian, the monolithic, factorized scheme using the exact chemical Jacobian is shown to be both more stable and more economical. This is due to an improved convergence rate of the iterative procedure, and the difference between the two schemes in convergence rate grows as the time step increases. The stability properties of the Strang splitting scheme are demonstrated to outpace those of Lie splitting and monolithic schemes in simulations at high Damköhler number; however, in this regime, the monolithic scheme using the approximately factorized exact Jacobian is found to be the most economical at practical CFL numbers. The performance of the schemes is further evaluated in a simulation of a three-dimensional, spatially evolving, turbulent nonpremixed planar jet flame.

Efficient, massively parallel eigenvalue computation

NASA Technical Reports Server (NTRS)

Huo, Yan; Schreiber, Robert

1993-01-01

In numerical simulations of disordered electronic systems, one of the most common approaches is to diagonalize random Hamiltonian matrices and to study the eigenvalues and eigenfunctions of a single electron in the presence of a random potential. An effort to implement a matrix diagonalization routine for real symmetric dense matrices on massively parallel SIMD computers, the Maspar MP-1 and MP-2 systems, is described. Results of numerical tests and timings are also presented.

Angular-momentum couplings in ultra-long-range giant dipole molecules

NASA Astrophysics Data System (ADS)

Stielow, Thomas; Scheel, Stefan; Kurz, Markus

2018-02-01

In this article we extend the theory of ultra-long-range giant dipole molecules, formed by an atom in a giant dipole state and a ground-state alkali-metal atom, by angular-momentum couplings known from recent works on Rydberg molecules. In addition to s -wave scattering, the next higher order of p -wave scattering in the Fermi pseudopotential describing the binding mechanism is considered. Furthermore, the singlet and triplet channels of the scattering interaction as well as angular-momentum couplings such as hyperfine interaction and Zeeman interactions are included. Within the framework of Born-Oppenheimer theory, potential energy surfaces are calculated in both first-order perturbation theory and exact diagonalization. Besides the known pure triplet states, mixed-spin character states are obtained, opening up a whole new landscape of molecular potentials. We determine exact binding energies and wave functions of the nuclear rotational and vibrational motion numerically from the various potential energy surfaces.

Matrix-Product-State Algorithm for Finite Fractional Quantum Hall Systems

NASA Astrophysics Data System (ADS)

Liu, Zhao; Bhatt, R. N.

2015-09-01

Exact diagonalization is a powerful tool to study fractional quantum Hall (FQH) systems. However, its capability is limited by the exponentially increasing computational cost. In order to overcome this difficulty, density-matrix-renormalization-group (DMRG) algorithms were developed for much larger system sizes. Very recently, it was realized that some model FQH states have exact matrix-product-state (MPS) representation. Motivated by this, here we report a MPS code, which is closely related to, but different from traditional DMRG language, for finite FQH systems on the cylinder geometry. By representing the many-body Hamiltonian as a matrix-product-operator (MPO) and using single-site update and density matrix correction, we show that our code can efficiently search the ground state of various FQH systems. We also compare the performance of our code with traditional DMRG. The possible generalization of our code to infinite FQH systems and other physical systems is also discussed.

(p,q) deformations and (p,q)-vector coherent states of the Jaynes-Cummings model in the rotating wave approximation

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

Ben Geloun, Joseph; Govaerts, Jan; Hounkonnou, M. Norbert

2007-03-15

Classes of (p,q) deformations of the Jaynes-Cummings model in the rotating wave approximation are considered. Diagonalization of the Hamiltonian is performed exactly, leading to useful spectral decompositions of a series of relevant operators. The latter include ladder operators acting between adjacent energy eigenstates within two separate infinite discrete towers, except for a singleton state. These ladder operators allow for the construction of (p,q)-deformed vector coherent states. Using (p,q) arithmetics, explicit and exact solutions to the associated moment problem are displayed, providing new classes of coherent states for such models. Finally, in the limit of decoupled spin sectors, our analysis translatesmore » into (p,q) deformations of the supersymmetric harmonic oscillator, such that the two supersymmetric sectors get intertwined through the action of the ladder operators as well as in the associated coherent states.« less

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

NASA Astrophysics Data System (ADS)

Mejía, José; Zapata, Camilo; Botero, Alonso

2017-01-01

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

Spatial correlations in driven-dissipative photonic lattices

NASA Astrophysics Data System (ADS)

Biondi, Matteo; Lienhard, Saskia; Blatter, Gianni; Türeci, Hakan E.; Schmidt, Sebastian

2017-12-01

We study the nonequilibrium steady-state of interacting photons in cavity arrays as described by the driven-dissipative Bose–Hubbard and spin-1/2 XY model. For this purpose, we develop a self-consistent expansion in the inverse coordination number of the array (∼ 1/z) to solve the Lindblad master equation of these systems beyond the mean-field approximation. Our formalism is compared and benchmarked with exact numerical methods for small systems based on an exact diagonalization of the Liouvillian and a recently developed corner-space renormalization technique. We then apply this method to obtain insights beyond mean-field in two particular settings: (i) we show that the gas–liquid transition in the driven-dissipative Bose–Hubbard model is characterized by large density fluctuations and bunched photon statistics. (ii) We study the antibunching–bunching transition of the nearest-neighbor correlator in the driven-dissipative spin-1/2 XY model and provide a simple explanation of this phenomenon.

Corner-corrected diagonal-norm summation-by-parts operators for the first derivative with increased order of accuracy

NASA Astrophysics Data System (ADS)

Del Rey Fernández, David C.; Boom, Pieter D.; Zingg, David W.

2017-02-01

Combined with simultaneous approximation terms, summation-by-parts (SBP) operators offer a versatile and efficient methodology that leads to consistent, conservative, and provably stable discretizations. However, diagonal-norm operators with a repeating interior-point operator that have thus far been constructed suffer from a loss of accuracy. While on the interior, these operators are of degree 2p, at a number of nodes near the boundaries, they are of degree p, and therefore of global degree p - meaning the highest degree monomial for which the operators are exact at all nodes. This implies that for hyperbolic problems and operators of degree greater than unity they lead to solutions with a global order of accuracy lower than the degree of the interior-point operator. In this paper, we develop a procedure to construct diagonal-norm first-derivative SBP operators that are of degree 2p at all nodes and therefore can lead to solutions of hyperbolic problems of order 2 p + 1. This is accomplished by adding nonzero entries in the upper-right and lower-left corners of SBP operator matrices with a repeating interior-point operator. This modification necessitates treating these new operators as elements, where mesh refinement is accomplished by increasing the number of elements in the mesh rather than increasing the number of nodes. The significant improvements in accuracy of this new family, for the same repeating interior-point operator, are demonstrated in the context of the linear convection equation.

Useful lower limits to polarization contributions to intermolecular interactions using a minimal basis of localized orthogonal orbitals: theory and analysis of the water dimer.

PubMed

Azar, R Julian; Horn, Paul Richard; Sundstrom, Eric Jon; Head-Gordon, Martin

2013-02-28

The problem of describing the energy-lowering associated with polarization of interacting molecules is considered in the overlapping regime for self-consistent field wavefunctions. The existing approach of solving for absolutely localized molecular orbital (ALMO) coefficients that are block-diagonal in the fragments is shown based on formal grounds and practical calculations to often overestimate the strength of polarization effects. A new approach using a minimal basis of polarized orthogonal local MOs (polMOs) is developed as an alternative. The polMO basis is minimal in the sense that one polarization function is provided for each unpolarized orbital that is occupied; such an approach is exact in second-order perturbation theory. Based on formal grounds and practical calculations, the polMO approach is shown to underestimate the strength of polarization effects. In contrast to the ALMO method, however, the polMO approach yields results that are very stable to improvements in the underlying AO basis expansion. Combining the ALMO and polMO approaches allows an estimate of the range of energy-lowering due to polarization. Extensive numerical calculations on the water dimer using a large range of basis sets with Hartree-Fock theory and a variety of different density functionals illustrate the key considerations. Results are also presented for the polarization-dominated Na(+)CH4 complex. Implications for energy decomposition analysis of intermolecular interactions are discussed.

Coherent optical excitations in superconducting qubit chain

NASA Astrophysics Data System (ADS)

Ian, Hou; Liu, Yu-Xi

2012-06-01

In the recent years, the theories of quantum optics have been borrowed to study the flows of electron pairs and their interactions with the circuit photon in the superconducting qubit circuits. These studies bring about new theories of quantum optics, such as the tunable electromagnetically induced transparency effect, peculiar to the Cooper pairs in circuits. In this talk, we focus on a special type of superconducting qubit circuits: superconducting qubit chain (SQC), which comprises dozens of qubits linearly placed along a stripline resonator. Since the dimensions of the qubits and the stripline have made their interactions inhomogeneous, the SQC cannot be diagonalized using the usual Dicke model. We present a new theoretical method, the deformation-projection method, for the exact diagonalization of the collective excitations of the qubits. This method allows us to predict that these excitations emulate the behaviors of Wannier and Frenckel excitons in the solid-state systems. The spontaneous emissions from the individual qubits in SQC are relayed to their neighbors, eventually arriving at a coherent emission, known as superradiance. We present a quantum relay model, which is crucial to quantum information processing, based on this finding.

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

Volkas, R. R.; Foot, R.; He, X.

The universal QCD color theory is extended to an SU(3)/sub 1//direct product/SU(3)/sub 2//direct product/SU(3)/sub 3/ gauge theory, where quarks of the /ital i/th generation transform as triplets under SU(3)/sub /ital i// and singlets under the other two factors. The usual color group is then identified with the diagonal subgroup, which remains exact after symmetry breaking. The gauge bosons associated with the 16 broken generators then form two massive octets under ordinary color. The interactions between quarks and these heavy gluonlike particles are explicitly nonuniversal and thus an exploration of their physical implications allows us to shed light on the fundamentalmore » issue of strong-interaction universality. Nonuniversality and weak flavor mixing are shown to generate heavy-gluon-induced flavor-changing neutral currents. The phenomenology of these processes is studied, as they provide the major experimental constraint on the extended theory. Three symmetry-breaking scenarios are presented. The first has color breaking occurring at the weak scale, while the second and third divorce the two scales. The third model has the interesting feature of radiatively induced off-diagonal Kobayashi-Maskawa matrix elements.« less

Solving an inverse eigenvalue problem with triple constraints on eigenvalues, singular values, and diagonal elements

NASA Astrophysics Data System (ADS)

Wu, Sheng-Jhih; Chu, Moody T.

2017-08-01

An inverse eigenvalue problem usually entails two constraints, one conditioned upon the spectrum and the other on the structure. This paper investigates the problem where triple constraints of eigenvalues, singular values, and diagonal entries are imposed simultaneously. An approach combining an eclectic mix of skills from differential geometry, optimization theory, and analytic gradient flow is employed to prove the solvability of such a problem. The result generalizes the classical Mirsky, Sing-Thompson, and Weyl-Horn theorems concerning the respective majorization relationships between any two of the arrays of main diagonal entries, eigenvalues, and singular values. The existence theory fills a gap in the classical matrix theory. The problem might find applications in wireless communication and quantum information science. The technique employed can be implemented as a first-step numerical method for constructing the matrix. With slight modification, the approach might be used to explore similar types of inverse problems where the prescribed entries are at general locations.

On generalized Mulliken-Hush approach of electronic transfer: Inclusion of non-zero off-diagonal diabatic dipole moment

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

Kryachko, E.S.

1999-06-03

The electronic coupling between the initial and final diabatic states is the major factor that determines the rate of electron transfer. A general formula for the adiabatic-to-diabatic mixing angle in terms of the electronic dipole moments is derived within a two-state model. It expresses the electronic coupling determining the rate of electronic transfer in terms of the off-diagonal diabatic dipole moment.

A Partitioning Algorithm for Block-Diagonal Matrices With Overlap

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

Guy Antoine Atenekeng Kahou; Laura Grigori; Masha Sosonkina

2008-02-02

We present a graph partitioning algorithm that aims at partitioning a sparse matrix into a block-diagonal form, such that any two consecutive blocks overlap. We denote this form of the matrix as the overlapped block-diagonal matrix. The partitioned matrix is suitable for applying the explicit formulation of Multiplicative Schwarz preconditioner (EFMS) described in [3]. The graph partitioning algorithm partitions the graph of the input matrix into K partitions, such that every partition {Omega}{sub i} has at most two neighbors {Omega}{sub i-1} and {Omega}{sub i+1}. First, an ordering algorithm, such as the reverse Cuthill-McKee algorithm, that reduces the matrix profile ismore » performed. An initial overlapped block-diagonal partition is obtained from the profile of the matrix. An iterative strategy is then used to further refine the partitioning by allowing nodes to be transferred between neighboring partitions. Experiments are performed on matrices arising from real-world applications to show the feasibility and usefulness of this approach.« less

Quantum phases of dimerized and frustrated Heisenberg spin chains with s = 1/2, 1 and 3/2: an entanglement entropy and fidelity study.

PubMed

Goli, V M L Durga Prasad; Sahoo, Shaon; Ramasesha, S; Sen, Diptiman

2013-03-27

We study here different regions in phase diagrams of the spin-1/2, spin-1 and spin-3/2 one-dimensional antiferromagnetic Heisenberg systems with frustration (next-nearest-neighbor interaction J2) and dimerization (δ). In particular, we analyze the behaviors of the bipartite entanglement entropy and fidelity at the gapless to gapped phase transitions and across the lines separating different phases in the J2-δ plane. All the calculations in this work are based on numerical exact diagonalizations of finite systems.

Finite-size effects in Anderson localization of one-dimensional Bose-Einstein condensates

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

Cestari, J. C. C.; Foerster, A.; Gusmao, M. A.

We investigate the disorder-induced localization transition in Bose-Einstein condensates for the Anderson and Aubry-Andre models in the noninteracting limit using exact diagonalization. We show that, in addition to the standard superfluid fraction, other tools such as the entanglement and fidelity can provide clear signatures of the transition. Interestingly, the fidelity exhibits good sensitivity even for small lattices. Effects of the system size on these quantities are analyzed in detail, including the determination of a finite-size-scaling law for the critical disorder strength in the case of the Anderson model.

Wigner molecules in carbon-nanotube quantum dots

NASA Astrophysics Data System (ADS)

Secchi, Andrea; Rontani, Massimo

2010-07-01

We demonstrate that electrons in quantum dots defined by electrostatic gates in semiconductor nanotubes freeze orderly in space realizing a “Wigner molecule.” Our exact diagonalization calculations uncover the features of the electron molecule, which may be accessed by tunneling spectroscopy—indeed some of them have already been observed by Deshpande and Bockrath [Nat. Phys. 4, 314 (2008)]10.1038/nphys895. We show that numerical results are satisfactorily reproduced by a simple ansatz vibrational wave function: electrons have localized wave functions, like nuclei in an ordinary molecule, whereas low-energy excitations are collective vibrations of electrons around their equilibrium positions.

Quantum Quenches and Relaxation Dynamics in the Thermodynamic Limit

NASA Astrophysics Data System (ADS)

Mallayya, Krishnanand; Rigol, Marcos

2018-02-01

We implement numerical linked cluster expansions (NLCEs) to study dynamics of lattice systems following quantum quenches, and focus on a hard-core boson model in one-dimensional lattices. We find that, in the nonintegrable regime and within the accessible times, local observables exhibit exponential relaxation. We determine the relaxation rate as one departs from the integrable point and show that it scales quadratically with the strength of the integrability breaking perturbation. We compare the NLCE results with those from exact diagonalization calculations on finite chains with periodic boundary conditions, and show that NLCEs are far more accurate.

Bound States in Dimerized and Frustrated Heisenberg Chains

NASA Astrophysics Data System (ADS)

Bouzerar, G.; Sil, S.

Using the Bond-Operator Technique (BOT), we have studied the low energy excitation spectrum of a frustrated dimerized antiferromagnetic Heisenberg chain. In particular, we have compared our analytical results with previous Exact Diagonalization (ED) data. Qualitatively, the BOT results are in good agreement with the ED data. And even a very good quantitative agreement is obtained in some parameter region. It is clearly shown that there is only one elementary excitation branch (lowest triplet branch) and that the two other well defined excitations which appear below the continuum, one singlet and one triplet, are bound states of two elementary triplets.

Diagonalization of transfer matrix of supersymmetry U{sub q}(sl-caret(M+1|N+1)) chain with a boundary

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

Kojima, Takeo

2013-04-15

We study the supersymmetry U{sub q}(sl-caret(M+1|N+1)) analogue of the supersymmetric t-J model with a boundary. Our approach is based on the algebraic analysis method of solvable lattice models. We diagonalize the commuting transfer matrix by using the bosonizations of the vertex operators associated with the quantum affine supersymmetry U{sub q}(sl-caret(M+1|N+1)).

Exact decoupling of the Dirac Hamiltonian. II. The generalized Douglas-Kroll-Hess transformation up to arbitrary order

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

Reiher, Markus; Wolf, Alexander

In order to achieve exact decoupling of the Dirac Hamiltonian within a unitary transformation scheme, we have discussed in part I of this series that either a purely numerical iterative technique (the Barysz-Sadlej-Snijders method) or a stepwise analytic approach (the Douglas-Kroll-Hess method) are possible. For the evaluation of Douglas-Kroll-Hess Hamiltonians up to a pre-defined order it was shown that a symbolic scheme has to be employed. In this work, an algorithm for this analytic derivation of Douglas-Kroll-Hess Hamiltonians up to any arbitrary order in the external potential is presented. We discuss how an estimate for the necessary order for exactmore » decoupling (within machine precision) for a given system can be determined from the convergence behavior of the Douglas-Kroll-Hess expansion prior to a quantum chemical calculation. Once this maximum order has been accomplished, the spectrum of the positive-energy part of the decoupled Hamiltonian, e.g., for electronic bound states, cannot be distinguished from the corresponding part of the spectrum of the Dirac operator. An efficient scalar-relativistic implementation of the symbolic operations for the evaluation of the positive-energy part of the block-diagonal Hamiltonian is presented, and its accuracy is tested for ground-state energies of one-electron ions over the whole periodic table. Furthermore, the first many-electron calculations employing sixth up to fourteenth order DKH Hamiltonians are presented.« less

Low temperature EPR investigation of Co2+ ion doped into rutile TiO2 single crystal: Experiments and simulations

NASA Astrophysics Data System (ADS)

Zerentürk, A.; Açıkgöz, M.; Kazan, S.; Yıldız, F.; Aktaş, B.

2017-02-01

In this paper, we present the results of X-band EPR spectra of Co2+ ion doped rutile (TiO2) which is one of the most promising memristor material. We obtained the angular variation of spectra in three mutually perpendicular planes at liquid helium (7-13 K) temperatures. Since the impurity ions have ½ effective spin and 7/2 nuclear spin, a relatively simple spin Hamiltonian containing only electronic Zeeman and hyperfine terms was utilized. Two different methods were used in theoretical analysis. Firstly, a linear regression analysis of spectra based on perturbation theory was studied. However, this approach is not sufficient for analyzing Co+2 spectra and leads to complex eigenvectors for G and A tensors due to large anisotropy of eigenvalues. Therefore, all spectra were analyzed again with exact diagonalization of spin Hamiltonian and the high accuracy eigenvalues and eigenvectors of G and A tensors were obtained by taking into account the effect of small sample misalignment from the exact crystallographic planes due to experimental conditions. Our results show that eigen-axes of g and A tensors are parallel to crystallographic directions. Hence, our EPR experiments proves that Co2+ ions substitute for Ti4+ ions in lattice. The obtained principal values of g tensor are gx=2.110(6), gy=5.890(2), gz=3.725(7) and principal values of hyperfine tensor are Ax=42.4, Ay=152.7, Az=26 (in 10-4/cm).

A discrete Fourier-encoded, diagonal-free experiment to simplify homonuclear 2D NMR correlations.

PubMed

Huang, Zebin; Guan, Quanshuai; Chen, Zhong; Frydman, Lucio; Lin, Yulan

2017-07-21

Nuclear magnetic resonance (NMR) spectroscopy has long served as an irreplaceable, versatile tool in physics, chemistry, biology, and materials sciences, owing to its ability to study molecular structure and dynamics in detail. In particular, the connectivity of chemical sites within molecules, and thereby molecular structure, becomes visible by multi-dimensional NMR. Homonuclear correlation experiments are a powerful tool for identifying coupled spins. Generally, diagonal peaks in these correlation spectra display the strongest intensities and do not offer any new information beyond the standard one-dimensional spectrum, whereas weaker, symmetrically placed cross peaks contain most of the coupling information. The cross peaks near the diagonal are often affected by the tails of strong diagonal peaks or even obscured entirely by the diagonal. In this paper, we demonstrate a homonuclear encoding approach based on imparting a discrete phase modulation of the targeted cross peaks and combine it with a site-selective sculpting scheme, capable of simplifying the patterns arising in these 2D correlation spectra. The theoretical principles of the new methods are laid out, and experimental observations are rationalized on the basis of theoretical analyses. The ensuing techniques provide a new way to retrieve 2D coupling information within homonuclear spin systems, with enhanced sensitivity, speed, and clarity.

A discrete Fourier-encoded, diagonal-free experiment to simplify homonuclear 2D NMR correlations

NASA Astrophysics Data System (ADS)

Huang, Zebin; Guan, Quanshuai; Chen, Zhong; Frydman, Lucio; Lin, Yulan

2017-07-01

Nuclear magnetic resonance (NMR) spectroscopy has long served as an irreplaceable, versatile tool in physics, chemistry, biology, and materials sciences, owing to its ability to study molecular structure and dynamics in detail. In particular, the connectivity of chemical sites within molecules, and thereby molecular structure, becomes visible by multi-dimensional NMR. Homonuclear correlation experiments are a powerful tool for identifying coupled spins. Generally, diagonal peaks in these correlation spectra display the strongest intensities and do not offer any new information beyond the standard one-dimensional spectrum, whereas weaker, symmetrically placed cross peaks contain most of the coupling information. The cross peaks near the diagonal are often affected by the tails of strong diagonal peaks or even obscured entirely by the diagonal. In this paper, we demonstrate a homonuclear encoding approach based on imparting a discrete phase modulation of the targeted cross peaks and combine it with a site-selective sculpting scheme, capable of simplifying the patterns arising in these 2D correlation spectra. The theoretical principles of the new methods are laid out, and experimental observations are rationalized on the basis of theoretical analyses. The ensuing techniques provide a new way to retrieve 2D coupling information within homonuclear spin systems, with enhanced sensitivity, speed, and clarity.

Generalized approximate spin projection calculations of effective exchange integrals of the CaMn4O5 cluster in the S1 and S3 states of the oxygen evolving complex of photosystem II.

PubMed

Isobe, H; Shoji, M; Yamanaka, S; Mino, H; Umena, Y; Kawakami, K; Kamiya, N; Shen, J-R; Yamaguchi, K

2014-06-28

Full geometry optimizations followed by the vibrational analysis were performed for eight spin configurations of the CaMn4O4X(H2O)3Y (X = O, OH; Y = H2O, OH) cluster in the S1 and S3 states of the oxygen evolution complex (OEC) of photosystem II (PSII). The energy gaps among these configurations obtained by vertical, adiabatic and adiabatic plus zero-point-energy (ZPE) correction procedures have been used for computation of the effective exchange integrals (J) in the spin Hamiltonian model. The J values are calculated by the (1) analytical method and the (2) generalized approximate spin projection (AP) method that eliminates the spin contamination errors of UB3LYP solutions. Using J values derived from these methods, exact diagonalization of the spin Hamiltonian matrix was carried out, yielding excitation energies and spin densities of the ground and lower-excited states of the cluster. The obtained results for the right (R)- and left (L)-opened structures in the S1 and S3 states are found to be consistent with available optical and magnetic experimental results. Implications of the computational results are discussed in relation to (a) the necessity of the exact diagonalization for computations of reliable energy levels, (b) magneto-structural correlations in the CaMn4O5 cluster of the OEC of PSII, (c) structural symmetry breaking in the S1 and S3 states, and (d) the right- and left-handed scenarios for the O-O bond formation for water oxidation.

A mesh-free approach to acoustic scattering from multiple spheres nested inside a large sphere by using diagonal translation operators.

PubMed

Hesford, Andrew J; Astheimer, Jeffrey P; Greengard, Leslie F; Waag, Robert C

2010-02-01

A multiple-scattering approach is presented to compute the solution of the Helmholtz equation when a number of spherical scatterers are nested in the interior of an acoustically large enclosing sphere. The solution is represented in terms of partial-wave expansions, and a linear system of equations is derived to enforce continuity of pressure and normal particle velocity across all material interfaces. This approach yields high-order accuracy and avoids some of the difficulties encountered when using integral equations that apply to surfaces of arbitrary shape. Calculations are accelerated by using diagonal translation operators to compute the interactions between spheres when the operators are numerically stable. Numerical results are presented to demonstrate the accuracy and efficiency of the method.

A mesh-free approach to acoustic scattering from multiple spheres nested inside a large sphere by using diagonal translation operators

PubMed Central

Hesford, Andrew J.; Astheimer, Jeffrey P.; Greengard, Leslie F.; Waag, Robert C.

2010-01-01

A multiple-scattering approach is presented to compute the solution of the Helmholtz equation when a number of spherical scatterers are nested in the interior of an acoustically large enclosing sphere. The solution is represented in terms of partial-wave expansions, and a linear system of equations is derived to enforce continuity of pressure and normal particle velocity across all material interfaces. This approach yields high-order accuracy and avoids some of the difficulties encountered when using integral equations that apply to surfaces of arbitrary shape. Calculations are accelerated by using diagonal translation operators to compute the interactions between spheres when the operators are numerically stable. Numerical results are presented to demonstrate the accuracy and efficiency of the method. PMID:20136208

Photoinduced piezooptics effect in TeO2-Ga2O3 glasses

NASA Astrophysics Data System (ADS)

Ozga, K.; Fedorchuk, A. O.; Armand, P.

2015-08-01

We have found that during the bicolor illumination by two boicolor coherent wavelengths 1540 nm/770 nm there occurred substantial changes of the elastooptical non-diagonal coefficients at 1150 nm cw laser wavelength. They are maximal at power densities 400 … 500 MW/cm2. The studies have shown that the maximal effect exists for ultra-fast quenching glasses and occurs after the 1-2 min of the treatment. The switching off of the optical treatment leads to the disappearance of the photoinduced piezooptics at about 100 ms. The observed changes are explained within the photoinduced changes of the charge density distribution for the principal structural clusters within a framework of the DFT approach. The studies were done both for diagonal as well as off-diagonal piezooptical effect (POE) tensor components.

Wigner crystalline edges in ν<~1 quantum dots

NASA Astrophysics Data System (ADS)

Goldmann, Eyal; Renn, Scot R.

1999-12-01

We investigate the edge reconstruction phenomenon believed to occur in quantum dots in the quantum Hall regime when the filling fraction is ν<~1. Our approach involves the examination of large dots (<= 40 electrons) using a partial diagonalization technique in which the occupancies of the deep interior orbitals are frozen. To interpret the results of this calculation, we evaluate the overlap between the diagonalized ground state and a set of trial wave functions which we call projected necklace (PN) states. A PN state is simply the angular momentum projection of a maximum density droplet surrounded by a ring of localized electrons. Our calculations reveal that PN states have up to 99% overlap with the diagonalized ground states, and are lower in energy than the states identified in Chamon and Wen's study of the edge reconstruction.

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

Sun, Ke-Wei; Division of Materials Science, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798; Fujihashi, Yuta

A master equation approach based on an optimized polaron transformation is adopted for dynamics simulation with simultaneous diagonal and off-diagonal spin-boson coupling. Two types of bath spectral density functions are considered, the Ohmic and the sub-Ohmic. The off-diagonal coupling leads asymptotically to a thermal equilibrium with a nonzero population difference P{sub z}(t → ∞) ≠ 0, which implies localization of the system, and it also plays a role in restraining coherent dynamics for the sub-Ohmic case. Since the new method can extend to the stronger coupling regime, we can investigate the coherent-incoherent transition in the sub-Ohmic environment. Relevant phase diagramsmore » are obtained for different temperatures. It is found that the sub-Ohmic environment allows coherent dynamics at a higher temperature than the Ohmic environment.« less

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.

Is a Trineutron Resonance Lower in Energy than a Tetraneutron Resonance?

NASA Astrophysics Data System (ADS)

Gandolfi, S.; Hammer, H.-W.; Klos, P.; Lynn, J. E.; Schwenk, A.

2017-06-01

We present quantum Monte Carlo calculations of few-neutron systems confined in external potentials based on local chiral interactions at next-to-next-to-leading order in chiral effective field theory. The energy and radial densities for these systems are calculated in different external Woods-Saxon potentials. We assume that their extrapolation to zero external-potential depth provides a quantitative estimate of three- and four-neutron resonances. The validity of this assumption is demonstrated by benchmarking with an exact diagonalization in the two-body case. We find that the extrapolated trineutron resonance, as well as the energy for shallow well depths, is lower than the tetraneutron resonance energy. This suggests that a three-neutron resonance exists below a four-neutron resonance in nature and is potentially measurable. To confirm that the relative ordering of three- and four-neutron resonances is not an artifact of the external confinement, we test that the odd-even staggering in the helium isotopic chain is reproduced within this approach. Finally, we discuss similarities between our results and ultracold Fermi gases.

A real-frequency solver for the Anderson impurity model based on bath optimization and cluster perturbation theory

NASA Astrophysics Data System (ADS)

Zingl, Manuel; Nuss, Martin; Bauernfeind, Daniel; Aichhorn, Markus

2018-05-01

Recently solvers for the Anderson impurity model (AIM) working directly on the real-frequency axis have gained much interest. A simple and yet frequently used impurity solver is exact diagonalization (ED), which is based on a discretization of the AIM bath degrees of freedom. Usually, the bath parameters cannot be obtained directly on the real-frequency axis, but have to be determined by a fit procedure on the Matsubara axis. In this work we present an approach where the bath degrees of freedom are first discretized directly on the real-frequency axis using a large number of bath sites (≈ 50). Then, the bath is optimized by unitary transformations such that it separates into two parts that are weakly coupled. One part contains the impurity site and its interacting Green's functions can be determined with ED. The other (larger) part is a non-interacting system containing all the remaining bath sites. Finally, the Green's function of the full AIM is calculated via coupling these two parts with cluster perturbation theory.

Is a Trineutron Resonance Lower in Energy than a Tetraneutron Resonance?

DOE PAGES

Gandolfi, Stefano; Hammer, Hans -Werner; Klos, P.; ...

2017-06-08

Here, we present quantum Monte Carlo calculations of few-neutron systems confined in external potentials based on local chiral interactions at next-to-next-to-leading order in chiral effective field theory. The energy and radial densities for these systems are calculated in different external Woods-Saxon potentials. We assume that their extrapolation to zero external-potential depth provides a quantitative estimate of three- and four-neutron resonances. The validity of this assumption is demonstrated by benchmarking with an exact diagonalization in the two-body case. We find that the extrapolated trineutron resonance, as well as the energy for shallow well depths, is lower than the tetraneutron resonance energy.more » This suggests that a three-neutron resonance exists below a four-neutron resonance in nature and is potentially measurable. To confirm that the relative ordering of three- and four-neutron resonances is not an artifact of the external confinement, we test that the odd-even staggering in the helium isotopic chain is reproduced within this approach. Finally, we discuss similarities between our results and ultracold Fermi gases.« less

Nonlocal torque operators in ab initio theory of the Gilbert damping in random ferromagnetic alloys

NASA Astrophysics Data System (ADS)

Turek, I.; Kudrnovský, J.; Drchal, V.

2015-12-01

We present an ab initio theory of the Gilbert damping in substitutionally disordered ferromagnetic alloys. The theory rests on introduced nonlocal torques which replace traditional local torque operators in the well-known torque-correlation formula and which can be formulated within the atomic-sphere approximation. The formalism is sketched in a simple tight-binding model and worked out in detail in the relativistic tight-binding linear muffin-tin orbital method and the coherent potential approximation (CPA). The resulting nonlocal torques are represented by nonrandom, non-site-diagonal, and spin-independent matrices, which simplifies the configuration averaging. The CPA-vertex corrections play a crucial role for the internal consistency of the theory and for its exact equivalence to other first-principles approaches based on the random local torques. This equivalence is also illustrated by the calculated Gilbert damping parameters for binary NiFe and FeCo random alloys, for pure iron with a model atomic-level disorder, and for stoichiometric FePt alloys with a varying degree of L 10 atomic long-range order.

Modified homotopy perturbation method for solving hypersingular integral equations of the first kind.

PubMed

Eshkuvatov, Z K; Zulkarnain, F S; Nik Long, N M A; Muminov, Z

2016-01-01

Modified homotopy perturbation method (HPM) was used to solve the hypersingular integral equations (HSIEs) of the first kind on the interval [-1,1] with the assumption that the kernel of the hypersingular integral is constant on the diagonal of the domain. Existence of inverse of hypersingular integral operator leads to the convergence of HPM in certain cases. Modified HPM and its norm convergence are obtained in Hilbert space. Comparisons between modified HPM, standard HPM, Bernstein polynomials approach Mandal and Bhattacharya (Appl Math Comput 190:1707-1716, 2007), Chebyshev expansion method Mahiub et al. (Int J Pure Appl Math 69(3):265-274, 2011) and reproducing kernel Chen and Zhou (Appl Math Lett 24:636-641, 2011) are made by solving five examples. Theoretical and practical examples revealed that the modified HPM dominates the standard HPM and others. Finally, it is found that the modified HPM is exact, if the solution of the problem is a product of weights and polynomial functions. For rational solution the absolute error decreases very fast by increasing the number of collocation points.

New Priorities for a Changing U.S. Economy

DTIC Science & Technology

1999-01-08

Stockholm, Sweden, 1991. [73] R . Malladi , J. Sethian, B. and Vermuri, "Shape modelling with front propagation: a level set approach," IEEE PAMI17...represented as n x n matrices of operators in £(£), and r (") is represented by a diagonal matrix, with diagonal entries equal to T. Denote by An...also has independent interest. Theorem 1 Assume that A’ is a *-algebra of finite dimension n. Then fa(A) = ^..(Art) for every A 6 £(£)~ r ~ Remark

Many-body Green’s function theory for electron-phonon interactions: Ground state properties of the Holstein dimer

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

Säkkinen, Niko; Leeuwen, Robert van; Peng, Yang

2015-12-21

We study ground-state properties of a two-site, two-electron Holstein model describing two molecules coupled indirectly via electron-phonon interaction by using both exact diagonalization and self-consistent diagrammatic many-body perturbation theory. The Hartree and self-consistent Born approximations used in the present work are studied at different levels of self-consistency. The governing equations are shown to exhibit multiple solutions when the electron-phonon interaction is sufficiently strong, whereas at smaller interactions, only a single solution is found. The additional solutions at larger electron-phonon couplings correspond to symmetry-broken states with inhomogeneous electron densities. A comparison to exact results indicates that this symmetry breaking is stronglymore » correlated with the formation of a bipolaron state in which the two electrons prefer to reside on the same molecule. The results further show that the Hartree and partially self-consistent Born solutions obtained by enforcing symmetry do not compare well with exact energetics, while the fully self-consistent Born approximation improves the qualitative and quantitative agreement with exact results in the same symmetric case. This together with a presented natural occupation number analysis supports the conclusion that the fully self-consistent approximation describes partially the bipolaron crossover. These results contribute to better understanding how these approximations cope with the strong localizing effect of the electron-phonon interaction.« less

Ab initio excited states from the in-medium similarity renormalization group

NASA Astrophysics Data System (ADS)

Parzuchowski, N. M.; Morris, T. D.; Bogner, S. K.

2017-04-01

We present two new methods for performing ab initio calculations of excited states for closed-shell systems within the in-medium similarity renormalization group (IMSRG) framework. Both are based on combining the IMSRG with simple many-body methods commonly used to target excited states, such as the Tamm-Dancoff approximation (TDA) and equations-of-motion (EOM) techniques. In the first approach, a two-step sequential IMSRG transformation is used to drive the Hamiltonian to a form where a simple TDA calculation (i.e., diagonalization in the space of 1 p 1 h excitations) becomes exact for a subset of eigenvalues. In the second approach, EOM techniques are applied to the IMSRG ground-state-decoupled Hamiltonian to access excited states. We perform proof-of-principle calculations for parabolic quantum dots in two dimensions and the closed-shell nuclei 16O and 22O. We find that the TDA-IMSRG approach gives better accuracy than the EOM-IMSRG when calculations converge, but it is otherwise lacking the versatility and numerical stability of the latter. Our calculated spectra are in reasonable agreement with analogous EOM-coupled-cluster calculations. This work paves the way for more interesting applications of the EOM-IMSRG approach to calculations of consistently evolved observables such as electromagnetic strength functions and nuclear matrix elements, and extensions to nuclei within one or two nucleons of a closed shell by generalizing the EOM ladder operator to include particle-number nonconserving terms.

Yet another family of diagonal metrics for de Sitter and anti-de Sitter spacetimes

NASA Astrophysics Data System (ADS)

Podolský, Jiří; Hruška, Ondřej

2017-06-01

In this work we present and analyze a new class of coordinate representations of de Sitter and anti-de Sitter spacetimes for which the metrics are diagonal and (typically) static and axially symmetric. Contrary to the well-known forms of these fundamental geometries, that usually correspond to a 1 +3 foliation with the 3-space of a constant spatial curvature, the new metrics are adapted to a 2 +2 foliation, and are warped products of two 2-spaces of constant curvature. This new class of (anti-)de Sitter metrics depends on the value of cosmological constant Λ and two discrete parameters +1 ,0 ,-1 related to the curvature of the 2-spaces. The class admits 3 distinct subcases for Λ >0 and 8 subcases for Λ <0 . We systematically study all these possibilities. In particular, we explicitly present the corresponding parametrizations of the (anti-)de Sitter hyperboloid, visualize the coordinate lines and surfaces within the global conformal cylinder, investigate their mutual relations, present some closely related forms of the metrics, and give transformations to standard de Sitter and anti-de Sitter metrics. Using these results, we also provide a physical interpretation of B -metrics as exact gravitational fields of a tachyon.

A new family of high-order compact upwind difference schemes with good spectral resolution

NASA Astrophysics Data System (ADS)

Zhou, Qiang; Yao, Zhaohui; He, Feng; Shen, M. Y.

2007-12-01

This paper presents a new family of high-order compact upwind difference schemes. Unknowns included in the proposed schemes are not only the values of the function but also those of its first and higher derivatives. Derivative terms in the schemes appear only on the upwind side of the stencil. One can calculate all the first derivatives exactly as one solves explicit schemes when the boundary conditions of the problem are non-periodic. When the proposed schemes are applied to periodic problems, only periodic bi-diagonal matrix inversions or periodic block-bi-diagonal matrix inversions are required. Resolution optimization is used to enhance the spectral representation of the first derivative, and this produces a scheme with the highest spectral accuracy among all known compact schemes. For non-periodic boundary conditions, boundary schemes constructed in virtue of the assistant scheme make the schemes not only possess stability for any selective length scale on every point in the computational domain but also satisfy the principle of optimal resolution. Also, an improved shock-capturing method is developed. Finally, both the effectiveness of the new hybrid method and the accuracy of the proposed schemes are verified by executing four benchmark test cases.

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.

Electronic States and Persistent Currents in Nanowire Quantum Ring

NASA Astrophysics Data System (ADS)

Kokurin, I. A.

2018-04-01

The new model of a quantum ring (QR) defined inside a nanowire (NW) is proposed. The one-particle Hamiltonian for electron in [111]-oriented NW QR is constructed taking into account both Rashba and Dresselhaus spin-orbit coupling (SOC). The energy levels as a function of magnetic field are found using the exact numerical diagonalization. The persistent currents (both charge and spin) are calculated. The specificity of SOC and arising anticrossings in energy spectrum lead to unusual features in persistent current behavior. The variation of magnetic field or carrier concentration by means of gate can lead to pure spin persistent current with the charge current being zero.

Duality-mediated critical amplitude ratios for the (2 + 1)-dimensional S = 1XY model

NASA Astrophysics Data System (ADS)

Nishiyama, Yoshihiro

2017-09-01

The phase transition for the (2 + 1)-dimensional spin-S = 1XY model was investigated numerically. Because of the boson-vortex duality, the spin stiffness ρs in the ordered phase and the vortex-condensate stiffness ρv in the disordered phase should have a close relationship. We employed the exact diagonalization method, which yields the excitation gap directly. As a result, we estimate the amplitude ratios ρs,v/Δ (Δ: Mott insulator gap) by means of the scaling analyses for the finite-size cluster with N ≤ 22 spins. The ratio ρs/ρv admits a quantitative measure of deviation from selfduality.

Fidelity Study of Superconductivity in Extended Hubbard Models

NASA Astrophysics Data System (ADS)

Plonka, Nachum; Jia, Chunjing; Moritz, Brian; Wang, Yao; Devereaux, Thomas

2015-03-01

The role of strong electronic correlations on unconventional superconductivity remains an important open question. Here, we explore the influence of long-range Coulomb interactions, present in real material systems, through nearest and next-nearest neighbor extended Hubbard interactions in addition to the usual on-site terms. Utilizing large scale, numerical exact diagonalization, we analyze the signatures of superconductivity in the ground states through the fidelity metric of quantum information theory. We find that these extended interactions enhance charge fluctuations with various wave vectors. These suppress superconductivity in general, but in certain parameter regimes superconductivity is sustained. This has implications for tuning extended interactions in real materials.

Diagonal and off-diagonal susceptibilities of conserved quantities in relativistic heavy-ion collisions

NASA Astrophysics Data System (ADS)

Chatterjee, Arghya; Chatterjee, Sandeep; Nayak, Tapan K.; Ranjan Sahoo, Nihar

2016-12-01

Susceptibilities of conserved quantities, such as baryon number, strangeness and electric charge are sensitive to the onset of quantum chromodynamics phase transition, and are expected to provide information on the matter produced in heavy-ion collision experiments. A comprehensive study of the second order diagonal susceptibilities and cross correlations has been made within a thermal model approach of the hadron resonance gas model as well as with a hadronic transport model, ultra-relativistic quantum molecular dynamics. We perform a detailed analysis of the effect of detector acceptances and choice of particle species in the experimental measurements of the susceptibilities for heavy-ion collisions corresponding to \\sqrt{{s}{NN}} = 4 GeV to 200 GeV. The transverse momentum cutoff dependence of suitably normalised susceptibilities are proposed as useful observables to probe the properties of the medium at freezeout.

Understanding the determinants of volatility clustering in terms of stationary Markovian processes

NASA Astrophysics Data System (ADS)

Miccichè, S.

2016-11-01

Volatility is a key variable in the modeling of financial markets. The most striking feature of volatility is that it is a long-range correlated stochastic variable, i.e. its autocorrelation function decays like a power-law τ-β for large time lags. In the present work we investigate the determinants of such feature, starting from the empirical observation that the exponent β of a certain stock's volatility is a linear function of the average correlation of such stock's volatility with all other volatilities. We propose a simple approach consisting in diagonalizing the cross-correlation matrix of volatilities and investigating whether or not the diagonalized volatilities still keep some of the original volatility stylized facts. As a result, the diagonalized volatilities result to share with the original volatilities either the power-law decay of the probability density function and the power-law decay of the autocorrelation function. This would indicate that volatility clustering is already present in the diagonalized un-correlated volatilities. We therefore present a parsimonious univariate model based on a non-linear Langevin equation that well reproduces these two stylized facts of volatility. The model helps us in understanding that the main source of volatility clustering, once volatilities have been diagonalized, is that the economic forces driving volatility can be modeled in terms of a Smoluchowski potential with logarithmic tails.

Bilinear Inverse Problems: Theory, Algorithms, and Applications

NASA Astrophysics Data System (ADS)

Ling, Shuyang

We will discuss how several important real-world signal processing problems, such as self-calibration and blind deconvolution, can be modeled as bilinear inverse problems and solved by convex and nonconvex optimization approaches. In Chapter 2, we bring together three seemingly unrelated concepts, self-calibration, compressive sensing and biconvex optimization. We show how several self-calibration problems can be treated efficiently within the framework of biconvex compressive sensing via a new method called SparseLift. More specifically, we consider a linear system of equations y = DAx, where the diagonal matrix D (which models the calibration error) is unknown and x is an unknown sparse signal. By "lifting" this biconvex inverse problem and exploiting sparsity in this model, we derive explicit theoretical guarantees under which both x and D can be recovered exactly, robustly, and numerically efficiently. In Chapter 3, we study the question of the joint blind deconvolution and blind demixing, i.e., extracting a sequence of functions [special characters omitted] from observing only the sum of their convolutions [special characters omitted]. In particular, for the special case s = 1, it becomes the well-known blind deconvolution problem. We present a non-convex algorithm which guarantees exact recovery under conditions that are competitive with convex optimization methods, with the additional advantage of being computationally much more efficient. We discuss several applications of the proposed framework in image processing and wireless communications in connection with the Internet-of-Things. In Chapter 4, we consider three different self-calibration models of practical relevance. We show how their corresponding bilinear inverse problems can be solved by both the simple linear least squares approach and the SVD-based approach. As a consequence, the proposed algorithms are numerically extremely efficient, thus allowing for real-time deployment. Explicit theoretical guarantees and stability theory are derived and the number of sampling complexity is nearly optimal (up to a poly-log factor). Applications in imaging sciences and signal processing are discussed and numerical simulations are presented to demonstrate the effectiveness and efficiency of our approach.

Kato expansion in quantum canonical perturbation theory

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

Nikolaev, Andrey, E-mail: Andrey.Nikolaev@rdtex.ru

2016-06-15

This work establishes a connection between canonical perturbation series in quantum mechanics and a Kato expansion for the resolvent of the Liouville superoperator. Our approach leads to an explicit expression for a generator of a block-diagonalizing Dyson’s ordered exponential in arbitrary perturbation order. Unitary intertwining of perturbed and unperturbed averaging superprojectors allows for a description of ambiguities in the generator and block-diagonalized Hamiltonian. We compare the efficiency of the corresponding computational algorithm with the efficiencies of the Van Vleck and Magnus methods for high perturbative orders.

Electrophoresis for genotyping: microtiter array diagonal gel electrophoresis on horizontal polyacrylamide gels, hydrolink, or agarose.

PubMed

Day, I N; Humphries, S E

1994-11-01

Electrophoresis of DNA has been performed traditionally in either an agarose or acrylamide gel matrix. Considerable effort has been directed to improved quality agaroses capable of high resolution, but for small fragments, such as those from polymerase chain reaction (PCR) and post-PCR digests, acrylamide still offers the highest resolution. Although agarose gels can easily be prepared in an open-faced format to gain the conveniences of horizontal electrophoresis, acrylamide does not polymerize in the presence of air and the usual configurations for gel preparation lead to electrophoresis in the vertical dimension. We describe here a very simple device and method to prepare and manipulate horizontal polyacrylamide gels (H-PAGE). In addition, the open-faced horizontal arrangement enables loading of arrays of wells. Since many procedures are undertaken in standard 96-well microtiter plates, we have also designed a device which preserves the exact configuration of the 8 x 12 array and enables electrophoresis in tracks following a 71.6 degrees diagonal between wells (MADGE, microtiter array diagonal gel electrophoresis), using either acrylamide or agarose. This eliminates almost all of the staff time taken in setup, loading, and recordkeeping and offers high resolution for genotyping pattern recognition. The nature and size of the gels allow direct stacking of gels in one tank, so that a tank used typically to analyze 30-60 samples can readily be used to analyze 1000-2000 samples. The gels would also enable robotic loading. Electrophoresis allows analysis of size and charge, parameters inaccessible to liquid-phase methods: thus, genotyping size patterns, variable length repeats, and haplotypes is possible, as well as adaptability to typing of point variations using protocols which create a difference detectable by electrophoresis.

A new algorithm for real-time optimal dispatch of active and reactive power generation retaining nonlinearity

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

Roy, L.; Rao, N.D.

1983-04-01

This paper presents a new method for optimal dispatch of real and reactive power generation which is based on cartesian coordinate formulation of economic dispatch problem and reclassification of state and control variables associated with generator buses. The voltage and power at these buses are classified as parametric and functional inequality constraints, and are handled by reduced gradient technique and penalty factor approach respectively. The advantage of this classification is the reduction in the size of the equality constraint model, leading to less storage requirement. The rectangular coordinate formulation results in an exact equality constraint model in which the coefficientmore » matrix is real, sparse, diagonally dominant, smaller in size and need be computed and factorized once only in each gradient step. In addition, Lagragian multipliers are calculated using a new efficient procedure. A natural outcome of these features is the solution of the economic dispatch problem, faster than other methods available to date in the literature. Rapid and reliable convergence is an additional desirable characteristic of the method. Digital simulation results are presented on several IEEE test systems to illustrate the range of application of the method visa-vis the popular Dommel-Tinney (DT) procedure. It is found that the proposed method is more reliable, 3-4 times faster and requires 20-30 percent less storage compared to the DT algorithm, while being just as general. Thus, owing to its exactness, robust mathematical model and less computational requirements, the method developed in the paper is shown to be a practically feasible algorithm for on-line optimal power dispatch.« less

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

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

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

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

On the cross-stream spectral method for the Orr-Sommerfeld equation

NASA Technical Reports Server (NTRS)

Zorumski, William E.; Hodge, Steven L.

1993-01-01

Cross-stream models are defined as solutions to the Orr-Sommerfeld equation which are propagating normal to the flow direction. These models are utilized as a basis for a Hilbert space to approximate the spectrum of the Orr-Sommerfeld equation with plane Poiseuille flow. The cross-stream basis leads to a standard eigenvalue problem for the frequencies of Poiseuille flow instability waves. The coefficient matrix in the eigenvalue problem is shown to be the sum of a real matrix and a negative-imaginary diagonal matrix which represents the frequencies of the cross-stream modes. The real coefficient matrix is shown to approach a Toeplitz matrix when the row and column indices are large. The Toeplitz matrix is diagonally dominant, and the diagonal elements vary inversely in magnitude with diagonal position. The Poiseuille flow eigenvalues are shown to lie within Gersgorin disks with radii bounded by the product of the average flow speed and the axial wavenumber. It is shown that the eigenvalues approach the Gersgorin disk centers when the mode index is large, so that the method may be used to compute spectra with an essentially unlimited number of elements. When the mode index is large, the real part of the eigenvalue is the product of the axial wavenumber and the average flow speed, and the imaginary part of the eigen value is identical to the corresponding cross-stream mode frequency. The cross-stream method is numerically well-conditioned in comparison to Chebyshev based methods, providing equivalent accuracy for small mode indices and superior accuracy for large indices.

Functional renormalization group approach to electronic structure calculations for systems without translational symmetry

NASA Astrophysics Data System (ADS)

Seiler, Christian; Evers, Ferdinand

2016-10-01

A formalism for electronic-structure calculations is presented that is based on the functional renormalization group (FRG). The traditional FRG has been formulated for systems that exhibit a translational symmetry with an associated Fermi surface, which can provide the organization principle for the renormalization group (RG) procedure. We here advance an alternative formulation, where the RG flow is organized in the energy-domain rather than in k space. This has the advantage that it can also be applied to inhomogeneous matter lacking a band structure, such as disordered metals or molecules. The energy-domain FRG (ɛ FRG) presented here accounts for Fermi-liquid corrections to quasiparticle energies and particle-hole excitations. It goes beyond the state of the art G W -BSE , because in ɛ FRG the Bethe-Salpeter equation (BSE) is solved in a self-consistent manner. An efficient implementation of the approach that has been tested against exact diagonalization calculations and calculations based on the density matrix renormalization group is presented. Similar to the conventional FRG, also the ɛ FRG is able to signalize the vicinity of an instability of the Fermi-liquid fixed point via runaway flow of the corresponding interaction vertex. Embarking upon this fact, in an application of ɛ FRG to the spinless disordered Hubbard model we calculate its phase boundary in the plane spanned by the interaction and disorder strength. Finally, an extension of the approach to finite temperatures and spin S =1 /2 is also given.

Almost conserved operators in nearly many-body localized systems

NASA Astrophysics Data System (ADS)

Pancotti, Nicola; Knap, Michael; Huse, David A.; Cirac, J. Ignacio; Bañuls, Mari Carmen

2018-03-01

We construct almost conserved local operators, that possess a minimal commutator with the Hamiltonian of the system, near the many-body localization transition of a one-dimensional disordered spin chain. We collect statistics of these slow operators for different support sizes and disorder strengths, both using exact diagonalization and tensor networks. Our results show that the scaling of the average of the smallest commutators with the support size is sensitive to Griffiths effects in the thermal phase and the onset of many-body localization. Furthermore, we demonstrate that the probability distributions of the commutators can be analyzed using extreme value theory and that their tails reveal the difference between diffusive and subdiffusive dynamics in the thermal phase.

Is the ground state of 5d4 double-perovskite Iridate Ba2YIrO6 magnetic or nonmagnetic?

NASA Astrophysics Data System (ADS)

Gong, Hoshin; Kim, Kyoo; Kim, Beom Hyun; Kim, Bongjae; Kim, Junwon; Min, B. I.

2018-05-01

We have investigated electronic structures and magnetic properties of double perovskite Iridate Ba2YIrO6 with 5d4 configuration, employing the exact diagonalization method for multi-site clusters. We have considered a many-body Hamiltonian for all d states (eg and t2g) including all relevant physical parameters such as the Coulomb correlation, spin-orbit coupling, crystal-field effect, and Hund coupling. We have found that the ground state of Ba2YIrO6 is nonmagnetic and that the Hund coupling plays an important role in the magnetic properties of the 5d4 systems, unlike the well-studied 5d5 systems.

Hole pairing and thermodynamic properties of the two dimensional frustrated t-J model

NASA Astrophysics Data System (ADS)

Roy, K.; Pal, P.; Nath, S.; Ghosh, N. K.

2018-04-01

The frustrated t-J model is investigated by using the exact-diagonalization (ED) method on an 8-site cluster. The effect on next-nearest-neighbor (NNN) exchange interaction J' (frustration) on the hole pairing and the thermodynamic properties of the system is considered. Two holes initially remain unbound at smaller value of J'/t, but tend to bind at larger value. The maximum possibility of pair formation has been observed to be at NNN sites. Entropy calculation shows that the system goes to more disordered state with J'. The specific heat curves show a single peak structure. A decrease in effective exchange energy is observed due to the frustration.

Stress Response of Granular Systems

NASA Astrophysics Data System (ADS)

Ramola, Kabir; Chakraborty, Bulbul

2017-10-01

We develop a framework for stress response in two dimensional granular media, with and without friction, that respects vector force balance at the microscopic level. We introduce local gauge degrees of freedom that determine the response of contact forces between constituent grains on a given, disordered, contact network, to external perturbations. By mapping this response to the spectral properties of the graph Laplacian corresponding to the underlying contact network, we show that this naturally leads to spatial localization of forces. We present numerical evidence for localization using exact diagonalization studies of network Laplacians of soft disk packings. Finally, we discuss the role of other constraints, such as torque balance, in determining the stability of a granular packing to external perturbations.

Time-dependent mean-field theory for x-ray near-edge spectroscopy

NASA Astrophysics Data System (ADS)

Bertsch, G. F.; Lee, A. J.

2014-02-01

We derive equations of motion for calculating the near-edge x-ray absorption spectrum in molecules and condensed matter, based on a two-determinant approximation and Dirac's variational principle. The theory provides an exact solution for the linear response when the Hamiltonian or energy functional has only diagonal interactions in some basis. We numerically solve the equations to compare with the Mahan-Nozières-De Dominicis theory of the edge singularity in metallic conductors. Our extracted power-law exponents are similar to those of the analytic theory, but are not in quantitative agreement. The calculational method can be readily generalized to treat Kohn-Sham Hamiltonians with electron-electron interactions derived from correlation-exchange potentials.

Dynamical spin structure factors of α-RuCl3

NASA Astrophysics Data System (ADS)

Suzuki, Takafumi; Suga, Sei-ichiro

2018-03-01

Honeycomb-lattice magnet α-RuCl3 is considered to be a potential candidate of realizing Kitaev spin liquid, although this material undergoes a phase transition to the zigzag magnetically ordered state at T N ∼ 7 K. Quite recently, inelastic neutron-scattering experiments using single crystal α-RuCl3 have unveiled characteristic dynamical properties. We calculate dynamical spin structure factors of three ab-initio models for α-RuCl3 with an exact numerical diagonalization method. We also calculate temperature dependences of the specific heat by employing thermal pure quantum states. We compare our numerical results with the experiments and discuss characteristics obtained by using three ab-initio models.

Optical coefficients in a semiconductor quantum ring: Electric field and donor impurity effects

NASA Astrophysics Data System (ADS)

Duque, C. M.; Acosta, Ruben E.; Morales, A. L.; Mora-Ramos, M. E.; Restrepo, R. L.; Ojeda, J. H.; Kasapoglu, E.; Duque, C. A.

2016-10-01

The electron states in a two-dimensional quantum dot ring are calculated in the presence of a donor impurity atom under the effective mass and parabolic band approximations. The effect of an externally applied electric field is also taken into account. The wavefunctions are obtained via the exact diagonalization of the problem Hamiltonian using a 2D expansion within the adiabatic approximation. The impurity-related optical response is analyzed via the optical absorption, relative refractive index change and the second harmonics generation. The dependencies of the electron states and these optical coefficients with the changes in the configuration of the quantum ring system are discussed in detail.

Fidelity study of superconductivity in extended Hubbard models

NASA Astrophysics Data System (ADS)

Plonka, N.; Jia, C. J.; Wang, Y.; Moritz, B.; Devereaux, T. P.

2015-07-01

The Hubbard model with local on-site repulsion is generally thought to possess a superconducting ground state for appropriate parameters, but the effects of more realistic long-range Coulomb interactions have not been studied extensively. We study the influence of these interactions on superconductivity by including nearest- and next-nearest-neighbor extended Hubbard interactions in addition to the usual on-site terms. Utilizing numerical exact diagonalization, we analyze the signatures of superconductivity in the ground states through the fidelity metric of quantum information theory. We find that nearest and next-nearest neighbor interactions have thresholds above which they destabilize superconductivity regardless of whether they are attractive or repulsive, seemingly due to competing charge fluctuations.

Singular perturbation and time scale approaches in discrete control systems

NASA Technical Reports Server (NTRS)

Naidu, D. S.; Price, D. B.

1988-01-01

After considering a singularly perturbed discrete control system, a singular perturbation approach is used to obtain outer and correction subsystems. A time scale approach is then applied via block diagonalization transformations to decouple the system into slow and fast subsystems. To a zeroth-order approximation, the singular perturbation and time-scale approaches are found to yield equivalent results.

Anomalous dynamical phase in quantum spin chains with long-range interactions

NASA Astrophysics Data System (ADS)

Homrighausen, Ingo; Abeling, Nils O.; Zauner-Stauber, Valentin; Halimeh, Jad C.

2017-09-01

The existence or absence of nonanalytic cusps in the Loschmidt-echo return rate is traditionally employed to distinguish between a regular dynamical phase (regular cusps) and a trivial phase (no cusps) in quantum spin chains after a global quench. However, numerical evidence in a recent study (J. C. Halimeh and V. Zauner-Stauber, arXiv:1610.02019) suggests that instead of the trivial phase, a distinct anomalous dynamical phase characterized by a novel type of nonanalytic cusps occurs in the one-dimensional transverse-field Ising model when interactions are sufficiently long range. Using an analytic semiclassical approach and exact diagonalization, we show that this anomalous phase also arises in the fully connected case of infinite-range interactions, and we discuss its defining signature. Our results show that the transition from the regular to the anomalous dynamical phase coincides with Z2-symmetry breaking in the infinite-time limit, thereby showing a connection between two different concepts of dynamical criticality. Our work further expands the dynamical phase diagram of long-range interacting quantum spin chains, and can be tested experimentally in ion-trap setups and ultracold atoms in optical cavities, where interactions are inherently long range.

Closed-form eigensolutions of nonviscously, nonproportionally damped systems based on continuous damping sensitivity

NASA Astrophysics Data System (ADS)

Lázaro, Mario

2018-01-01

In this paper, nonviscous, nonproportional, vibrating structures are considered. Nonviscously damped systems are characterized by dissipative mechanisms which depend on the history of the response velocities via hereditary kernel functions. Solutions of the free motion equation lead to a nonlinear eigenvalue problem involving mass, stiffness and damping matrices. Viscoelasticity leads to a frequency dependence of this latter. In this work, a novel closed-form expression to estimate complex eigenvalues is derived. The key point is to consider the damping model as perturbed by a continuous fictitious parameter. Assuming then the eigensolutions as function of this parameter, the computation of the eigenvalues sensitivity leads to an ordinary differential equation, from whose solution arises the proposed analytical formula. The resulting expression explicitly depends on the viscoelasticity (frequency derivatives of the damping function), the nonproportionality (influence of the modal damping matrix off-diagonal terms). Eigenvectors are obtained using existing methods requiring only the corresponding eigenvalue. The method is validated using a numerical example which compares proposed with exact ones and with those determined from the linear first order approximation in terms of the damping matrix. Frequency response functions are also plotted showing that the proposed approach is valid even for moderately or highly damped systems.

Numerical algorithms for cold-relativistic plasma models in the presence of discontinuties

NASA Astrophysics Data System (ADS)

Hakim, Ammar; Cary, John; Bruhwiler, David; Geddes, Cameron; Leemans, Wim; Esarey, Eric

2006-10-01

A numerical algorithm is presented to solve cold-relativistic electron fluid equations in the presence of sharp gradients and discontinuities. The intended application is to laser wake-field accelerator simulations in which the laser induces accelerating fields thousands of times those achievable in conventional RF accelerators. The relativistic cold-fluid equations are formulated as non-classical system of hyperbolic balance laws. It is shown that the flux Jacobian for this system can not be diagonalized which causes numerical difficulties when developing shock-capturing algorithms. Further, the system is shown to admit generalized delta-shock solutions, first discovered in the context of sticky-particle dynamics (Bouchut, Ser. Adv. Math App. Sci., 22 (1994) pp. 171--190). A new approach, based on relaxation schemes proposed by Jin and Xin (Comm. Pure Appl. Math. 48 (1995) pp. 235--276) and LeVeque and Pelanti (J. Comput. Phys. 172 (2001) pp. 572--591) is developed to solve this system of equations. The method consists of finding an exact solution to a Riemann problem at each cell interface and coupling these to advance the solution in time. Applications to an intense laser propagating in an under-dense plasma are presented.

Field Impact Evaluation Process on Electronic Tabular Display Subsystem (ETABS).

DTIC Science & Technology

1979-10-01

structural and process techniques are described. These include a diagonal slice approach to team formulation and several different methods of team building, process control and conflict management . (Author)

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

Mazzarella, G.; Toigo, F.; Salasnich, L.

We consider a bosonic Josephson junction made of N ultracold and dilute atoms confined by a quasi-one-dimensional double-well potential within the two-site Bose-Hubbard model framework. The behavior of the system is investigated at zero temperature by varying the interatomic interaction from the strongly attractive regime to the repulsive one. We show that the ground state exhibits a crossover from a macroscopic Schroedinger-cat state to a separable Fock state through an atomic coherent regime. By diagonalizing the Bose-Hubbard Hamiltonian we characterize the emergence of the macroscopic cat states by calculating the Fisher information F, the coherence by means of the visibilitymore » {alpha} of the interference fringes in the momentum distribution, and the quantum correlations by using the entanglement entropy S. Both Fisher information and visibility are shown to be related to the ground-state energy by employing the Hellmann-Feynman theorem. This result, together with a perturbative calculation of the ground-state energy, allows simple analytical formulas for F and {alpha} to be obtained over a range of interactions, in excellent agreement with the exact diagonalization of the Bose-Hubbard Hamiltonian. In the attractive regime the entanglement entropy attains values very close to its upper limit for a specific interaction strength lying in the region where coherence is lost and self-trapping sets in.« less

A simple molecular mechanics integrator in mixed rigid body and dihedral angle space

PubMed Central

Vitalis, Andreas; Pappu, Rohit V.

2014-01-01

We propose a numerical scheme to integrate equations of motion in a mixed space of rigid-body and dihedral angle coordinates. The focus of the presentation is biomolecular systems and the framework is applicable to polymers with tree-like topology. By approximating the effective mass matrix as diagonal and lumping all bias torques into the time dependencies of the diagonal elements, we take advantage of the formal decoupling of individual equations of motion. We impose energy conservation independently for every degree of freedom and this is used to derive a numerical integration scheme. The cost of all auxiliary operations is linear in the number of atoms. By coupling the scheme to one of two popular thermostats, we extend the method to sample constant temperature ensembles. We demonstrate that the integrator of choice yields satisfactory stability and is free of mass-metric tensor artifacts, which is expected by construction of the algorithm. Two fundamentally different systems, viz., liquid water and an α-helical peptide in a continuum solvent are used to establish the applicability of our method to a wide range of problems. The resultant constant temperature ensembles are shown to be thermodynamically accurate. The latter relies on detailed, quantitative comparisons to data from reference sampling schemes operating on exactly the same sets of degrees of freedom. PMID:25053299

Multidimensional Coherent Spectroscopy of GaAs Excitons and Quantum Microcavity Polaritons

NASA Astrophysics Data System (ADS)

Wilmer, Brian L.

Light-matter interactions associated with excitons and exciton related complexes are explored in bulk GaAs and semiconductor microcavities using multidimensional coherent spectroscopy (MDCS). This approach provides rich spectra determining quantum excitation pathways, structural influences on the excitons, and coherence times. Polarization, excitation density, and temperature-dependent MDCS is performed on excitons in strained bulk GaAs layers, probing the coherent response for differing amounts of strain. Biaxial tensile strain lifts the degeneracy of heavy-hole and light-hole valence states, leading to an observed splitting of the associated excitons at low temperature. Increasing the strain increases the magnitude of the heavy-/light- hole exciton peak splitting, induces an asymmetry in the off-diagonal interaction coherences, increases the difference in the heavy- and light- hole exciton homogenous linewidths, and increases the inhomogeneous broadening of both exciton species. All results arise from strain-induced variations in the local electronic environment, which is not uniform along the growth direction of the thin layers. For cross-linear polarized excitation, wherein excitonic signals give way to biexcitonic signals, the high-strain sample shows evidence of bound light-, heavy- and mixed- hole biexcitons. 2DCS maps the anticrossing associated with normal mode splitting in a semiconductor microcavity. For a detuning range near zero, it is observed that there are two diagonal features related to the intra-action of exciton-polariton branches and two off-diagonal features related to coherent interaction between the polaritons. At negative detuning, the line shape properties of the diagonal intra-action features are distinguishable and can be associated with cavity-like and exciton-like modes. A biexcitonic companion feature is observed, shifted from the exciton feature by the biexciton binding energy. Closer to zero detuning, all features are enhanced and the diagonal intra-action features become nearly equal in amplitude and linewidth. At positive detuning the exciton-like and cavity-like characteristics return to the diagonal intra-action features. Off-diagonal interaction features exhibit asymmetry in their amplitudes throughout the detuning range. The amplitudes are strongly modulated as the lower polariton branch crosses the bound biexciton energy determined from negatively detuned spectra.

Scaling of the polarization amplitude in quantum many-body systems in one dimension

NASA Astrophysics Data System (ADS)

Kobayashi, Ryohei; Nakagawa, Yuya O.; Fukusumi, Yoshiki; Oshikawa, Masaki

2018-04-01

Resta proposed a definition of the electric polarization in one-dimensional systems in terms of the ground-state expectation value of the large gauge transformation operator. Vanishing of the expectation value in the thermodynamic limit implies that the system is a conductor. We study Resta's polarization amplitude (expectation value) in the S =1 /2 XXZ chain and its several generalizations, in the gapless conducting Tomonaga-Luttinger liquid phase. We obtain an analytical expression in the lowest-order perturbation theory about the free fermion point (XY chain) and an exact result for the Haldane-Shastry model with long-range interactions. We also obtain numerical results, mostly using the exact diagonalization method. We find that the amplitude exhibits a power-law scaling in the system size (chain length) and vanishes in the thermodynamic limit. On the other hand, the exponent depends on the model even when the low-energy limit is described by the Tomonaga-Luttinger liquid with the same Luttinger parameter. We find that a change in the exponent occurs when the Umklapp term(s) are eliminated, suggesting the importance of the Umklapp terms.

Confined One Dimensional Harmonic Oscillator as a Two-Mode System

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

Gueorguiev, V G; Rau, A P; Draayer, J P

2005-07-11

The one-dimensional harmonic oscillator in a box problem is possibly the simplest example of a two-mode system. This system has two exactly solvable limits, the harmonic oscillator and a particle in a (one-dimensional) box. Each of the two limits has a characteristic spectral structure describing the two different excitation modes of the system. Near each of these limits, one can use perturbation theory to achieve an accurate description of the eigenstates. Away from the exact limits, however, one has to carry out a matrix diagonalization because the basis-state mixing that occurs is typically too large to be reproduced in anymore » other way. An alternative to casting the problem in terms of one or the other basis set consists of using an ''oblique'' basis that uses both sets. Through a study of this alternative in this one-dimensional problem, we are able to illustrate practical solutions and infer the applicability of the concept for more complex systems, such as in the study of complex nuclei where oblique-basis calculations have been successful.« less

Rashba quantum wire: exact solution and ballistic transport.

PubMed

Perroni, C A; Bercioux, D; Ramaglia, V Marigliano; Cataudella, V

2007-05-08

The effect of Rashba spin-orbit interaction in quantum wires with hard-wall boundaries is discussed. The exact wavefunction and eigenvalue equation are worked out, pointing out the mixing between the spin and spatial parts. The spectral properties are also studied within perturbation theory with respect to the strength of the spin-orbit interaction and diagonalization procedure. A comparison is made with the results of a simple model, the two-band model, that takes account only of the first two sub-bands of the wire. Finally, the transport properties within the ballistic regime are analytically calculated for the two-band model and through a tight-binding Green function for the entire system. Single and double interfaces separating regions with different strengths of spin-orbit interaction are analysed by injecting carriers into the first and the second sub-band. It is shown that in the case of a single interface the spin polarization in the Rashba region is different from zero, and in the case of two interfaces the spin polarization shows oscillations due to spin-selective bound states.

Block-diagonalization as a tool for the robust diabatization of high-dimensional potential energy surfaces

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

Venghaus, Florian; Eisfeld, Wolfgang, E-mail: wolfgang.eisfeld@uni-bielefeld.de

2016-03-21

Robust diabatization techniques are key for the development of high-dimensional coupled potential energy surfaces (PESs) to be used in multi-state quantum dynamics simulations. In the present study we demonstrate that, besides the actual diabatization technique, common problems with the underlying electronic structure calculations can be the reason why a diabatization fails. After giving a short review of the theoretical background of diabatization, we propose a method based on the block-diagonalization to analyse the electronic structure data. This analysis tool can be used in three different ways: First, it allows to detect issues with the ab initio reference data and ismore » used to optimize the setup of the electronic structure calculations. Second, the data from the block-diagonalization are utilized for the development of optimal parametrized diabatic model matrices by identifying the most significant couplings. Third, the block-diagonalization data are used to fit the parameters of the diabatic model, which yields an optimal initial guess for the non-linear fitting required by standard or more advanced energy based diabatization methods. The new approach is demonstrated by the diabatization of 9 electronic states of the propargyl radical, yielding fully coupled full-dimensional (12D) PESs in closed form.« less

Quench action and Rényi entropies in integrable systems

NASA Astrophysics Data System (ADS)

Alba, Vincenzo; Calabrese, Pasquale

2017-09-01

Entropy is a fundamental concept in equilibrium statistical mechanics, yet its origin in the nonequilibrium dynamics of isolated quantum systems is not fully understood. A strong consensus is emerging around the idea that the stationary thermodynamic entropy is the von Neumann entanglement entropy of a large subsystem embedded in an infinite system. Also motivated by cold-atom experiments, here we consider the generalization to Rényi entropies. We develop a new technique to calculate the diagonal Rényi entropy in the quench action formalism. In the spirit of the replica treatment for the entanglement entropy, the diagonal Rényi entropies are generalized free energies evaluated over a thermodynamic macrostate which depends on the Rényi index and, in particular, is not the same state describing von Neumann entropy. The technical reason for this perhaps surprising result is that the evaluation of the moments of the diagonal density matrix shifts the saddle point of the quench action. An interesting consequence is that different Rényi entropies encode information about different regions of the spectrum of the postquench Hamiltonian. Our approach provides a very simple proof of the long-standing issue that, for integrable systems, the diagonal entropy is half of the thermodynamic one and it allows us to generalize this result to the case of arbitrary Rényi entropy.

Tunneling splitting in double-proton transfer: direct diagonalization results for porphycene.

PubMed

Smedarchina, Zorka; Siebrand, Willem; Fernández-Ramos, Antonio

2014-11-07

Zero-point and excited level splittings due to double-proton tunneling are calculated for porphycene and the results are compared with experiment. The calculation makes use of a multidimensional imaginary-mode Hamiltonian, diagonalized directly by an effective reduction of its dimensionality. Porphycene has a complex potential energy surface with nine stationary configurations that allow a variety of tunneling paths, many of which include classically accessible regions. A symmetry-based approach is used to show that the zero-point level, although located above the cis minimum, corresponds to concerted tunneling along a direct trans - trans path; a corresponding cis - cis path is predicted at higher energy. This supports the conclusion of a previous paper [Z. Smedarchina, W. Siebrand, and A. Fernández-Ramos, J. Chem. Phys. 127, 174513 (2007)] based on the instanton approach to a model Hamiltonian of correlated double-proton transfer. A multidimensional tunneling Hamiltonian is then generated, based on a double-minimum potential along the coordinate of concerted proton motion, which is newly evaluated at the RI-CC2/cc-pVTZ level of theory. To make it suitable for diagonalization, its dimensionality is reduced by treating fast weakly coupled modes in the adiabatic approximation. This results in a coordinate-dependent mass of tunneling, which is included in a unique Hermitian form into the kinetic energy operator. The reduced Hamiltonian contains three symmetric and one antisymmetric mode coupled to the tunneling mode and is diagonalized by a modified Jacobi-Davidson algorithm implemented in the Jadamilu software for sparse matrices. The results are in satisfactory agreement with the observed splitting of the zero-point level and several vibrational fundamentals after a partial reassignment, imposed by recently derived selection rules. They also agree well with instanton calculations based on the same Hamiltonian.

Molecular origin of differences in hole and electron mobility in amorphous Alq3--a multiscale simulation study.

PubMed

Fuchs, Andreas; Steinbrecher, Thomas; Mommer, Mario S; Nagata, Yuki; Elstner, Marcus; Lennartz, Christian

2012-03-28

In order to determine the molecular origin of the difference in electron and hole mobilities of amorphous thin films of Alq(3) (meridional Alq(3) (tris(8-hydroxyquinoline) aluminium)) we performed multiscale simulations covering quantum mechanics, molecular mechanics and lattice models. The study includes realistic disordered morphologies, polarized site energies to describe diagonal disorder, quantum chemically calculated transfer integrals for the off-diagonal disorder, inner sphere reorganization energies and an approximative scheme for outer sphere reorganization energies. Intermolecular transfer rates were calculated via Marcus-theory and mobilities were simulated via kinetic Monte Carlo simulations and by a Master Equation approach. The difference in electron and hole mobility originates from the different localization of charge density in the radical anion (more delocalized) compared to the radical cation (more confined). This results in higher diagonal disorder for holes and less favourable overlap properties for the hole transfer integrals leading to an overall higher electron mobility.

Extraction-controlled terahertz frequency quantum cascade lasers with a diagonal LO-phonon extraction and injection stage.

PubMed

Han, Y J; Li, L H; Grier, A; Chen, L; Valavanis, A; Zhu, J; Freeman, J R; Isac, N; Colombelli, R; Dean, P; Davies, A G; Linfield, E H

2016-12-12

We report an extraction-controlled terahertz (THz)-frequency quantum cascade laser design in which a diagonal LO-phonon scattering process is used to achieve efficient current injection into the upper laser level of each period and simultaneously extract electrons from the adjacent period. The effects of the diagonality of the radiative transition are investigated, and a design with a scaled oscillator strength of 0.45 is shown experimentally to provide the highest temperature performance. A 3.3 THz device processed into a double-metal waveguide configuration operated up to 123 K in pulsed mode, with a threshold current density of 1.3 kA/cm² at 10 K. The QCL structures are modeled using an extended density matrix approach, and the large threshold current is attributed to parasitic current paths associated with the upper laser levels. The simplicity of this design makes it an ideal platform to investigate the scattering injection process.

Symmetry of semi-reduced lattices.

PubMed

Stróż, Kazimierz

2015-05-01

The main result of this work is extension of the famous characterization of Bravais lattices according to their metrical, algebraic and geometric properties onto a wide class of primitive lattices (including Buerger-reduced, nearly Buerger-reduced and a substantial part of Delaunay-reduced) related to low-restricted semi-reduced descriptions (s.r.d.'s). While the `geometric' operations in Bravais lattices map the basis vectors into themselves, the `arithmetic' operators in s.r.d. transform the basis vectors into cell vectors (basis vectors, face or space diagonals) and are represented by matrices from the set {\\bb V} of all 960 matrices with the determinant ±1 and elements {0, ±1} of the matrix powers. A lattice is in s.r.d. if the moduli of off-diagonal elements in both the metric tensors M and M(-1) are smaller than corresponding diagonal elements sharing the same column or row. Such lattices are split into 379 s.r.d. types relative to the arithmetic holohedries. Metrical criteria for each type do not need to be explicitly given but may be modelled as linear derivatives {\\bb M}(p,q,r), where {\\bb M} denotes the set of 39 highest-symmetry metric tensors, and p,q,r describe changes of appropriate interplanar distances. A sole filtering of {\\bb V} according to an experimental s.r.d. metric and subsequent geometric interpretation of the filtered matrices lead to mathematically stable and rich information on the Bravais-lattice symmetry and deviations from the exact symmetry. The emphasis on the crystallographic features of lattices was obtained by shifting the focus (i) from analysis of a lattice metric to analysis of symmetry matrices [Himes & Mighell (1987). Acta Cryst. A43, 375-384], (ii) from the isometric approach and invariant subspaces to the orthogonality concept {some ideas in Le Page [J. Appl. Cryst. (1982), 15, 255-259]} and splitting indices [Stróż (2011). Acta Cryst. A67, 421-429] and (iii) from fixed cell transformations to transformations derivable via geometric information (Himes & Mighell, 1987; Le Page, 1982). It is illustrated that corresponding arithmetic and geometric holohedries share space distribution of symmetry elements. Moreover, completeness of the s.r.d. types reveals their combinatorial structure and simplifies the crystallographic description of structural phase transitions, especially those observed with the use of powder diffraction. The research proves that there are excellent theoretical and practical reasons for looking at crystal lattice symmetry from an entirely new and surprising point of view - the combinatorial set {\\bb V} of matrices, their semi-reduced lattice context and their geometric properties.

State Counting for Excited Bands of the Fractional Quantum Hall Effect: Exclusion Rules for Bound Excitons

NASA Astrophysics Data System (ADS)

Coimbatore Balram, Ajit; Wójs, Arkadiusz; Jain, Jainendra

2014-03-01

Exact diagonalization studies have revealed that the energy spectrum of interacting electrons in the lowest Landau level splits, non-perturbatively, into bands. The theory of nearly free composite fermions (CFs) has been shown to be valid for the lowest band, and thus to capture the low temperature physics, but it over-predicts the number of states for the excited bands. We explain the state counting of higher bands in terms of composite fermions with an infinitely strong short range interaction between a CF particle and a CF hole. This interaction, the form of which we derive from the microscopic CF theory, eliminates configurations containing certain tightly bound CF excitons. With this modification, the CF theory reproduces, for all well-defined excited bands, an exact counting for ν > 1 / 3 , and an almost exact counting for ν <= 1 / 3 . The resulting insight clarifies that the corrections to the nearly free CF theory are not thermodynamically significant at sufficiently low temperatures, thus providing a microscopic explanation for why it has proved successful for the analysis of the various properties of the CF Fermi sea. NSF grants DMR-1005536 and DMR-0820404, Polish NCN grant 2011/01/B/ST3/04504 and EU Marie Curie Grant PCIG09-GA-2011-294186, Research Computing and Cyberinfrastructure, PSU and Wroclaw Centre for Networking and Supercomputing

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

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

Ma, Xiaoyao; Hall, Randall W.; Löffler, Frank

The Sign Learning Kink (SiLK) based Quantum Monte Carlo (QMC) method is used to calculate the ab initio ground state energies for multiple geometries of the H2O, N2, and F2 molecules. The method is based on Feynman’s path integral formulation of quantum mechanics and has two stages. The first stage is called the learning stage and reduces the well-known QMC minus sign problem by optimizing the linear combinations of Slater determinants which are used in the second stage, a conventional QMC simulation. The method is tested using different vector spaces and compared to the results of other quantum chemical methodsmore » and to exact diagonalization. Our findings demonstrate that the SiLK method is accurate and reduces or eliminates the minus sign problem.« less

Dynamics of a Dirac oscillator coupled to an external field: a new class of solvable problems

NASA Astrophysics Data System (ADS)

Sadurní, E.; Torres, J. M.; Seligman, T. H.

2010-07-01

The Dirac oscillator coupled to an external two-component field can retain its solvability, if couplings are appropriately chosen. This provides a new class of integrable systems. A simplified way of a solution is given by recasting the known solution of the Dirac oscillator into matrix form; there one notes that a block-diagonal form arises in a Hamiltonian formulation. The blocks are two dimensional. Choosing couplings that do not affect the block structure, these blow up the 2 × 2 matrices to 4 × 4 matrices, thus conserving solvability. The result can be cast again in covariant form. By way of an example we apply this exact solution to calculate the evolution of entanglement.

Spin-state transition in LaCoO3 by variational cluster approximation

NASA Astrophysics Data System (ADS)

Eder, R.

2010-01-01

The variational cluster approximation (VCA) is applied to the calculation of thermodynamical quantities and single-particle spectra of LaCoO3 . Trial self-energies and the numerical value of the Luttinger-Ward functional are obtained by exact diagonalization of a CoO6 cluster. The VCA correctly predicts LaCoO3 as a paramagnetic insulator, and a gradual and relatively smooth increase in the occupation of high-spin Co3+ ions causes the temperature dependence of entropy and magnetic susceptibility. The single-particle spectral function agrees well with experiment; the experimentally observed temperature dependence of photoelectron spectra is reproduced satisfactorily. Remaining discrepancies with experiment highlight the importance of spin-orbit coupling and local lattice relaxation.

Ground-state energies of the nonlinear sigma model and the Heisenberg spin chains

NASA Technical Reports Server (NTRS)

Zhang, Shoucheng; Schulz, H. J.; Ziman, Timothy

1989-01-01

A theorem on the O(3) nonlinear sigma model with the topological theta term is proved, which states that the ground-state energy at theta = pi is always higher than the ground-state energy at theta = 0, for the same value of the coupling constant g. Provided that the nonlinear sigma model gives the correct description for the Heisenberg spin chains in the large-s limit, this theorem makes a definite prediction relating the ground-state energies of the half-integer and the integer spin chains. The ground-state energies obtained from the exact Bethe ansatz solution for the spin-1/2 chain and the numerical diagonalization on the spin-1, spin-3/2, and spin-2 chains support this prediction.

Hubbard pair cluster in the external fields. Studies of the magnetic properties

NASA Astrophysics Data System (ADS)

Balcerzak, T.; Szałowski, K.

2018-06-01

The magnetic properties of the two-site Hubbard cluster (dimer or pair), embedded in the external electric and magnetic fields and treated as the open system, are studied by means of the exact diagonalization of the Hamiltonian. The formalism of the grand canonical ensemble is adopted. The phase diagrams, on-site magnetizations, spin-spin correlations, mean occupation numbers and hopping energy are investigated and illustrated in figures. An influence of temperature, mean electron concentration, Coulomb U parameter and external fields on the quantities of interest is presented and discussed. In particular, the anomalous behaviour of the magnetization and correlation function vs. temperature near the critical magnetic field is found. Also, the effect of magnetization switching by the external fields is demonstrated.

Competing orders in the Hofstadter t -J model

NASA Astrophysics Data System (ADS)

Tu, Wei-Lin; Schindler, Frank; Neupert, Titus; Poilblanc, Didier

2018-01-01

The Hofstadter model describes noninteracting fermions on a lattice in the presence of an external magnetic field. Motivated by the plethora of solid-state phases emerging from electron interactions, we consider an interacting version of the Hofstadter model, including a Hubbard repulsion U . We investigate this model in the large-U limit corresponding to a t -J Hamiltonian with an external (orbital) magnetic field. By using renormalized mean-field theory supplemented by exact diagonalization calculations of small clusters, we find evidence for competing symmetry-breaking phases, exhibiting (possibly coexisting) charge, bond, and superconducting orders. Topological properties of the states are also investigated, and some of our results are compared to related experiments involving ultracold atoms loaded on optical lattices in the presence of a synthetic gauge field.

Fidelity study of superconductivity in extended Hubbard models

DOE PAGES

Plonka, N.; Jia, C. J.; Wang, Y.; ...

2015-07-08

The Hubbard model with local on-site repulsion is generally thought to possess a superconducting ground state for appropriate parameters, but the effects of more realistic long-range Coulomb interactions have not been studied extensively. We study the influence of these interactions on superconductivity by including nearest- and next-nearest-neighbor extended Hubbard interactions in addition to the usual on-site terms. Utilizing numerical exact diagonalization, we analyze the signatures of superconductivity in the ground states through the fidelity metric of quantum information theory. Finally, we find that nearest and next-nearest neighbor interactions have thresholds above which they destabilize superconductivity regardless of whether they aremore » attractive or repulsive, seemingly due to competing charge fluctuations.« less

Exact diagonalization of quantum lattice models on coprocessors

NASA Astrophysics Data System (ADS)

Siro, T.; Harju, A.

2016-10-01

We implement the Lanczos algorithm on an Intel Xeon Phi coprocessor and compare its performance to a multi-core Intel Xeon CPU and an NVIDIA graphics processor. The Xeon and the Xeon Phi are parallelized with OpenMP and the graphics processor is programmed with CUDA. The performance is evaluated by measuring the execution time of a single step in the Lanczos algorithm. We study two quantum lattice models with different particle numbers, and conclude that for small systems, the multi-core CPU is the fastest platform, while for large systems, the graphics processor is the clear winner, reaching speedups of up to 7.6 compared to the CPU. The Xeon Phi outperforms the CPU with sufficiently large particle number, reaching a speedup of 2.5.

Novel half-magnetization plateau and nematiclike transition in the S =1 skew chain Ni2V2O7

NASA Astrophysics Data System (ADS)

Ouyang, Z. W.; Sun, Y. C.; Wang, J. F.; Yue, X. Y.; Chen, R.; Wang, Z. X.; He, Z. Z.; Xia, Z. C.; Liu, Y.; Rao, G. H.

2018-04-01

A quantized magnetization plateau is usually not expected when a classic spin-flop transition occurs in a low-dimensional antiferromagnet. Here, we report an experimental observation of a spin-flop transition followed by a wide half-magnetization plateau in the S =1 skew-chain system Ni2V2O7 . This plateau, which is stabilized in fields of 8-30 T, is realized through an exotic nematiclike phase transition for magnetic fields applied along all three crystallographic axes, resulting in rich anisotropic phase diagrams. We discuss a possible mechanism whereby the magnetic frustration and interchain interactions may cause this half-magnetization plateau, which is in agreement with our exact diagonalization result.

Quantum phases of spinful Fermi gases in optical cavities

NASA Astrophysics Data System (ADS)

Colella, E.; Citro, R.; Barsanti, M.; Rossini, D.; Chiofalo, M.-L.

2018-04-01

We explore the quantum phases emerging from the interplay between spin and motional degrees of freedom of a one-dimensional quantum fluid of spinful fermionic atoms, effectively interacting via a photon-mediating mechanism with tunable sign and strength g , as it can be realized in present-day experiments with optical cavities. We find the emergence, in the very same system, of spin- and atomic-density wave ordering, accompanied by the occurrence of superfluidity for g >0 , while cavity photons are seen to drive strong correlations at all g values, with fermionic character for g >0 , and bosonic character for g <0 . Due to the long-range nature of interactions, to infer these results we combine mean-field and exact-diagonalization methods supported by bosonization analysis.

Current collapse in tunneling transport through benzene.

PubMed

Hettler, M H; Wenzel, W; Wegewijs, M R; Schoeller, H

2003-02-21

We investigate the electrical transport through a system of benzene coupled to metal electrodes by electron tunneling. Using electronic structure calculations, a semiquantitative model for the pi electrons of the benzene is derived that includes general two-body interactions. After exact diagonalization of the benzene model the transport is computed using perturbation theory for weak electrode-benzene coupling (golden rule approximation). We include the effect of an applied electric field on the molecular states, as well as radiative relaxation. We predict a current collapse and strong negative differential conductance due to a "blocking" state when the electrode is coupled to the para-position of benzene. In contrast, for coupling to the meta-position, a series of steps in the I-V curve is found.

Many-body localization in a long range XXZ model with random-field

NASA Astrophysics Data System (ADS)

Li, Bo

2016-12-01

Many-body localization (MBL) in a long range interaction XXZ model with random field are investigated. Using the exact diagonal method, the MBL phase diagram with different tuning parameters and interaction range is obtained. It is found that the phase diagram of finite size results supplies strong evidence to confirm that the threshold interaction exponent α = 2. The tuning parameter Δ can efficiently change the MBL edge in high energy density stats, thus the system can be controlled to transfer from thermal phase to MBL phase by changing Δ. The energy level statistics data are consistent with result of the MBL phase diagram. However energy level statistics data cannot detect the thermal phase correctly in extreme long range case.

Landau problem with time dependent mass in time dependent electric and harmonic background fields

NASA Astrophysics Data System (ADS)

Lawson, Latévi M.; Avossevou, Gabriel Y. H.

2018-04-01

The spectrum of a Hamiltonian describing the dynamics of a Landau particle with time-dependent mass and frequency undergoing the influence of a uniform time-dependent electric field is obtained. The configuration space wave function of the model is expressed in terms of the generalised Laguerre polynomials. To diagonalize the time-dependent Hamiltonian, we employ the Lewis-Riesenfeld method of invariants. To this end, we introduce a unitary transformation in the framework of the algebraic formalism to construct the invariant operator of the system and then to obtain the exact solution of the Hamiltonian. We recover the solutions of the ordinary Landau problem in the absence of the electric and harmonic fields for a constant particle mass.

Electron spin resonance modes in a strong-leg ladder in the Tomonaga-Luttinger liquid phase

NASA Astrophysics Data System (ADS)

Ozerov, M.; Maksymenko, M.; Wosnitza, J.; Honecker, A.; Landee, C. P.; Turnbull, M. M.; Furuya, S. C.; Giamarchi, T.; Zvyagin, S. A.

2015-12-01

Magnetic excitations in the strong-leg quantum spin ladder compound (C7H10N) 2CuBr4 (known as DIMPY) in the field-induced Tomonaga-Luttinger spin-liquid phase are studied by means of high-field electron spin resonance (ESR) spectroscopy. The presence of a gapped ESR mode with unusual nonlinear frequency-field dependence is revealed experimentally. Using a combination of analytic and exact-diagonalization methods, we compute the dynamical structure factor and identify this mode with longitudinal excitations in the antisymmetric channel. We argue that these excitations constitute a fingerprint of the spin dynamics in a strong-leg spin-1/2 Heisenberg antiferromagnetic ladder and owe their ESR observability to the uniform Dzyaloshinskii-Moriya interaction.

Measurement of Residual Flexibility for Substructures Having Prominent Flexible Interfaces

NASA Technical Reports Server (NTRS)

Tinker, Michael L.; Bookout, Paul S.

1994-01-01

Verification of a dynamic model of a constrained structure requires a modal survey test of the physical structure and subsequent modification of the model to obtain the best agreement possible with test data. Constrained-boundary or fixed-base testing has historically been the most common approach for verifying constrained mathematical models, since the boundary conditions of the test article are designed to match the actual constraints in service. However, there are difficulties involved with fixed-base testing, in some cases making the approach impractical. It is not possible to conduct a truly fixed-base test due to coupling between the test article and the fixture. In addition, it is often difficult to accurately simulate the actual boundary constraints, and the cost of designing and constructing the fixture may be prohibitive. For use when fixed-base testing proves impractical or undesirable, alternate free-boundary test methods have been investigated, including the residual flexibility technique. The residual flexibility approach has been treated analytically in considerable detail and has had limited frequency response measurements for the method. This concern is well-justified for a number of reasons. First, residual flexibilities are very small numbers, typically on the order of 1.0E-6 in/lb for translational diagonal terms, and orders of magnitude smaller for off-diagonal values. This poses difficulty in obtaining accurate and noise-free measurements, especially for points removed from the excitation source. A second difficulty encountered in residual measurements lies in obtaining a clean residual function in the process of subtracting synthesized modal data from a measured response function. Inaccuracies occur since modes are not subtracted exactly, but only to the accuracy of the curve fits for each mode; these errors are compounded with increasing distance from the excitation point. In this paper, the residual flexibility method is applied to a simple structure in both test and analysis. Measured and predicted residual functions are compared, and regions of poor data in the measured curves are described. It is found that for accurate residual measurements, frequency response functions having prominent stiffness lines in the acceleration/force format are needed. The lack of such stiffness lines increases measurement errors. Interface drive point frequency respose functions for shuttle orbiter payloads exhibit dominant stiffness lines, making the residual test approach a good candidate for payload modal tests when constrained tests are inappropriate. Difficulties in extracting a residual flexibility value from noisy test data are discussed. It is shown that use of a weighted second order least-squares curve fit of the measured residual function allows identification of residual flexibility that compares very well with predictions for the simple structure. This approach also provides an estimate of second order residual mass effects.

A multi-state fragment charge difference approach for diabatic states in electron transfer: Extension and automation

NASA Astrophysics Data System (ADS)

Yang, Chou-Hsun; Hsu, Chao-Ping

2013-10-01

The electron transfer (ET) rate prediction requires the electronic coupling values. The Generalized Mulliken-Hush (GMH) and Fragment Charge Difference (FCD) schemes have been useful approaches to calculate ET coupling from an excited state calculation. In their typical form, both methods use two eigenstates in forming the target charge-localized diabatic states. For problems involve three or four states, a direct generalization is possible, but it is necessary to pick and assign the locally excited or charge-transfer states involved. In this work, we generalize the 3-state scheme for a multi-state FCD without the need of manual pick or assignment for the states. In this scheme, the diabatic states are obtained separately in the charge-transfer or neutral excited subspaces, defined by their eigenvalues in the fragment charge-difference matrix. In each subspace, the Hamiltonians are diagonalized, and there exist off-diagonal Hamiltonian matrix elements between different subspaces, particularly the charge-transfer and neutral excited diabatic states. The ET coupling values are obtained as the corresponding off-diagonal Hamiltonian matrix elements. A similar multi-state GMH scheme can also be developed. We test the new multi-state schemes for the performance in systems that have been studied using more than two states with FCD or GMH. We found that the multi-state approach yields much better charge-localized states in these systems. We further test for the dependence on the number of state included in the calculation of ET couplings. The final coupling values are converged when the number of state included is increased. In one system where experimental value is available, the multi-state FCD coupling value agrees better with the previous experimental result. We found that the multi-state GMH and FCD are useful when the original two-state approach fails.

Modeling animal-vehicle collisions using diagonal inflated bivariate Poisson regression.

PubMed

Lao, Yunteng; Wu, Yao-Jan; Corey, Jonathan; Wang, Yinhai

2011-01-01

Two types of animal-vehicle collision (AVC) data are commonly adopted for AVC-related risk analysis research: reported AVC data and carcass removal data. One issue with these two data sets is that they were found to have significant discrepancies by previous studies. In order to model these two types of data together and provide a better understanding of highway AVCs, this study adopts a diagonal inflated bivariate Poisson regression method, an inflated version of bivariate Poisson regression model, to fit the reported AVC and carcass removal data sets collected in Washington State during 2002-2006. The diagonal inflated bivariate Poisson model not only can model paired data with correlation, but also handle under- or over-dispersed data sets as well. Compared with three other types of models, double Poisson, bivariate Poisson, and zero-inflated double Poisson, the diagonal inflated bivariate Poisson model demonstrates its capability of fitting two data sets with remarkable overlapping portions resulting from the same stochastic process. Therefore, the diagonal inflated bivariate Poisson model provides researchers a new approach to investigating AVCs from a different perspective involving the three distribution parameters (λ(1), λ(2) and λ(3)). The modeling results show the impacts of traffic elements, geometric design and geographic characteristics on the occurrences of both reported AVC and carcass removal data. It is found that the increase of some associated factors, such as speed limit, annual average daily traffic, and shoulder width, will increase the numbers of reported AVCs and carcass removals. Conversely, the presence of some geometric factors, such as rolling and mountainous terrain, will decrease the number of reported AVCs. Published by Elsevier Ltd.

Investigation of the scaling characteristics of LANDSAT temperature and vegetation data: a wavelet-based approach

NASA Astrophysics Data System (ADS)

Rathinasamy, Maheswaran; Bindhu, V. M.; Adamowski, Jan; Narasimhan, Balaji; Khosa, Rakesh

2017-10-01

An investigation of the scaling characteristics of vegetation and temperature data derived from LANDSAT data was undertaken for a heterogeneous area in Tamil Nadu, India. A wavelet-based multiresolution technique decomposed the data into large-scale mean vegetation and temperature fields and fluctuations in horizontal, diagonal, and vertical directions at hierarchical spatial resolutions. In this approach, the wavelet coefficients were used to investigate whether the normalized difference vegetation index (NDVI) and land surface temperature (LST) fields exhibited self-similar scaling behaviour. In this study, l-moments were used instead of conventional simple moments to understand scaling behaviour. Using the first six moments of the wavelet coefficients through five levels of dyadic decomposition, the NDVI data were shown to be statistically self-similar, with a slope of approximately -0.45 in each of the horizontal, vertical, and diagonal directions of the image, over scales ranging from 30 to 960 m. The temperature data were also shown to exhibit self-similarity with slopes ranging from -0.25 in the diagonal direction to -0.20 in the vertical direction over the same scales. These findings can help develop appropriate up- and down-scaling schemes of remotely sensed NDVI and LST data for various hydrologic and environmental modelling applications. A sensitivity analysis was also undertaken to understand the effect of mother wavelets on the scaling characteristics of LST and NDVI images.

Wake vortex capacity benefits for simultaneous approaches at St. Louis Airport

DOT National Transportation Integrated Search

1994-06-27

This paper details the results of FTA's investigation into the potential capacity gains of applying 1.5 nautical mile (NM) diagonal separation between parallel arrival operations at St. Louis Lambert International Airport (STL). Currently, dependent ...

A simple molecular mechanics integrator in mixed rigid body and dihedral angle space

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

Vitalis, Andreas, E-mail: a.vitalis@bioc.uzh.ch; Pappu, Rohit V.

2014-07-21

We propose a numerical scheme to integrate equations of motion in a mixed space of rigid-body and dihedral angle coordinates. The focus of the presentation is biomolecular systems and the framework is applicable to polymers with tree-like topology. By approximating the effective mass matrix as diagonal and lumping all bias torques into the time dependencies of the diagonal elements, we take advantage of the formal decoupling of individual equations of motion. We impose energy conservation independently for every degree of freedom and this is used to derive a numerical integration scheme. The cost of all auxiliary operations is linear inmore » the number of atoms. By coupling the scheme to one of two popular thermostats, we extend the method to sample constant temperature ensembles. We demonstrate that the integrator of choice yields satisfactory stability and is free of mass-metric tensor artifacts, which is expected by construction of the algorithm. Two fundamentally different systems, viz., liquid water and an α-helical peptide in a continuum solvent are used to establish the applicability of our method to a wide range of problems. The resultant constant temperature ensembles are shown to be thermodynamically accurate. The latter relies on detailed, quantitative comparisons to data from reference sampling schemes operating on exactly the same sets of degrees of freedom.« less

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

NASA Astrophysics Data System (ADS)

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

2018-02-01

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

An implict LU scheme for the Euler equations applied to arbitrary cascades. [new method of factoring

NASA Technical Reports Server (NTRS)

Buratynski, E. K.; Caughey, D. A.

1984-01-01

An implicit scheme for solving the Euler equations is derived and demonstrated. The alternating-direction implicit (ADI) technique is modified, using two implicit-operator factors corresponding to lower-block-diagonal (L) or upper-block-diagonal (U) algebraic systems which can be easily inverted. The resulting LU scheme is implemented in finite-volume mode and applied to 2D subsonic and transonic cascade flows with differing degrees of geometric complexity. The results are presented graphically and found to be in good agreement with those of other numerical and analytical approaches. The LU method is also 2.0-3.4 times faster than ADI, suggesting its value in calculating 3D problems.

Enrichment of Cross-Linked Peptides Using Charge-Based Fractional Diagonal Chromatography (ChaFRADIC).

PubMed

Tinnefeld, Verena; Venne, A Saskia; Sickmann, Albert; Zahedi, René P

2017-02-03

Chemical cross-linking of proteins is an emerging field with huge potential for the structural investigation of proteins and protein complexes. Owing to the often relatively low yield of cross-linking products, their identification in complex samples benefits from enrichment procedures prior to mass spectrometry analysis. So far, this is mainly accomplished by using biotin moieties in specific cross-linkers or by applying strong cation exchange chromatography (SCX) for a relatively crude enrichment. We present a novel workflow to enrich cross-linked peptides by utilizing charge-based fractional diagonal chromatography (ChaFRADIC). On the basis of two-dimensional diagonal SCX separation, we could increase the number of identified cross-linked peptides for samples of different complexity: pure cross-linked BSA, cross-linked BSA spiked into a simple protein mixture, and cross-linked BSA spiked into a HeLa lysate. We also compared XL-ChaFRADIC with size exclusion chromatography-based enrichment of cross-linked peptides. The XL-ChaFRADIC approach is straightforward, reproducible, and independent of the cross-linking chemistry and cross-linker properties.

The Distributed Diagonal Force Decomposition Method for Parallelizing Molecular Dynamics Simulations

PubMed Central

Boršnik, Urban; Miller, Benjamin T.; Brooks, Bernard R.; Janežič, Dušanka

2011-01-01

Parallelization is an effective way to reduce the computational time needed for molecular dynamics simulations. We describe a new parallelization method, the distributed-diagonal force decomposition method, with which we extend and improve the existing force decomposition methods. Our new method requires less data communication during molecular dynamics simulations than replicated data and current force decomposition methods, increasing the parallel efficiency. It also dynamically load-balances the processors' computational load throughout the simulation. The method is readily implemented in existing molecular dynamics codes and it has been incorporated into the CHARMM program, allowing its immediate use in conjunction with the many molecular dynamics simulation techniques that are already present in the program. We also present the design of the Force Decomposition Machine, a cluster of personal computers and networks that is tailored to running molecular dynamics simulations using the distributed diagonal force decomposition method. The design is expandable and provides various degrees of fault resilience. This approach is easily adaptable to computers with Graphics Processing Units because it is independent of the processor type being used. PMID:21793007

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'.

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

Ma, Xiaoyao; Hall, Randall W.; Department of Chemistry, Louisiana State University, Baton Rouge, Louisiana 70803

The Sign Learning Kink (SiLK) based Quantum Monte Carlo (QMC) method is used to calculate the ab initio ground state energies for multiple geometries of the H{sub 2}O, N{sub 2}, and F{sub 2} molecules. The method is based on Feynman’s path integral formulation of quantum mechanics and has two stages. The first stage is called the learning stage and reduces the well-known QMC minus sign problem by optimizing the linear combinations of Slater determinants which are used in the second stage, a conventional QMC simulation. The method is tested using different vector spaces and compared to the results of othermore » quantum chemical methods and to exact diagonalization. Our findings demonstrate that the SiLK method is accurate and reduces or eliminates the minus sign problem.« less

Infrared singularities of scattering amplitudes in perturbative QCD

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

Becher, Thomas; Neubert, Matthias

2013-11-01

An exact formula is derived for the infrared singularities of dimensionally regularized scattering amplitudes in massless QCD with an arbitrary number of legs, valid at any number of loops. It is based on the conjecture that the anomalous-dimension matrix of n-jet operators in soft-collinear effective theory contains only a single non-trivial color structure, whose coefficient is the cusp anomalous dimension of Wilson loops with light-like segments. Its color-diagonal part is characterized by two anomalous dimensions, which are extracted to three-loop order from known perturbative results for the quark and gluon form factors. This allows us to predict the three-loop coefficientsmore » of all 1/epsilon^k poles for an arbitrary n-parton scattering amplitudes, generalizing existing two-loop results.« less

High-Power Collective Charging of a Solid-State Quantum Battery

NASA Astrophysics Data System (ADS)

Ferraro, Dario; Campisi, Michele; Andolina, Gian Marcello; Pellegrini, Vittorio; Polini, Marco

2018-03-01

Quantum information theorems state that it is possible to exploit collective quantum resources to greatly enhance the charging power of quantum batteries (QBs) made of many identical elementary units. We here present and solve a model of a QB that can be engineered in solid-state architectures. It consists of N two-level systems coupled to a single photonic mode in a cavity. We contrast this collective model ("Dicke QB"), whereby entanglement is genuinely created by the common photonic mode, to the one in which each two-level system is coupled to its own separate cavity mode ("Rabi QB"). By employing exact diagonalization, we demonstrate the emergence of a quantum advantage in the charging power of Dicke QBs, which scales like √{N } for N ≫1 .

Perfect Diode in Quantum Spin Chains

NASA Astrophysics Data System (ADS)

Balachandran, Vinitha; Benenti, Giuliano; Pereira, Emmanuel; Casati, Giulio; Poletti, Dario

2018-05-01

We study the rectification of the spin current in X X Z chains segmented in two parts, each with a different anisotropy parameter. Using exact diagonalization and a matrix product state algorithm, we find that a large rectification (of the order of 1 04) is attainable even using a short chain of N =8 spins, when one-half of the chain is gapless while the other has a large enough anisotropy. We present evidence of diffusive transport when the current is driven in one direction and of a transition to an insulating behavior of the system when driven in the opposite direction, leading to a perfect diode in the thermodynamic limit. The above results are explained in terms of matching of the spectrum of magnon excitations between the two halves of the chain.

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.

Formation of helical domain walls in the fractional quantum Hall regime as a step toward realization of high-order non-Abelian excitations

NASA Astrophysics Data System (ADS)

Wu, Tailung; Wan, Zhong; Kazakov, Aleksandr; Wang, Ying; Simion, George; Liang, Jingcheng; West, Kenneth W.; Baldwin, Kirk; Pfeiffer, Loren N.; Lyanda-Geller, Yuli; Rokhinson, Leonid P.

2018-06-01

We propose an experimentally feasible platform to realize parafermions (high-order non-Abelian excitations) based on spin transitions in the fractional quantum Hall effect regime. As a proof of concept we demonstrate a local control of the spin transition at a filling factor 2/3 and formation of a conducting fractional helical domain wall (fhDW) along a gate boundary. Coupled to an s -wave superconductor these fhDWs are expected to support parafermionic excitations. We present exact diagonalization numerical studies of fhDWs and show that they indeed possess electronic and magnetic structures needed for the formation of parafermions. A reconfigurable network of fhDWs will allow manipulation and braiding of parafermionic excitations in multigate devices.

Emergent Fermi Sea in A System of Interacting Bosons

NASA Astrophysics Data System (ADS)

Wu, Yinghai; Jain, Jainendra

2015-03-01

An understanding of the possible ways in which interactions can produce fundamentally new emergent many-body states is a central problem of condensed matter physics. We ask if a Fermi sea can arise in a system of bosons subject to contact interaction. Based on exact diagonalization studies and variational wave functions, we predict that such a state is likely to occur when a system of two-component bosons in two dimensions, interacting via a species independent contact interaction, is exposed to a synthetic magnetic field of strength that corresponds to a filling factor of unity. The bosons each bind a single vortex as a result of the repulsive interaction, and these fermionic bound states, namely composite fermions, form a spin-singlet Fermi sea. Financial support from the DOE under Grant No. DE-SC0005042.

Numerical study of the Kitaev-Heisenberg chain

NASA Astrophysics Data System (ADS)

Agrapidis, Cliò Efthimia; van den Brink, Jeroen; Nishimoto, Satoshi

2018-05-01

We study the one-dimensional Kitaev-Heisenberg model as a possible realization of magnetic degrees of freedom of the K-intercalated honeycomb-lattice ruthenium trichloride α-RuCl3, denoted as K0.5RuClm. First, we discuss the possible charge ordering pattern in K0.5RuClm, where half of the j =1/2 spins are replaced by nonmagnetic ions in the honeycomb layer. Next, we investigate the low-energy excitations of the 1D Kitaev-Heisenberg model by calculating the dynamical spin structure factor using the Lanczos exact-diagonalization method. In the vicinity of Kitaev limit, there exist two well-separated dispersions. The bandwidth of each dispersion depends on the Heisenberg and Kitaev terms. This result may be relevant to the low-lying magnetic excitations of K0.5RuClm.

Accurate collision-induced line-coupling parameters for the fundamental band of CO in He - Close coupling and coupled states scattering calculations

NASA Technical Reports Server (NTRS)

Green, Sheldon; Boissoles, J.; Boulet, C.

1988-01-01

The first accurate theoretical values for off-diagonal (i.e., line-coupling) pressure-broadening cross sections are presented. Calculations were done for CO perturbed by He at thermal collision energies using an accurate ab initio potential energy surface. Converged close coupling, i.e., numerically exact values, were obtained for coupling to the R(0) and R(2) lines. These were used to test the coupled states (CS) and infinite order sudden (IOS) approximate scattering methods. CS was found to be of quantitative accuracy (a few percent) and has been used to obtain coupling values for lines to R(10). IOS values are less accurate, but, owing to their simplicity, may nonetheless prove useful as has been recently demonstrated.

Crossover between few and many fermions in a harmonic trap

NASA Astrophysics Data System (ADS)

Grining, Tomasz; Tomza, Michał; Lesiuk, Michał; Przybytek, Michał; Musiał, Monika; Moszynski, Robert; Lewenstein, Maciej; Massignan, Pietro

2015-12-01

The properties of a balanced two-component Fermi gas in a one-dimensional harmonic trap are studied by means of the coupled-cluster method. For few fermions we recover the results of exact diagonalization, yet with this method we are able to study much larger systems. We compute the energy, the chemical potential, the pairing gap, and the density profile of the trapped clouds, smoothly mapping the crossover between the few-body and many-body limits. The energy is found to converge surprisingly rapidly to the many-body result for every value of the interaction strength. Many more particles are instead needed to give rise to the nonanalytic behavior of the pairing gap, and to smoothen the pronounced even-odd oscillations of the chemical potential induced by the shell structure of the trap.

Benchmark of Dynamic Electron Correlation Models for Seniority-Zero Wave Functions and Their Application to Thermochemistry.

PubMed

Boguslawski, Katharina; Tecmer, Paweł

2017-12-12

Wave functions restricted to electron-pair states are promising models to describe static/nondynamic electron correlation effects encountered, for instance, in bond-dissociation processes and transition-metal and actinide chemistry. To reach spectroscopic accuracy, however, the missing dynamic electron correlation effects that cannot be described by electron-pair states need to be included a posteriori. In this Article, we extend the previously presented perturbation theory models with an Antisymmetric Product of 1-reference orbital Geminal (AP1roG) reference function that allows us to describe both static/nondynamic and dynamic electron correlation effects. Specifically, our perturbation theory models combine a diagonal and off-diagonal zero-order Hamiltonian, a single-reference and multireference dual state, and different excitation operators used to construct the projection manifold. We benchmark all proposed models as well as an a posteriori Linearized Coupled Cluster correction on top of AP1roG against CR-CC(2,3) reference data for reaction energies of several closed-shell molecules that are extrapolated to the basis set limit. Moreover, we test the performance of our new methods for multiple bond breaking processes in the homonuclear N 2 , C 2 , and F 2 dimers as well as the heteronuclear BN, CO, and CN + dimers against MRCI-SD, MRCI-SD+Q, and CR-CC(2,3) reference data. Our numerical results indicate that the best performance is obtained from a Linearized Coupled Cluster correction as well as second-order perturbation theory corrections employing a diagonal and off-diagonal zero-order Hamiltonian and a single-determinant dual state. These dynamic corrections on top of AP1roG provide substantial improvements for binding energies and spectroscopic properties obtained with the AP1roG approach, while allowing us to approach chemical accuracy for reaction energies involving closed-shell species.

Assessment of electron propagator methods for the simulation of vibrationally-resolved valence and core photoionization spectra

PubMed Central

Baiardi, A.; Paoloni, L.; Barone, V.; Zakrzewski, V.G.; Ortiz, J.V.

2017-01-01

The analysis of photoelectron spectra is usually facilitated by quantum mechanical simulations. Due to the recent improvement of experimental techniques, the resolution of experimental spectra is rapidly increasing, and the inclusion of vibrational effects is usually mandatory to obtain a reliable reproduction of the spectra. With the aim of defining a robust computational protocol, a general time-independent formulation to compute different kinds of vibrationally-resolved electronic spectra has been generalized to support also photoelectron spectroscopy. The electronic structure data underlying the simulation are computed using different electron propagator approaches. In addition to the more standard approaches, a new and robust implementation of the second-order self-energy approximation of the electron propagator based on a transition operator reference (TOEP2) is presented. To validate our implementation, a series of molecules has been used as test cases. The result of the simulations shows that, for ultraviolet photoionization spectra, the more accurate non-diagonal approaches are needed to obtain a reliable reproduction of vertical ionization energies, but diagonal approaches are sufficient for energy gradients and pole strengths. For X-ray photoelectron spectroscopy, the TOEP2 approach, besides being more efficient, is also the most accurate in the reproduction of both vertical ionization energies and vibrationally-resolved bandshapes. PMID:28521087

Distilling perfect GHZ states from two copies of non-GHZ-diagonal mixed states

NASA Astrophysics Data System (ADS)

Wang, Xin-Wen; Tang, Shi-Qing; Yuan, Ji-Bing; Zhang, Deng-Yu

2017-06-01

It has been shown that a nearly pure Greenberger-Horne-Zeilinger (GHZ) state could be distilled from a large (even infinite) number of GHZ-diagonal states that can be obtained by depolarizing general multipartite mixed states (non-GHZ-diagonal states) through sequences of (probabilistic) local operations and classical communications. We here demonstrate that perfect GHZ states can be extracted, with certain probabilities, from two copies of non-GHZ-diagonal mixed states when some conditions are satisfied. This result implies that it is not necessary to depolarize these entangled mixed states to the GHZ-diagonal type, and that they are better than GHZ-diagonal states for distillation of pure GHZ states. We find a wide class of multipartite entangled mixed states that fulfill the requirements. Moreover, we display that the obtained result can be applied to practical noisy environments, e.g., amplitude-damping channels. Our findings provide an important complementarity to conventional GHZ-state distillation protocols (designed for GHZ-diagonal states) in theory, as well as having practical applications.

Iterative algorithm for joint zero diagonalization with application in blind source separation.

PubMed

Zhang, Wei-Tao; Lou, Shun-Tian

2011-07-01

A new iterative algorithm for the nonunitary joint zero diagonalization of a set of matrices is proposed for blind source separation applications. On one hand, since the zero diagonalizer of the proposed algorithm is constructed iteratively by successive multiplications of an invertible matrix, the singular solutions that occur in the existing nonunitary iterative algorithms are naturally avoided. On the other hand, compared to the algebraic method for joint zero diagonalization, the proposed algorithm requires fewer matrices to be zero diagonalized to yield even better performance. The extension of the algorithm to the complex and nonsquare mixing cases is also addressed. Numerical simulations on both synthetic data and blind source separation using time-frequency distributions illustrate the performance of the algorithm and provide a comparison to the leading joint zero diagonalization schemes.

E-beam generated holographic masks for optical vector-matrix multiplication

NASA Technical Reports Server (NTRS)

Arnold, S. M.; Case, S. K.

1981-01-01

An optical vector matrix multiplication scheme that encodes the matrix elements as a holographic mask consisting of linear diffraction gratings is proposed. The binary, chrome on glass masks are fabricated by e-beam lithography. This approach results in a fairly simple optical system that promises both large numerical range and high accuracy. A partitioned computer generated hologram mask was fabricated and tested. This hologram was diagonally separated outputs, compact facets and symmetry about the axis. The resultant diffraction pattern at the output plane is shown. Since the grating fringes are written at 45 deg relative to the facet boundaries, the many on-axis sidelobes from each output are seen to be diagonally separated from the adjacent output signals.

Photographic zoom fisheye lens design for DSLR cameras

NASA Astrophysics Data System (ADS)

Yan, Yufeng; Sasian, Jose

2017-09-01

Photographic fisheye lenses with fixed focal length for cameras with different sensor formats have been well developed for decades. However, photographic fisheye lenses with variable focal length are rare on the market due in part to the greater design difficulty. This paper presents a large aperture zoom fisheye lens for DSLR cameras that produces both circular and diagonal fisheye imaging for 35-mm sensors and diagonal fisheye imaging for APS-C sensors. The history and optical characteristics of fisheye lenses are briefly reviewed. Then, a 9.2- to 16.1-mm F/2.8 to F/3.5 zoom fisheye lens design is presented, including the design approach and aberration control. Image quality and tolerance performance analysis for this lens are also presented.

Applications of finite-size scaling for atomic and non-equilibrium systems

NASA Astrophysics Data System (ADS)

Antillon, Edwin A.

We apply the theory of Finite-size scaling (FSS) to an atomic and a non-equilibrium system in order to extract critical parameters. In atomic systems, we look at the energy dependence on the binding charge near threshold between bound and free states, where we seek the critical nuclear charge for stability. We use different ab initio methods, such as Hartree-Fock, Density Functional Theory, and exact formulations implemented numerically with the finite-element method (FEM). Using Finite-size scaling formalism, where in this case the size of the system is related to the number of elements used in the basis expansion of the wavefunction, we predict critical parameters in the large basis limit. Results prove to be in good agreement with previous Slater-basis set calculations and demonstrate that this combined approach provides a promising first-principles approach to describe quantum phase transitions for materials and extended systems. In the second part we look at non-equilibrium one-dimensional model known as the raise and peel model describing a growing surface which grows locally and has non-local desorption. For a specific values of adsorption ( ua) and desorption (ud) the model shows interesting features. At ua = ud, the model is described by a conformal field theory (with conformal charge c = 0) and its stationary probability can be mapped to the ground state of a quantum chain and can also be related a two dimensional statistical model. For ua ≥ ud, the model shows a scale invariant phase in the avalanche distribution. In this work we study the surface dynamics by looking at avalanche distributions using FSS formalism and explore the effect of changing the boundary conditions of the model. The model shows the same universality for the cases with and with our the wall for an odd number of tiles removed, but we find a new exponent in the presence of a wall for an even number of avalanches released. We provide new conjecture for the probability distribution of avalanches with a wall obtained by using exact diagonalization of small lattices and Monte-Carlo simulations.

Laser-Scanner Survey of Structural Disorders: AN Instrument to Inspect the History of Parma Cathedral's Central Nave

NASA Astrophysics Data System (ADS)

Bruno, N.; Coïsson, E.; Cotti, M.

2017-05-01

This paper presents the use of laser scanner derived data for the study of the structural disorders in the central nave of the Parma Cathedral. An accurate three-dimensional model of the entire nave was realized to investigate deformations, in order to reconstruct the original conformation and the subsequent evolutions, also in comparison with previous surveys. Specifically, for the analysis presented in the paper, seven scans were performed, one for each bay: the results allowed to compare the deformations on the seven vaults, on the transverse and diagonal arches, giving first hints on the possible differences in the behaviour between the different elements. The measures on the levels of floor and pillars bases were analysed in a historical monitoring approach, in order to retrace the evolution of the differential settlements in time, since the construction of the building. Moreover, a structural analysis has been carried out on one transverse arch with distinct element analysis, with two different approaches. In one case, the structure was inserted exactly as surveyed, and then subjected to the actions. In the second case, the original geometry, before the deformation, was retraced through a parametric approach and the structural analysis basically started at the beginning of the building's life, thus trying to model not only the present structural situation, but also the path which led to the current deformation. The results were particularly meaningful as they showed that in the first case, disregarding the footsteps of history, the stress pattern inside the masonry was very different from the one obtained in the second case, which is more likely to represent the present conditions.

Real-time decay of a highly excited charge carrier in the one-dimensional Holstein model

NASA Astrophysics Data System (ADS)

Dorfner, F.; Vidmar, L.; Brockt, C.; Jeckelmann, E.; Heidrich-Meisner, F.

2015-03-01

We study the real-time dynamics of a highly excited charge carrier coupled to quantum phonons via a Holstein-type electron-phonon coupling. This is a prototypical example for the nonequilibrium dynamics in an interacting many-body system where excess energy is transferred from electronic to phononic degrees of freedom. We use diagonalization in a limited functional space (LFS) to study the nonequilibrium dynamics on a finite one-dimensional chain. This method agrees with exact diagonalization and the time-evolving block-decimation method, in both the relaxation regime and the long-time stationary state, and among these three methods it is the most efficient and versatile one for this problem. We perform a comprehensive analysis of the time evolution by calculating the electron, phonon and electron-phonon coupling energies, and the electronic momentum distribution function. The numerical results are compared to analytical solutions for short times, for a small hopping amplitude and for a weak electron-phonon coupling. In the latter case, the relaxation dynamics obtained from the Boltzmann equation agrees very well with the LFS data. We also study the time dependence of the eigenstates of the single-site reduced density matrix, which defines the so-called optimal phonon modes. We discuss their structure in nonequilibrium and the distribution of their weights. Our analysis shows that the structure of optimal phonon modes contains very useful information for the interpretation of the numerical data.

Anamorphic quasiperiodic universes in modified and Einstein gravity with loop quantum gravity corrections

NASA Astrophysics Data System (ADS)

Amaral, Marcelo M.; Aschheim, Raymond; Bubuianu, Laurenţiu; Irwin, Klee; Vacaru, Sergiu I.; Woolridge, Daniel

2017-09-01

The goal of this work is to elaborate on new geometric methods of constructing exact and parametric quasiperiodic solutions for anamorphic cosmology models in modified gravity theories, MGTs, and general relativity, GR. There exist previously studied generic off-diagonal and diagonalizable cosmological metrics encoding gravitational and matter fields with quasicrystal like structures, QC, and holonomy corrections from loop quantum gravity, LQG. We apply the anholonomic frame deformation method, AFDM, in order to decouple the (modified) gravitational and matter field equations in general form. This allows us to find integral varieties of cosmological solutions determined by generating functions, effective sources, integration functions and constants. The coefficients of metrics and connections for such cosmological configurations depend, in general, on all spacetime coordinates and can be chosen to generate observable (quasi)-periodic/aperiodic/fractal/stochastic/(super) cluster/filament/polymer like (continuous, stochastic, fractal and/or discrete structures) in MGTs and/or GR. In this work, we study new classes of solutions for anamorphic cosmology with LQG holonomy corrections. Such solutions are characterized by nonlinear symmetries of generating functions for generic off-diagonal cosmological metrics and generalized connections, with possible nonholonomic constraints to Levi-Civita configurations and diagonalizable metrics depending only on a time like coordinate. We argue that anamorphic quasiperiodic cosmological models integrate the concept of quantum discrete spacetime, with certain gravitational QC-like vacuum and nonvacuum structures. And, that of a contracting universe that homogenizes, isotropizes and flattens without introducing initial conditions or multiverse problems.

Tight-binding chains with off-diagonal disorder: Bands of extended electronic states induced by minimal quasi-one-dimensionality

NASA Astrophysics Data System (ADS)

Nandy, Atanu; Pal, Biplab; Chakrabarti, Arunava

2016-08-01

It is shown that an entire class of off-diagonally disordered linear lattices composed of two basic building blocks and described within a tight-binding model can be tailored to generate absolutely continuous energy bands. It can be achieved if linear atomic clusters of an appropriate size are side-coupled to a suitable subset of sites in the backbone, and if the nearest-neighbor hopping integrals, in the backbone and in the side-coupled cluster, bear a certain ratio. We work out the precise relationship between the number of atoms in one of the building blocks in the backbone and that in the side attachment. In addition, we also evaluate the definite correlation between the numerical values of the hopping integrals at different subsections of the chain, that can convert an otherwise point spectrum (or a singular continuous one for deterministically disordered lattices) with exponentially (or power law) localized eigenfunctions to an absolutely continuous spectrum comprising one or more bands (subbands) populated by extended, totally transparent eigenstates. The results, which are analytically exact, put forward a non-trivial variation of the Anderson localization (Anderson P. W., Phys. Rev., 109 (1958) 1492), pointing towards its unusual sensitivity to the numerical values of the system parameters and, go well beyond the other related models such as the Random Dimer Model (RDM) (Dunlap D. H. et al., Phys. Rev. Lett., 65 (1990) 88).

Trace identities and their semiclassical implications

NASA Astrophysics Data System (ADS)

Smilansky, Uzy

2000-03-01

The compatibility of the semiclassical quantization of area-preserving maps with some exact identities which follow from the unitarity of the quantum evolution operator is discussed. The quantum identities involve relations between traces of powers of the evolution operator. For classically integrable maps, the semiclassical approximation is shown to be compatible with the trace identities. This is done by the identification of stationary phase manifolds which give the main contributions to the result. The compatibility of the semiclassical quantization with the trace identities demonstrates the crucial importance of non-diagonal contributions. The same technique is not applicable for chaotic maps, and the compatibility of the semiclassical theory in this case remains unsettled. However, the trace identities are applied to maps which appear naturally in the theory of quantum graphs, revealing some features of the periodic orbit theory for these paradigms of quantum chaos.

Cobalt adatoms on graphene: Effects of anisotropies on the correlated electronic structure

NASA Astrophysics Data System (ADS)

Mozara, R.; Valentyuk, M.; Krivenko, I.; Şaşıoǧlu, E.; Kolorenč, J.; Lichtenstein, A. I.

2018-02-01

Impurities on surfaces experience a geometric symmetry breaking induced not only by the on-site crystal-field splitting and the orbital-dependent hybridization, but also by different screening of the Coulomb interaction in different directions. We present a many-body study of the Anderson impurity model representing a Co adatom on graphene, taking into account all anisotropies of the effective Coulomb interaction, which we obtained by the constrained random-phase approximation. The most pronounced differences are naturally displayed by the many-body self-energy projected onto the single-particle states. For the solution of the Anderson impurity model and analytical continuation of the Matsubara data, we employed new implementations of the continuous-time hybridization expansion quantum Monte Carlo and the stochastic optimization method, and we verified the results in parallel with the exact diagonalization method.

Fermionic Symmetry-Protected Topological Phase in a Two-Dimensional Hubbard Model

DOE PAGES

Chen, Cheng-Chien; Muechler, Lukas; Car, Roberto; ...

2016-08-25

We study the two-dimensional (2D) Hubbard model using exact diagonalization for spin-1/2 fermions on the triangular and honeycomb lattices decorated with a single hexagon per site. In certain parameter ranges, the Hubbard model maps to a quantum compass model on those lattices. On the triangular lattice, the compass model exhibits collinear stripe antiferromagnetism, implying d-density wave charge order in the original Hubbard model. On the honeycomb lattice, the compass model has a unique, quantum disordered ground state that transforms nontrivially under lattice reflection. The ground state of the Hubbard model on the decorated honeycomb lattice is thus a 2D fermionicmore » symmetry-protected topological phase. This state—protected by time-reversal and reflection symmetries—cannot be connected adiabatically to a free-fermion topological phase.« less

Conservative DEC Discretization of Incompressible Navier-Stokes Equations on Arbitrary Surface Simplicial Meshes

NASA Astrophysics Data System (ADS)

Mohamed, Mamdouh; Hirani, Anil; Samtaney, Ravi

2017-11-01

A conservative discretization of incompressible Navier-Stokes equations over surfaces is developed using discrete exterior calculus (DEC). The mimetic character of many of the DEC operators provides exact conservation of both mass and vorticity, in addition to superior kinetic energy conservation. The employment of signed diagonal Hodge star operators, while using the circumcentric dual defined on arbitrary meshes, is shown to produce correct solutions even when many non-Delaunay triangles pairs exist. This allows the DEC discretization to admit arbitrary surface simplicial meshes, in contrast to the previously held notion that DEC was limited only to Delaunay meshes. The discretization scheme is presented along with several numerical test cases demonstrating its numerical convergence and conservation properties. Recent developments regarding the extension to conservative higher order methods are also presented. KAUST Baseline Research Funds of R. Samtaney.

Theoretical treatment of the spin-orbit coupling in the rare gas oxides NeO, ArO, KrO, and XeO

NASA Technical Reports Server (NTRS)

Langhoff, S. R.

1980-01-01

Off-diagonal spin-orbit matrix elements are calculated as a function of internuclear distance for the rare gas oxides NeO, ArO, KrO, and XeO using the full microscopic spin-orbit Hamiltonian, including all one- and two-electron integrals, and POL-CI wave functions comparable to those of Dunning and Hay (1977). A good agreement was found when comparing these results in detail with the calculations of Cohen, Wadt and Hay (1979) that utilize an effective one-electron one-center spin-orbit operator. For the rare gas oxide molecules, it is suggested that the numerical results are a more sensitive test of the wave functions (particularly to the extent of charge transfer) than the exact evaluation of all terms in the full spin-orbit operator.

Raman Scattering from Higgs Mode Oscillations in the Two-Dimensional Antiferromagnet Ca_{2}RuO_{4}.

PubMed

Souliou, Sofia-Michaela; Chaloupka, Jiří; Khaliullin, Giniyat; Ryu, Gihun; Jain, Anil; Kim, B J; Le Tacon, Matthieu; Keimer, Bernhard

2017-08-11

We present and analyze Raman spectra of the Mott insulator Ca_{2}RuO_{4}, whose quasi-two-dimensional antiferromagnetic order has been described as a condensate of low-lying spin-orbit excitons with angular momentum J_{eff}=1. In the A_{g} polarization geometry, the amplitude (Higgs) mode of the spin-orbit condensate is directly probed in the scalar channel, thus avoiding infrared-singular magnon contributions. In the B_{1g} geometry, we observe a single-magnon peak as well as two-magnon and two-Higgs excitations. Model calculations using exact diagonalization quantitatively agree with the observations. Together with recent neutron scattering data, our study provides strong evidence for excitonic magnetism in Ca_{2}RuO_{4} and points out new perspectives for research on the Higgs mode in two dimensions.

Electron-Phonon Systems on a Universal Quantum Computer

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

Macridin, Alexandru; Spentzouris, Panagiotis; Amundson, James

We present an algorithm that extends existing quantum algorithms forsimulating fermion systems in quantum chemistry and condensed matter physics toinclude phonons. The phonon degrees of freedom are represented with exponentialaccuracy on a truncated Hilbert space with a size that increases linearly withthe cutoff of the maximum phonon number. The additional number of qubitsrequired by the presence of phonons scales linearly with the size of thesystem. The additional circuit depth is constant for systems with finite-rangeelectron-phonon and phonon-phonon interactions and linear for long-rangeelectron-phonon interactions. Our algorithm for a Holstein polaron problem wasimplemented on an Atos Quantum Learning Machine (QLM) quantum simulatoremployingmore » the Quantum Phase Estimation method. The energy and the phonon numberdistribution of the polaron state agree with exact diagonalization results forweak, intermediate and strong electron-phonon coupling regimes.« less

Raman Scattering from Higgs Mode Oscillations in the Two-Dimensional Antiferromagnet Ca2RuO4

NASA Astrophysics Data System (ADS)

Souliou, Sofia-Michaela; Chaloupka, Jiří; Khaliullin, Giniyat; Ryu, Gihun; Jain, Anil; Kim, B. J.; Le Tacon, Matthieu; Keimer, Bernhard

2017-08-01

We present and analyze Raman spectra of the Mott insulator Ca2RuO4 , whose quasi-two-dimensional antiferromagnetic order has been described as a condensate of low-lying spin-orbit excitons with angular momentum Jeff=1 . In the Ag polarization geometry, the amplitude (Higgs) mode of the spin-orbit condensate is directly probed in the scalar channel, thus avoiding infrared-singular magnon contributions. In the B1 g geometry, we observe a single-magnon peak as well as two-magnon and two-Higgs excitations. Model calculations using exact diagonalization quantitatively agree with the observations. Together with recent neutron scattering data, our study provides strong evidence for excitonic magnetism in Ca2 RuO4 and points out new perspectives for research on the Higgs mode in two dimensions.

Excitation spectrum for an inhomogeneously dipole-field-coupled superconducting qubit chain

NASA Astrophysics Data System (ADS)

Ian, Hou; Liu, Yu-xi; Nori, Franco

2012-05-01

When a chain of N superconducting qubits couples to a coplanar resonator, each of the qubits experiences a different dipole-field coupling strength due to the wave form of the cavity field. We find that this inhomogeneous coupling leads to a dependence of the collective ladder operators of the qubit chain on the qubit-interspacing l. Varying the spacing l changes the transition amplitudes between the angular momentum levels. We derive an exact diagonalization of the general N-qubit Hamiltonian and, through the N=4 case, demonstrate how the l-dependent operators lead to a denser one-excitation spectrum and a probability redistribution of the eigenstates. Moreover, we show that the variation of l between its two limiting values coincides with the crossover between Frenkel- and Wannier-type excitons in the superconducting qubit chain.

Quantum Monte Carlo calculations of two neutrons in finite volume

DOE PAGES

Klos, P.; Lynn, J. E.; Tews, I.; ...

2016-11-18

Ab initio calculations provide direct access to the properties of pure neutron systems that are challenging to study experimentally. In addition to their importance for fundamental physics, their properties are required as input for effective field theories of the strong interaction. In this work, we perform auxiliary-field diffusion Monte Carlo calculations of the ground state and first excited state of two neutrons in a finite box, considering a simple contact potential as well as chiral effective field theory interactions. We compare the results against exact diagonalizations and present a detailed analysis of the finite-volume effects, whose understanding is crucial formore » determining observables from the calculated energies. Finally, using the Lüscher formula, we extract the low-energy S-wave scattering parameters from ground- and excited-state energies for different box sizes.« less

Why do we need three levels to understand the molecular optical response?

NASA Astrophysics Data System (ADS)

Perez-Moreno, Javier; Clays, Koen; Kuzyk, Mark G.

2011-10-01

Traditionally, the nonlinear optical response at the molecular level has been modeled using the two-level approximation, under the assumption that the behavior of the exact sum-over-states (SOS) expressions for the molecular polarizabilities is well represented by the contribution of only two levels. We show how, a rigorous application of the Thomas-Kuhn sum-rules over the SOS expression for the diagonal component of the first-hyperpolarziability proves that the two-level approximation is unphysical. In addition, we indicate how the contributions of potentially infinite number of states to the SOS expressions for the first-hyperpolarizability are well represented by the contributions of a generic three-level system. This explains why the analysis of the three-level model in conjugation with the sum rules has lead to successful paradigms for the optimization of organic chromophores.

J dependence in the LSDA+U treatment of noncollinear magnets

NASA Astrophysics Data System (ADS)

Bousquet, Eric; Spaldin, Nicola

2010-12-01

We re-examine the commonly used density-functional theory plus Hubbard U (DFT+U) method for the case of noncollinear magnets. While many studies neglect to explicitly include the exchange-correction parameter J , or consider its exact value to be unimportant, here we show that in the case of noncollinear magnetism calculations the J parameter can strongly affect the magnetic ground state. We illustrate the strong J dependence of magnetic canting and magnetocrystalline anisotropy by calculating trends in the magnetic lithium orthophosphate family LiMPO4 ( M=Fe and Ni) and difluorite family MF2 ( M=Mn , Fe, Co, and Ni). Our results can be readily understood by expanding the usual DFT+U equations within the spinor scheme, in which the J parameter acts directly on the off-diagonal components which determine the spin canting.

Formulation of the relativistic quantum Hall effect and parity anomaly

NASA Astrophysics Data System (ADS)

Yonaga, Kouki; Hasebe, Kazuki; Shibata, Naokazu

2016-06-01

We present a relativistic formulation of the quantum Hall effect on Haldane sphere. An explicit form of the pseudopotential is derived for the relativistic quantum Hall effect with/without mass term. We clarify particular features of the relativistic quantum Hall states with the use of the exact diagonalization study of the pseudopotential Hamiltonian. Physical effects of the mass term to the relativistic quantum Hall states are investigated in detail. The mass term acts as an interpolating parameter between the relativistic and nonrelativistic quantum Hall effects. It is pointed out that the mass term unevenly affects the many-body physics of the positive and negative Landau levels as a manifestation of the "parity anomaly." In particular, we explicitly demonstrate the instability of the Laughlin state of the positive first relativistic Landau level with the reduction of the charge gap.

Ground state of a Heisenberg chain with next-nearest-neighbor bond alternation

NASA Astrophysics Data System (ADS)

Capriotti, Luca; Becca, Federico; Sorella, Sandro; Parola, Alberto

2003-05-01

We investigate the ground-state properties of the spin-half J1-J2 Heisenberg chain with a next-nearest-neighbor spin-Peierls dimerization using conformal field theory and Lanczos exact diagonalizations. In agreement with the results of a recent bosonization analysis by Sarkar and Sen [Phys. Rev. B 65, 172408 (2002)], we find that for small frustration (J2/J1) the system is in a Luttinger spin-fluid phase, with gapless excitations, and a finite spin-wave velocity. In the regime of strong frustration the ground state is spontaneously dimerized and the bond alternation reduces the triplet gap, leading to a slight enhancement of the critical point separating the Luttinger phase from the gapped one. An accurate determination of the phase boundary is obtained numerically from the study of the excitation spectrum.

Measles and rubella elimination: learning from polio eradication and moving forward with a diagonal approach.

PubMed

Goodson, James L; Alexander, James P; Linkins, Robert W; Orenstein, Walter A

2017-12-01

In 1988, an estimated 350,000 children were paralyzed by polio and 125 countries reported polio cases, the World Health Assembly passed a resolution to achieve polio eradication by 2000, and the Global Polio Eradication Initiative (GPEI) was established as a partnership focused on eradication. Today, following eradication efforts, polio cases have decreased >99% and eradication of all three types of wild polioviruses is approaching. However, since polio resources substantially support disease surveillance and other health programs, losing polio assets could reverse progress toward achieving Global Vaccine Action Plan goals. Areas covered: As the end of polio approaches and GPEI funds and capacity decrease, we document knowledge, experience, and lessons learned from 30 years of polio eradication. Expert commentary: Transitioning polio assets to measles and rubella (MR) elimination efforts would accelerate progress toward global vaccination coverage and equity. MR elimination feasibility and benefits have long been established. Focusing efforts on MR elimination after achieving polio eradication would make a permanent impact on reducing child mortality but should be done through a 'diagonal approach' of using measles disease transmission to identify areas possibly susceptible to other vaccine-preventable diseases and to strengthen the overall immunization and health systems to achieve disease-specific goals.

Gyrokinetic modelling of the quasilinear particle flux for plasmas with neutral-beam fuelling

NASA Astrophysics Data System (ADS)

Narita, E.; Honda, M.; Nakata, M.; Yoshida, M.; Takenaga, H.; Hayashi, N.

2018-02-01

A quasilinear particle flux is modelled based on gyrokinetic calculations. The particle flux is estimated by determining factors, namely, coefficients of off-diagonal terms and a particle diffusivity. In this paper, the methodology to estimate the factors is presented using a subset of JT-60U plasmas. First, the coefficients of off-diagonal terms are estimated by linear gyrokinetic calculations. Next, to obtain the particle diffusivity, a semi-empirical approach is taken. Most experimental analyses for particle transport have assumed that turbulent particle fluxes are zero in the core region. On the other hand, even in the stationary state, the plasmas in question have a finite turbulent particle flux due to neutral-beam fuelling. By combining estimates of the experimental turbulent particle flux and the coefficients of off-diagonal terms calculated earlier, the particle diffusivity is obtained. The particle diffusivity should reflect a saturation amplitude of instabilities. The particle diffusivity is investigated in terms of the effects of the linear instability and linear zonal flow response, and it is found that a formula including these effects roughly reproduces the particle diffusivity. The developed framework for prediction of the particle flux is flexible to add terms neglected in the current model. The methodology to estimate the quasilinear particle flux requires so low computational cost that a database consisting of the resultant coefficients of off-diagonal terms and particle diffusivity can be constructed to train a neural network. The development of the methodology is the first step towards a neural-network-based particle transport model for fast prediction of the particle flux.

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

Jin Jiasen; Yu Changshui; Song Heshan

We propose a scheme for identifying an unknown Bell diagonal state. In our scheme the measurements are performed on the probe qubits instead of the Bell diagonal state. The distinct advantage is that the quantum state of the evolved Bell diagonal state ensemble plus probe states will still collapse on the original Bell diagonal state ensemble after the measurement on probe states; i.e., our identification is quantum state nondestructive. How to realize our scheme in the framework of cavity electrodynamics is also shown.

Atom and Bond Fukui Functions and Matrices: A Hirshfeld-I Atoms-in-Molecule Approach.

PubMed

Oña, Ofelia B; De Clercq, Olivier; Alcoba, Diego R; Torre, Alicia; Lain, Luis; Van Neck, Dimitri; Bultinck, Patrick

2016-09-19

The Fukui function is often used in its atom-condensed form by isolating it from the molecular Fukui function using a chosen weight function for the atom in the molecule. Recently, Fukui functions and matrices for both atoms and bonds separately were introduced for semiempirical and ab initio levels of theory using Hückel and Mulliken atoms-in-molecule models. In this work, a double partitioning method of the Fukui matrix is proposed within the Hirshfeld-I atoms-in-molecule framework. Diagonalizing the resulting atomic and bond matrices gives eigenvalues and eigenvectors (Fukui orbitals) describing the reactivity of atoms and bonds. The Fukui function is the diagonal element of the Fukui matrix and may be resolved in atom and bond contributions. The extra information contained in the atom and bond resolution of the Fukui matrices and functions is highlighted. The effect of the choice of weight function arising from the Hirshfeld-I approach to obtain atom- and bond-condensed Fukui functions is studied. A comparison of the results with those generated by using the Mulliken atoms-in-molecule approach shows low correlation between the two partitioning schemes. © 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Pressure profiles in detonation cells with rectangular and diagonal structures

NASA Astrophysics Data System (ADS)

Hanana, M.; Lefebvre, M. H.

Experimental results presented in this work enable us to classify the three-dimensional structure of the detonation into two fundamental types: a rectangular structure and a diagonal structure. The rectangular structure is well documented in the literature and consists of orthogonal waves travelling independently from each another. The soot record in this case shows the classical diamond detonation cell exhibiting `slapping waves'. The experiments indicate that the diagonal structure is a structure with the triple point intersections moving along the diagonal line of the tube cross section. The axes of the transverse waves are canted at 45 degrees to the wall, accounting for the lack of slapping waves. It is possible to reproduce these diagonal structures by appropriately controlling the experimental ignition procedure. The characteristics of the diagonal structure show some similarities with detonation structure in round tube. Pressure measurements recorded along the central axis of the cellular structure show a series of pressure peaks, depending on the type of structure and the position inside the detonation cell. Pressure profiles measured for the whole length of the two types of detonation cells show that the intensity of the shock front is higher and the length of the detonation cell is shorter for the diagonal structures.

2. VIEW OF CENTRAL BEND OF LOWER DIAGONAL NO. 1 ...

Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

2. VIEW OF CENTRAL BEND OF LOWER DIAGONAL NO. 1 DRAIN, LOOKING 2932 EAST OF NORTH. - Truckee-Carson Irrigation District, Lower Diagonal No. 1 Drain, Bounded by West Gate Road & Weapons Delivery Road, Naval Air Station Fallon, Fallon, Churchill County, NV

Tradeoffs between oscillator strength and lifetime in terahertz quantum cascade lasers

DOE PAGES

Chan, Chun Wang I.; Albo, Asaf; Hu, Qing; ...

2016-11-14

Contemporary research into diagonal active region terahertz quantum cascade lasers for high temperature operation has yielded little success. We present evidence that the failure of high diagonality alone as a design strategy is due to a fundamental trade-off between large optical oscillator strength and long upper-level lifetime. Here, we hypothesize that diagonality needs to be paired with increased doping in order to succeed, and present evidence that highly diagonal designs can benefit from much higher doping than normally found in terahertz quantum cascade lasers. In assuming the benefits of high diagonality paired with high doping, we also highlight important challengesmore » that need to be overcome, specifically the increased importance of carrier induced band-bending and impurity scattering.« less

6. VIEW OF WEST GATE ROAD CULVERT OF LOWER DIAGONAL ...

Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

6. VIEW OF WEST GATE ROAD CULVERT OF LOWER DIAGONAL NO. 1 DRAIN, LOOKING 2502 EAST OF NORTH. - Truckee-Carson Irrigation District, Lower Diagonal No. 1 Drain, Bounded by West Gate Road & Weapons Delivery Road, Naval Air Station Fallon, Fallon, Churchill County, NV

7. VIEW OF WEAPONS DELIVERY ROAD CULVERT OF LOWER DIAGONAL ...

Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

7. VIEW OF WEAPONS DELIVERY ROAD CULVERT OF LOWER DIAGONAL NO. 1 DRAIN, LOOKING 522 EAST OF NORTH. - Truckee-Carson Irrigation District, Lower Diagonal No. 1 Drain, Bounded by West Gate Road & Weapons Delivery Road, Naval Air Station Fallon, Fallon, Churchill County, NV

5. VIEW OF WEST GATE ROAD CULVERT OF LOWER DIAGONAL ...

Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

5. VIEW OF WEST GATE ROAD CULVERT OF LOWER DIAGONAL NO. 1 DRAIN, LOOKING 323' EAST OF NORTH. - Truckee-Carson Irrigation District, Lower Diagonal No. 1 Drain, Bounded by West Gate Road & Weapons Delivery Road, Naval Air Station Fallon, Fallon, Churchill County, NV

Quantum entanglement and criticality of the antiferromagnetic Heisenberg model in an external field.

PubMed

Liu, Guang-Hua; Li, Ruo-Yan; Tian, Guang-Shan

2012-06-27

By Lanczos exact diagonalization and the infinite time-evolving block decimation (iTEBD) technique, the two-site entanglement as well as the bipartite entanglement, the ground state energy, the nearest-neighbor correlations, and the magnetization in the antiferromagnetic Heisenberg (AFH) model under an external field are investigated. With increasing external field, the small size system shows some distinct upward magnetization stairsteps, accompanied synchronously with some downward two-site entanglement stairsteps. In the thermodynamic limit, the two-site entanglement, as well as the bipartite entanglement, the ground state energy, the nearest-neighbor correlations, and the magnetization are calculated, and the critical magnetic field h(c) = 2.0 is determined exactly. Our numerical results show that the quantum entanglement is sensitive to the subtle changing of the ground state, and can be used to describe the magnetization and quantum phase transition. Based on the discontinuous behavior of the first-order derivative of the entanglement entropy and fidelity per site, we think that the quantum phase transition in this model should belong to the second-order category. Furthermore, in the magnon existence region (h < 2.0), a logarithmically divergent behavior of block entanglement which can be described by a free bosonic field theory is observed, and the central charge c is determined to be 1.

Excited state correlations of the finite Heisenberg chain

NASA Astrophysics Data System (ADS)

Pozsgay, Balázs

2017-02-01

We consider short range correlations in excited states of the finite XXZ and XXX Heisenberg spin chains. We conjecture that the known results for the factorized ground state correlations can be applied to the excited states too, if the so-called physical part of the construction is changed appropriately. For the ground state we derive simple algebraic expressions for the physical part; the formulas only use the ground state Bethe roots as an input. We conjecture that the same formulas can be applied to the excited states as well, if the exact Bethe roots of the excited states are used instead. In the XXZ chain the results are expected to be valid for all states (except certain singular cases where regularization is needed), whereas in the XXX case they only apply to singlet states or group invariant operators. Our conjectures are tested against numerical data from exact diagonalization and coordinate Bethe Ansatz calculations, and perfect agreement is found in all cases. In the XXX case we also derive a new result for the nearest-neighbour correlator < σ 1zσ 2z> , which is valid for non-singlet states as well. Our results build a bridge between the known theory of factorized correlations, and the recently conjectured TBA-like description for the building blocks of the construction.

Formalism for the solution of quadratic Hamiltonians with large cosine terms

NASA Astrophysics Data System (ADS)

Ganeshan, Sriram; Levin, Michael

2016-02-01

We consider quantum Hamiltonians of the form H =H0-U ∑jcos(Cj) , where H0 is a quadratic function of position and momentum variables {x1,p1,x2,p2,⋯} and the Cj's are linear in these variables. We allow H0 and Cj to be completely general with only two restrictions: we require that (1) the Cj's are linearly independent and (2) [Cj,Ck] is an integer multiple of 2 π i for all j ,k so that the different cosine terms commute with one another. Our main result is a recipe for solving these Hamiltonians and obtaining their exact low-energy spectrum in the limit U →∞ . This recipe involves constructing creation and annihilation operators and is similar in spirit to the procedure for diagonalizing quadratic Hamiltonians. In addition to our exact solution in the infinite U limit, we also discuss how to analyze these systems when U is large but finite. Our results are relevant to a number of different physical systems, but one of the most natural applications is to understanding the effects of electron scattering on quantum Hall edge modes. To demonstrate this application, we use our formalism to solve a toy model for a fractional quantum spin Hall edge with different types of impurities.

Line mixing effects in isotropic Raman spectra of pure N{sub 2}: A classical trajectory study

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

Ivanov, Sergey V., E-mail: serg.vict.ivanov@gmail.com; Boulet, Christian; Buzykin, Oleg G.

2014-11-14

Line mixing effects in the Q branch of pure N{sub 2} isotropic Raman scattering are studied at room temperature using a classical trajectory method. It is the first study using an extended modified version of Gordon's classical theory of impact broadening and shift of rovibrational lines. The whole relaxation matrix is calculated using an exact 3D classical trajectory method for binary collisions of rigid N{sub 2} molecules employing the most up-to-date intermolecular potential energy surface (PES). A simple symmetrizing procedure is employed to improve off-diagonal cross-sections to make them obeying exactly the principle of detailed balance. The adequacy of themore » results is confirmed by the sum rule. The comparison is made with available experimental data as well as with benchmark fully quantum close coupling [F. Thibault, C. Boulet, and Q. Ma, J. Chem. Phys. 140, 044303 (2014)] and refined semi-classical Robert-Bonamy [C. Boulet, Q. Ma, and F. Thibault, J. Chem. Phys. 140, 084310 (2014)] results. All calculations (classical, quantum, and semi-classical) were made using the same PES. The agreement between classical and quantum relaxation matrices is excellent, opening the way to the analysis of more complex molecular systems.« less

Fast computation of molecular random phase approximation correlation energies using resolution of the identity and imaginary frequency integration

NASA Astrophysics Data System (ADS)

Eshuis, Henk; Yarkony, Julian; Furche, Filipp

2010-06-01

The random phase approximation (RPA) is an increasingly popular post-Kohn-Sham correlation method, but its high computational cost has limited molecular applications to systems with few atoms. Here we present an efficient implementation of RPA correlation energies based on a combination of resolution of the identity (RI) and imaginary frequency integration techniques. We show that the RI approximation to four-index electron repulsion integrals leads to a variational upper bound to the exact RPA correlation energy if the Coulomb metric is used. Auxiliary basis sets optimized for second-order Møller-Plesset (MP2) calculations are well suitable for RPA, as is demonstrated for the HEAT [A. Tajti et al., J. Chem. Phys. 121, 11599 (2004)] and MOLEKEL [F. Weigend et al., Chem. Phys. Lett. 294, 143 (1998)] benchmark sets. Using imaginary frequency integration rather than diagonalization to compute the matrix square root necessary for RPA, evaluation of the RPA correlation energy requires O(N4 log N) operations and O(N3) storage only; the price for this dramatic improvement over existing algorithms is a numerical quadrature. We propose a numerical integration scheme that is exact in the two-orbital case and converges exponentially with the number of grid points. For most systems, 30-40 grid points yield μH accuracy in triple zeta basis sets, but much larger grids are necessary for small gap systems. The lowest-order approximation to the present method is a post-Kohn-Sham frequency-domain version of opposite-spin Laplace-transform RI-MP2 [J. Jung et al., Phys. Rev. B 70, 205107 (2004)]. Timings for polyacenes with up to 30 atoms show speed-ups of two orders of magnitude over previous implementations. The present approach makes it possible to routinely compute RPA correlation energies of systems well beyond 100 atoms, as is demonstrated for the octapeptide angiotensin II.

Fast computation of molecular random phase approximation correlation energies using resolution of the identity and imaginary frequency integration.

PubMed

Eshuis, Henk; Yarkony, Julian; Furche, Filipp

2010-06-21

The random phase approximation (RPA) is an increasingly popular post-Kohn-Sham correlation method, but its high computational cost has limited molecular applications to systems with few atoms. Here we present an efficient implementation of RPA correlation energies based on a combination of resolution of the identity (RI) and imaginary frequency integration techniques. We show that the RI approximation to four-index electron repulsion integrals leads to a variational upper bound to the exact RPA correlation energy if the Coulomb metric is used. Auxiliary basis sets optimized for second-order Møller-Plesset (MP2) calculations are well suitable for RPA, as is demonstrated for the HEAT [A. Tajti et al., J. Chem. Phys. 121, 11599 (2004)] and MOLEKEL [F. Weigend et al., Chem. Phys. Lett. 294, 143 (1998)] benchmark sets. Using imaginary frequency integration rather than diagonalization to compute the matrix square root necessary for RPA, evaluation of the RPA correlation energy requires O(N(4) log N) operations and O(N(3)) storage only; the price for this dramatic improvement over existing algorithms is a numerical quadrature. We propose a numerical integration scheme that is exact in the two-orbital case and converges exponentially with the number of grid points. For most systems, 30-40 grid points yield muH accuracy in triple zeta basis sets, but much larger grids are necessary for small gap systems. The lowest-order approximation to the present method is a post-Kohn-Sham frequency-domain version of opposite-spin Laplace-transform RI-MP2 [J. Jung et al., Phys. Rev. B 70, 205107 (2004)]. Timings for polyacenes with up to 30 atoms show speed-ups of two orders of magnitude over previous implementations. The present approach makes it possible to routinely compute RPA correlation energies of systems well beyond 100 atoms, as is demonstrated for the octapeptide angiotensin II.

A tensor product state approach to spin-1/2 square J1-J2 antiferromagnetic Heisenberg model: evidence for deconfined quantum criticality

NASA Astrophysics Data System (ADS)

Wang, Ling; Gu, Zheng-Cheng; Verstraete, Frank; Wen, Xiang-Gang

We study this model using the cluster update algorithm for tensor product states (TPSs). We find that the ground state energies at finite sizes and in the thermodynamic limit are in good agreement with the exact diagonalization study. At the largest bond dimension available D = 9 and through finite size scaling of the magnetization order near the transition point, we accurately determine the critical point J2c1 = 0 . 53 (1) J1 and the critical exponents β = 0 . 50 (4) . In the intermediate region we find a paramagnetic ground state without any static valence bond solid (VBS) order, supported by an exponentially decaying spin-spin correlation while a power law decaying dimer-dimer correlation. By fitting a universal scaling function for the spin-spin correlation we find the critical exponents ν = 0 . 68 (3) and ηs = 0 . 34 (6) , which is very close to the observed critical exponents for deconfined quantum critical point (DQCP) in other systems. Thus our numerical results strongly suggest a Landau forbidden phase transition from Neel order to VBS order at J2c1 = 0 . 53 (1) J1 . This project is supported by the EU Strep project QUEVADIS, the ERC Grant QUERG, and the FWF SFB Grants FoQuS and ViCoM; and the Institute for Quantum Information and Matter.

Accurate ab Initio Quartic Force Fields, Vibrational Frequencies, and Heats of Formation for FCN, FNC, ClCN, and ClNC

NASA Technical Reports Server (NTRS)

Lee, Timothy J.; Martin, Jan M. L.; Dateo, Christopher E.; Taylor, Peter R.

1995-01-01

The XCN and XNC (X = F, Cl) isomers have been investigated using the CCSD(T) method in conjunction with correlation consistent basis sets. Equilibrium geometries, harmonic frequencies, anharmonic constants, fundamental frequencies, and heats of formation have been evaluated. Agreement with experiment for the fundamental frequencies is very good, even for nu(sub 2), for CICN, which is subject to a strong Fermi resonance with 2nu(sub 3). It is also shown that a second-order perturbation theory approach to solving the nuclear Schroedinger equation gives results in excellent agreement with essentially exact variational calculations. This is true even for nu(sub 2) of ClCN, provided that near-singular terms are eliminated from the perturbation theory formulas and the appropriate Fermi interaction energy matrix is then diagonalized. A band at 615/cm, tentatively assigned as the Cl-N stretch in ClNC in matrix isolation experiments, is shown not to be due to ClNC. Accurate atomization energies are determined and are used to evaluate accurate heats of formation (3.1 +/- 1.5, 33.2 +/- 1.5, 72.6 +/- 1.5, and 75.9 +/- 1.5 kcal/mol for FCN, ClCN, FNC, and ClNC, respectively). It is expected that the theoretical heats of formation for FCN, FNC, and ClNC are the most accurate available.

Floquet engineering of Haldane Chern insulators and chiral bosonic phase transitions

NASA Astrophysics Data System (ADS)

Plekhanov, Kirill; Roux, Guillaume; Le Hur, Karyn

2017-01-01

The realization of synthetic gauge fields has attracted a lot of attention recently in relation to periodically driven systems and the Floquet theory. In ultracold atom systems in optical lattices and photonic networks, this allows one to simulate exotic phases of matter such as quantum Hall phases, anomalous quantum Hall phases, and analogs of topological insulators. In this paper, we apply the Floquet theory to engineer anisotropic Haldane models on the honeycomb lattice and two-leg ladder systems. We show that these anisotropic Haldane models still possess a topologically nontrivial band structure associated with chiral edge modes. Focusing on (interacting) boson systems in s -wave bands of the lattice, we show how to engineer through the Floquet theory, a quantum phase transition (QPT) between a uniform superfluid and a Bose-Einstein condensate analog of Fulde-Ferrell-Larkin-Ovchinnikov states, where bosons condense at nonzero wave vectors. We perform a Ginzburg-Landau analysis of the QPT on the graphene lattice, and compute observables such as chiral currents and the momentum distribution. The results are supported by exact diagonalization calculations and compared with those of the isotropic situation. The validity of high-frequency expansion in the Floquet theory is also tested using time-dependent simulations for various parameters of the model. Last, we show that the anisotropic choice for the effective vector potential allows a bosonization approach in equivalent ladder (strip) geometries.

Chaos in non-diagonal spatially homogeneous cosmological models in spacetime dimensions <=10

NASA Astrophysics Data System (ADS)

Demaret, Jacques; de Rop, Yves; Henneaux, Marc

1988-08-01

It is shown that the chaotic oscillatory behaviour, absent in diagonal homogeneous cosmological models in spacetime dimensions between 5 and 10, can be reestablished when off-diagonal terms are included. Also at Centro de Estudios Cientificos de Santiago, Casilla 16443, Santiago 9, Chile

4. VIEW OF EAST PORTION OF LOWER DIAGONAL NO. 1 ...

Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

4. VIEW OF EAST PORTION OF LOWER DIAGONAL NO. 1 DRAIN LOOKING TOWARDS THE CENTRAL BEND, LOOKING 270t EAST OF NORTH. - Truckee-Carson Irrigation District, Lower Diagonal No. 1 Drain, Bounded by West Gate Road & Weapons Delivery Road, Naval Air Station Fallon, Fallon, Churchill County, NV

1. VIEW OF WEST PORTION OF LOWER DIAGONAL NO. 1 ...

Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

1. VIEW OF WEST PORTION OF LOWER DIAGONAL NO. 1 DRAIN LOOKING TOWARDS THE WEST GATE ROAD CULVERT, LOOKING 3052 EAST OF NORTH. - Truckee-Carson Irrigation District, Lower Diagonal No. 1 Drain, Bounded by West Gate Road & Weapons Delivery Road, Naval Air Station Fallon, Fallon, Churchill County, NV

3. VIEW OF EAST PORTION OF LOWER DIAGONAL NO. 1 ...

Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

3. VIEW OF EAST PORTION OF LOWER DIAGONAL NO. 1 DRAIN LOOKING TOWARDS THE CENTRAL BEND, LOOKING 2742 EAST OF NORTH. - Truckee-Carson Irrigation District, Lower Diagonal No. 1 Drain, Bounded by West Gate Road & Weapons Delivery Road, Naval Air Station Fallon, Fallon, Churchill County, NV

Simplicity and Typical Rank Results for Three-Way Arrays

ERIC Educational Resources Information Center

ten Berge, Jos M. F.

2011-01-01

Matrices can be diagonalized by singular vectors or, when they are symmetric, by eigenvectors. Pairs of square matrices often admit simultaneous diagonalization, and always admit block wise simultaneous diagonalization. Generalizing these possibilities to more than two (non-square) matrices leads to methods of simplifying three-way arrays by…

Multiple quantum coherence spectroscopy.

PubMed

Mathew, Nathan A; Yurs, Lena A; Block, Stephen B; Pakoulev, Andrei V; Kornau, Kathryn M; Wright, John C

2009-08-20

Multiple quantum coherences provide a powerful approach for studies of complex systems because increasing the number of quantum states in a quantum mechanical superposition state increases the selectivity of a spectroscopic measurement. We show that frequency domain multiple quantum coherence multidimensional spectroscopy can create these superposition states using different frequency excitation pulses. The superposition state is created using two excitation frequencies to excite the symmetric and asymmetric stretch modes in a rhodium dicarbonyl chelate and the dynamic Stark effect to climb the vibrational ladders involving different overtone and combination band states. A monochromator resolves the free induction decay of different coherences comprising the superposition state. The three spectral dimensions provide the selectivity required to observe 19 different spectral features associated with fully coherent nonlinear processes involving up to 11 interactions with the excitation fields. The different features act as spectroscopic probes of the diagonal and off-diagonal parts of the molecular potential energy hypersurface. This approach can be considered as a coherent pump-probe spectroscopy where the pump is a series of excitation pulses that prepares a multiple quantum coherence and the probe is another series of pulses that creates the output coherence.

Transonic Navier-Stokes wing solution using a zonal approach. Part 1: Solution methodology and code validation

NASA Technical Reports Server (NTRS)

Flores, J.; Gundy, K.; Gundy, K.; Gundy, K.; Gundy, K.; Gundy, K.

1986-01-01

A fast diagonalized Beam-Warming algorithm is coupled with a zonal approach to solve the three-dimensional Euler/Navier-Stokes equations. The computer code, called Transonic Navier-Stokes (TNS), uses a total of four zones for wing configurations (or can be extended to complete aircraft configurations by adding zones). In the inner blocks near the wing surface, the thin-layer Navier-Stokes equations are solved, while in the outer two blocks the Euler equations are solved. The diagonal algorithm yields a speedup of as much as a factor of 40 over the original algorithm/zonal method code. The TNS code, in addition, has the capability to model wind tunnel walls. Transonic viscous solutions are obtained on a 150,000-point mesh for a NACA 0012 wing. A three-order-of-magnitude drop in the L2-norm of the residual requires approximately 500 iterations, which takes about 45 min of CPU time on a Cray-XMP processor. Simulations are also conducted for a different geometrical wing called WING C. All cases show good agreement with experimental data.

An Efficient numerical method to calculate the conductivity tensor for disordered topological matter

NASA Astrophysics Data System (ADS)

Garcia, Jose H.; Covaci, Lucian; Rappoport, Tatiana G.

2015-03-01

We propose a new efficient numerical approach to calculate the conductivity tensor in solids. We use a real-space implementation of the Kubo formalism where both diagonal and off-diagonal conductivities are treated in the same footing. We adopt a formulation of the Kubo theory that is known as Bastin formula and expand the Green's functions involved in terms of Chebyshev polynomials using the kernel polynomial method. Within this method, all the computational effort is on the calculation of the expansion coefficients. It also has the advantage of obtaining both conductivities in a single calculation step and for various values of temperature and chemical potential, capturing the topology of the band-structure. Our numerical technique is very general and is suitable for the calculation of transport properties of disordered systems. We analyze how the method's accuracy varies with the number of moments used in the expansion and illustrate our approach by calculating the transverse conductivity of different topological systems. T.G.R, J.H.G and L.C. acknowledge Brazilian agencies CNPq, FAPERJ and INCT de Nanoestruturas de Carbono, Flemish Science Foundation for financial support.

A cross-sectional study comparing lateral and diagonal maximum weight shift in people with stroke and healthy controls and the correlation with balance, gait and fear of falling

PubMed Central

Meyer, Sarah; Beyens, Hilde; Dejaeger, Eddy; Verheyden, Geert

2017-01-01

Impaired balance is common post stroke and can be assessed by means of force-platforms measuring center of pressure (COP) displacements during static standing, or more dynamically during lateral maximum weight shift (MWS). However, activities of daily life also include diagonal MWS and since force platforms are nowadays commercially available, investigating lateral and diagonal MWS in a clinical setting might be feasible and clinically relevant. We investigated lateral and diagonal MWS while standing in patients with stroke (PwS) and healthy controls (HC), evaluated MWS towards the affected and the non-affected side for PwS and correlated MWS with measures of balance, gait and fear of falling. In a cross-sectional observational study including 36 ambulatory sub-acute inpatients and 32 age-matched HC, a force platform (BioRescue, RM Ingénierie, France) was used to measure lateral and diagonal MWS in standing. Clinical outcome measures collected were Berg Balance Scale and Community Balance and Mobility Scale (CBMS) for balance, 10-meter walk test (10MWT) for gait speed and Falls Efficacy Scale–international version for fear of falling. MWS for PwS towards the affected side was significantly smaller compared to HC (lateral: p = 0.029; diagonal-forward: p = 0.000). MWS for PwS was also significantly reduced towards the affected side in the diagonal-forward direction (p = 0.019) compared to the non-affected side of PwS. Strong correlations were found for MWS for PwS in the diagonal-forward direction towards the affected side, and clinical measures of balance (CBMS: r = 0.66) and gait speed (10MWT: r = 0.66). Our study showed that ambulatory sub-acute PwS, in comparison to HC, have decreased ability to shift their body weight diagonally forward in standing towards their affected side. This reduced ability is strongly related to clinical measures of balance and gait speed. Our results suggest that MWS in a diagonal-forward direction should receive attention in rehabilitation of ambulatory sub-acute PwS in an inpatient setting. PMID:28809939

A cross-sectional study comparing lateral and diagonal maximum weight shift in people with stroke and healthy controls and the correlation with balance, gait and fear of falling.

PubMed

van Dijk, Margaretha M; Meyer, Sarah; Sandstad, Solveig; Wiskerke, Evelyne; Thuwis, Rhea; Vandekerckhove, Chesny; Myny, Charlotte; Ghosh, Nitesh; Beyens, Hilde; Dejaeger, Eddy; Verheyden, Geert

2017-01-01

Impaired balance is common post stroke and can be assessed by means of force-platforms measuring center of pressure (COP) displacements during static standing, or more dynamically during lateral maximum weight shift (MWS). However, activities of daily life also include diagonal MWS and since force platforms are nowadays commercially available, investigating lateral and diagonal MWS in a clinical setting might be feasible and clinically relevant. We investigated lateral and diagonal MWS while standing in patients with stroke (PwS) and healthy controls (HC), evaluated MWS towards the affected and the non-affected side for PwS and correlated MWS with measures of balance, gait and fear of falling. In a cross-sectional observational study including 36 ambulatory sub-acute inpatients and 32 age-matched HC, a force platform (BioRescue, RM Ingénierie, France) was used to measure lateral and diagonal MWS in standing. Clinical outcome measures collected were Berg Balance Scale and Community Balance and Mobility Scale (CBMS) for balance, 10-meter walk test (10MWT) for gait speed and Falls Efficacy Scale-international version for fear of falling. MWS for PwS towards the affected side was significantly smaller compared to HC (lateral: p = 0.029; diagonal-forward: p = 0.000). MWS for PwS was also significantly reduced towards the affected side in the diagonal-forward direction (p = 0.019) compared to the non-affected side of PwS. Strong correlations were found for MWS for PwS in the diagonal-forward direction towards the affected side, and clinical measures of balance (CBMS: r = 0.66) and gait speed (10MWT: r = 0.66). Our study showed that ambulatory sub-acute PwS, in comparison to HC, have decreased ability to shift their body weight diagonally forward in standing towards their affected side. This reduced ability is strongly related to clinical measures of balance and gait speed. Our results suggest that MWS in a diagonal-forward direction should receive attention in rehabilitation of ambulatory sub-acute PwS in an inpatient setting.

Kids in Communities Study (KiCS) study protocol: a cross-sectional mixed-methods approach to measuring community-level factors influencing early child development in Australia

PubMed Central

Goldfeld, Sharon; Villanueva, Karen; Tanton, Robert; Katz, Ilan; Brinkman, Sally; Woolcock, Geoffrey; Giles-Corti, Billie

2017-01-01

Introduction Healthy childhood development in the early years is critical for later adult health and well-being. Early childhood development (ECD) research has focused primarily on individual, family and school factors, but largely ignored community factors. The Kids in Communities Study (KiCS) will test and investigate community-level influences on child development across Australia. Methods and analysis Cross-sectional mixed-methods study exploring community-level effects in 25 Australian local communities; selection based on community socioeconomic status (SES) and ECD using the Australian Early Development Census (AEDC), a population measure of child development, to create a local community ‘diagonality type’, that is, those performing better or worse (off-diagonal), or as expected (on-diagonal) on the AEDC relative to their SES. Data collection includes stakeholder interviews, parent and service provider focus groups, and surveys with general community residents and service providers, mapping of neighbourhood design and local amenities and services, analysis of policy documents, and the use of existing sociodemographic and early childhood education and care data. Quantitative data will be used to test associations between local community diagonality type, and ECD based on AEDC scores. Qualitative data will provide complementary and deeper exploration of these same associations. Ethics and dissemination The Royal Children's Hospital Human Research Ethics Committee approved the study protocol (#30016). Further ethics approvals were obtained from State Education and Health departments and Catholic archdioceses where required. ECD community-level indicators will eventually be derived and made publically available. Findings will be published in peer-reviewed journals, community reports, websites and policy briefs to disseminate results to researchers, and key stakeholders including policymakers, practitioners and (most importantly) the communities involved. PMID:28289049

Estimation of geopotential from satellite-to-satellite range rate data: Numerical results

NASA Technical Reports Server (NTRS)

Thobe, Glenn E.; Bose, Sam C.

1987-01-01

A technique for high-resolution geopotential field estimation by recovering the harmonic coefficients from satellite-to-satellite range rate data is presented and tested against both a controlled analytical simulation of a one-day satellite mission (maximum degree and order 8) and then against a Cowell method simulation of a 32-day mission (maximum degree and order 180). Innovations include: (1) a new frequency-domain observation equation based on kinetic energy perturbations which avoids much of the complication of the usual Keplerian element perturbation approaches; (2) a new method for computing the normalized inclination functions which unlike previous methods is both efficient and numerically stable even for large harmonic degrees and orders; (3) the application of a mass storage FFT to the entire mission range rate history; (4) the exploitation of newly discovered symmetries in the block diagonal observation matrix which reduce each block to the product of (a) a real diagonal matrix factor, (b) a real trapezoidal factor with half the number of rows as before, and (c) a complex diagonal factor; (5) a block-by-block least-squares solution of the observation equation by means of a custom-designed Givens orthogonal rotation method which is both numerically stable and tailored to the trapezoidal matrix structure for fast execution.

General design approach and practical realization of decoupling matrices for parallel transmission coils.

PubMed

Mahmood, Zohaib; McDaniel, Patrick; Guérin, Bastien; Keil, Boris; Vester, Markus; Adalsteinsson, Elfar; Wald, Lawrence L; Daniel, Luca

2016-07-01

In a coupled parallel transmit (pTx) array, the power delivered to a channel is partially distributed to other channels because of coupling. This power is dissipated in circulators resulting in a significant reduction in power efficiency. In this study, a technique for designing robust decoupling matrices interfaced between the RF amplifiers and the coils is proposed. The decoupling matrices ensure that most forward power is delivered to the load without loss of encoding capabilities of the pTx array. The decoupling condition requires that the impedance matrix seen by the power amplifiers is a diagonal matrix whose entries match the characteristic impedance of the power amplifiers. In this work, the impedance matrix of the coupled coils is diagonalized by a successive multiplication by its eigenvectors. A general design procedure and software are developed to generate automatically the hardware that implements diagonalization using passive components. The general design method is demonstrated by decoupling two example parallel transmit arrays. Our decoupling matrices achieve better than -20 db decoupling in both cases. A robust framework for designing decoupling matrices for pTx arrays is presented and validated. The proposed decoupling strategy theoretically scales to any arbitrary number of channels. Magn Reson Med 76:329-339, 2016. © 2015 Wiley Periodicals, Inc. © 2015 Wiley Periodicals, Inc.

Entangled scalar and tensor fluctuations during inflation

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

Collins, Hael; Vardanyan, Tereza

2016-11-29

We show how the choice of an inflationary state that entangles scalar and tensor fluctuations affects the angular two-point correlation functions of the T, E, and B modes of the cosmic microwave background. The propagators for a state starting with some general quadratic entanglement are solved exactly, leading to predictions for the primordial scalar-scalar, tensor-tensor, and scalar-tensor power spectra. These power spectra are expressed in terms of general functions that describe the entangling structure of the initial state relative to the standard Bunch-Davies vacuum. We illustrate how such a state would modify the angular correlations in the CMB with amore » simple example where the initial state is a small perturbation away from the Bunch-Davies state. Because the state breaks some of the rotational symmetries, the angular power spectra no longer need be strictly diagonal.« less

Anisotropic exchange interaction induced by a single photon in semiconductor microcavities

NASA Astrophysics Data System (ADS)

Chiappe, G.; Fernández-Rossier, J.; Louis, E.; Anda, E. V.

2005-12-01

We investigate coupling of localized spins in a semiconductor quantum dot embedded in a microcavity. The lowest cavity mode and the quantum dot exciton are coupled and close in energy, forming a polariton. The fermions forming the exciton interact with localized spins via exchange. Exact diagonalization of a Hamiltonian in which photons, spins, and excitons are treated quantum mechanically shows that a single polariton induces a sizable indirect anisotropic exchange interaction between spins. At sufficiently low temperatures strong ferromagnetic correlations show up without an appreciable increase in exciton population. In the case of a (Cd,Mn)Te quantum dot, Mn-Mn ferromagnetic coupling is still significant at 1 K : spin-spin correlation around 3 for exciton occupation smaller than 0.3. We find that the interaction mediated by photon-polaritons is 10 times stronger than the one induced by a classical field for equal Rabi splitting.

Ground-state information geometry and quantum criticality in an inhomogeneous spin model

NASA Astrophysics Data System (ADS)

Ma, Yu-Quan

2015-09-01

We investigate the ground-state Riemannian metric and the cyclic quantum distance of an inhomogeneous quantum spin-1/2 chain in a transverse field. This model can be diagonalized by using a general canonical transformation to the fermionic Hamiltonian mapped from the spin system. The ground-state Riemannian metric is derived exactly on a parameter manifold ring S1, which is introduced by performing a gauge transformation to the spin Hamiltonian through a twist operator. The cyclic ground-state quantum distance and the second derivative of the ground-state energy are studied in different exchange coupling parameter regions. Particularly, we show that, in the case of exchange coupling parameter Ja = Jb, the quantum ferromagnetic phase can be characterized by an invariant quantum distance and this distance will decay to zero rapidly in the paramagnetic phase. Project supported by the National Natural Science Foundation of China (Grant Nos. 11404023 and 11347131).

Magnetic Phase Diagrams and Magnetization Plateaus of the Spin-1/2 Antiferromagnetic Heisenberg Model on a Square-Kagome Lattice with Three Nonequivalent Exchange Interactions

NASA Astrophysics Data System (ADS)

Morita, Katsuhiro; Tohyama, Takami

2018-04-01

Magnetization plateaus in quantum spin systems emerge in two-dimensional frustrated systems such as a kagome lattice. The spin-1/2 antiferromagnetic Heisenberg model on a square-kagome lattice is also appropriate for the study of the magnetization plateau. Motivated by recent experimental findings of such a square kagome lattice with three nonequivalent bonds, we investigate the phase diagrams and magnetization plateaus of the lattice using the exact diagonalization method. In addition to the previously reported 1/3 and 2/3 plateaus in the model with two equivalent bonds, we find a new 2/3 plateau whose magnetic structure is characterized by spontaneously broken four-fold rotational symmetry. The plateau appears only in the case of three nonequivalent bonds. We propose the possibility of finding plateaus including the new one.

Criticality of the low-frequency conductivity for the bilayer quantum Heisenberg model

NASA Astrophysics Data System (ADS)

Nishiyama, Yoshihiro

2018-04-01

The criticality of the low-frequency conductivity for the bilayer quantum Heisenberg model was investigated numerically. The dynamical conductivity (associated with the O(3) symmetry) displays the inductor σ( ω) = ( iωL)-1 and capacitor iωC behaviors for the ordered and disordered phases, respectively. Both constants, C and L, have the same scaling dimension as that of the reciprocal paramagnetic gap Δ -1. Then, there arose a question to fix the set of critical amplitude ratios among them. So far, the O(2) case has been investigated in the context of the boson-vortex duality. In this paper, we employ the exact diagonalization method, which enables us to calculate the paramagnetic gap Δ directly. Thereby, the set of critical amplitude ratios as to C, L and Δ are estimated with the finite-size-scaling analysis for the cluster with N ≤ 34 spins.

Role of spin-orbit coupling in the Kugel-Khomskii model on the honeycomb lattice

NASA Astrophysics Data System (ADS)

Koga, Akihisa; Nakauchi, Shiryu; Nasu, Joji

2018-03-01

We study the effective spin-orbital model for honeycomb-layered transition metal compounds, applying the second-order perturbation theory to the three-orbital Hubbard model with the anisotropic hoppings. This model is reduced to the Kitaev model in the strong spin-orbit coupling limit. Combining the cluster mean-field approximations with the exact diagonalization, we treat the Kugel-Khomskii type superexchange interaction and spin-orbit coupling on an equal footing to discuss ground-state properties. We find that a zigzag ordered state is realized in the model within nearest-neighbor interactions. We clarify how the ordered state competes with the nonmagnetic state, which is adiabatically connected to the quantum spin liquid state realized in a strong spin-orbit coupling limit. Thermodynamic properties are also addressed. The present paper should provide another route to account for the Kitaev-based magnetic properties in candidate materials.

Scrambling of quantum information in quantum many-body systems

NASA Astrophysics Data System (ADS)

Iyoda, Eiki; Sagawa, Takahiro

2018-04-01

We systematically investigate scrambling (or delocalizing) processes of quantum information encoded in quantum many-body systems by using numerical exact diagonalization. As a measure of scrambling, we adopt the tripartite mutual information (TMI) that becomes negative when quantum information is delocalized. We clarify that scrambling is an independent property of the integrability of Hamiltonians; TMI can be negative or positive for both integrable and nonintegrable systems. This implies that scrambling is a separate concept from conventional quantum chaos characterized by nonintegrability. Specifically, we argue that there are a few exceptional initial states that do not exhibit scrambling, and show that such exceptional initial states have small effective dimensions. Furthermore, we calculate TMI in the Sachdev-Ye-Kitaev (SYK) model, a fermionic toy model of quantum gravity. We find that disorder does not make scrambling slower but makes it smoother in the SYK model, in contrast to many-body localization in spin chains.

Concurrence of dynamical phase transitions at finite temperature in the fully connected transverse-field Ising model

NASA Astrophysics Data System (ADS)

Lang, Johannes; Frank, Bernhard; Halimeh, Jad C.

2018-05-01

We construct the finite-temperature dynamical phase diagram of the fully connected transverse-field Ising model from the vantage point of two disparate concepts of dynamical criticality. An analytical derivation of the classical dynamics and exact diagonalization simulations are used to study the dynamics after a quantum quench in the system prepared in a thermal equilibrium state. The different dynamical phases characterized by the type of nonanalyticities that emerge in an appropriately defined Loschmidt-echo return rate directly correspond to the dynamical phases determined by the spontaneous breaking of Z2 symmetry in the long-time steady state. The dynamical phase diagram is qualitatively different depending on whether the initial thermal state is ferromagnetic or paramagnetic. Whereas the former leads to a dynamical phase diagram that can be directly related to its equilibrium counterpart, the latter gives rise to a divergent dynamical critical temperature at vanishing final transverse-field strength.

Wave Function and Emergent SU(2) Symmetry in the νT=1 Quantum Hall Bilayer

NASA Astrophysics Data System (ADS)

Lian, Biao; Zhang, Shou-Cheng

2018-02-01

We propose a trial wave function for the quantum Hall bilayer system of total filling factor νT=1 at a layer distance d to magnetic length ℓ ratio d /ℓ=κc 1≈1.1 , where the lowest charged excitation is known to have a level crossing. The wave function has two-particle correlations, which fit well with those in previous numerical studies, and can be viewed as a Bose-Einstein condensate of free excitons formed by composite bosons and anticomposite bosons in different layers. We show the free nature of these excitons indicating an emergent SU(2) symmetry for the composite bosons at d /ℓ=κc 1, which leads to the level crossing in low-lying charged excitations. We further show the overlap between the trial wave function, and the ground state of a small size exact diagonalization is peaked near d /ℓ=κc 1, which supports our theory.

Magnetic anisotropy in the Kitaev model systems Na2IrO3 and RuCl3

NASA Astrophysics Data System (ADS)

Chaloupka, Jiří; Khaliullin, Giniyat

2016-08-01

We study the ordered moment direction in the extended Kitaev-Heisenberg model relevant to honeycomb lattice magnets with strong spin-orbit coupling. We utilize numerical diagonalization and analyze the exact cluster ground states using a particular set of spin-coherent states, obtaining thereby quantum corrections to the magnetic anisotropy beyond conventional perturbative methods. It is found that the quantum fluctuations strongly modify the moment direction obtained at a classical level and are thus crucial for a precise quantification of the interactions. The results show that the moment direction is a sensitive probe of the model parameters in real materials. Focusing on the experimentally relevant zigzag phases of the model, we analyze the currently available neutron-diffraction and resonant x-ray-diffraction data on Na2IrO3 and RuCl3 and discuss the parameter regimes plausible in these Kitaev-Heisenberg model systems.

Singular perturbations and time scales in the design of digital flight control systems

NASA Technical Reports Server (NTRS)

Naidu, Desineni S.; Price, Douglas B.

1988-01-01

The results are presented of application of the methodology of Singular Perturbations and Time Scales (SPATS) to the control of digital flight systems. A block diagonalization method is described to decouple a full order, two time (slow and fast) scale, discrete control system into reduced order slow and fast subsystems. Basic properties and numerical aspects of the method are discussed. A composite, closed-loop, suboptimal control system is constructed as the sum of the slow and fast optimal feedback controls. The application of this technique to an aircraft model shows close agreement between the exact solutions and the decoupled (or composite) solutions. The main advantage of the method is the considerable reduction in the overall computational requirements for the evaluation of optimal guidance and control laws. The significance of the results is that it can be used for real time, onboard simulation. A brief survey is also presented of digital flight systems.

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.

Anomalous bulk behavior in the free parafermion Z (N ) spin chain

NASA Astrophysics Data System (ADS)

Alcaraz, Francisco C.; Batchelor, Murray T.

2018-06-01

We demonstrate using direct numerical diagonalization and extrapolation methods that boundary conditions have a profound effect on the bulk properties of a simple Z (N ) model for N ≥3 for which the model Hamiltonian is non-Hermitian. For N =2 the model reduces to the well-known quantum Ising model in a transverse field. For open boundary conditions, the Z (N ) model is known to be solved exactly in terms of free parafermions. Once the ends of the open chain are connected by considering the model on a ring, the bulk properties, including the ground-state energy per site, are seen to differ dramatically with increasing N . Other properties, such as the leading finite-size corrections to the ground-state energy, the mass gap exponent, and the specific-heat exponent, are also seen to be dependent on the boundary conditions. We speculate that this anomalous bulk behavior is a topological effect.

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

Effects of geometrical frustration on ferromagnetism in the Hubbard model on the generalised Shastry-Sutherland lattice

NASA Astrophysics Data System (ADS)

Farkašovský, Pavol

2018-05-01

The small-cluster exact-diagonalization calculations and the projector quantum Monte Carlo method are used to examine the competing effects of geometrical frustration and interaction on ferromagnetism in the Hubbard model on the generalised Shastry-Sutherland lattice. It is shown that the geometrical frustration stabilizes the ferromagnetic state at high electron concentrations ( n ≳ 7/4), where strong correlations between ferromagnetism and the shape of the noninteracting density of states are observed. In particular, it is found that ferromagnetism is stabilized for these values of frustration parameters, which lead to the single-peaked noninterating density of states at the band edge. Once, two or more peaks appear in the noninteracting density of states at the band edge the ferromagnetic state is suppressed. This opens a new route towards the understanding of ferromagnetism in strongly correlated systems.

Nuclear spin-lattice relaxation at field-induced level crossings in a Cr8F8 pivalate single crystal

NASA Astrophysics Data System (ADS)

Yamamoto, Shoji

2016-01-01

We construct a microscopic theory for the proton spin-lattice relaxation-rate 1 /T1 measurements around field-induced level crossings in a single crystal of the trivalent chromium ion wheel complex [Cr8F8(OOCtBu)16] at sufficiently low temperatures [E. Micotti et al., Phys. Rev. B 72 (2005) 020405(R)]. Exactly diagonalizing a well-equipped spin Hamiltonian for the individual clusters and giving further consideration to their possible interactions, we reveal the mechanism of 1 /T1 being single-peaked normally at the first level crossing but double-peaked intriguingly around the second level crossing. We wipe out the doubt about poor crystallization and find out a solution-intramolecular alternating Dzyaloshinsky-Moriya interaction combined with intermolecular coupling of antiferromagnetic character, each of which is so weak as several tens of mK in magnitude.

Electronic entanglement in late transition metal oxides.

PubMed

Thunström, Patrik; Di Marco, Igor; Eriksson, Olle

2012-11-02

We present a study of the entanglement in the electronic structure of the late transition metal monoxides--MnO, FeO, CoO, and NiO--obtained by means of density-functional theory in the local density approximation combined with dynamical mean-field theory. The impurity problem is solved through exact diagonalization, which grants full access to the thermally mixed many-body ground state density operator. The quality of the electronic structure is affirmed through a direct comparison between the calculated electronic excitation spectrum and photoemission experiments. Our treatment allows for a quantitative investigation of the entanglement in the electronic structure. Two main sources of entanglement are explicitly resolved through the use of a fidelity based geometrical entanglement measure, and additional information is gained from a complementary entropic entanglement measure. We show that the interplay of crystal field effects and Coulomb interaction causes the entanglement in CoO to take a particularly intricate form.

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

Topological gapped edge states in fractional quantum Hall-superconductor heterostructures

NASA Astrophysics Data System (ADS)

Cook, Ashley; Repellin, Cécile; Regnault, Nicolas; Neupert, Titus

We propose and implement a numerical setup for studying edge states of fractional quantum Hall droplets with a superconducting instability. We focus on a time-reversal symmetric bilayer fractional quantum Hall system of Laughlin ν = 1 / 3 states. The fully gapped edges carry a topological parafermionic degree of freedom that can encode quantum information protected against local perturbations. We numerically simulate such a system using exact diagonalization by restricting the calculation to the Laughlin quasihole subspace. We study the quantization of the total charge on each edge and show that the ground states are permuted by spin flux insertion and the parafermionic Josephson effect, evidencing their topological nature and the Cooper pairing of fractionalized quasiparticles. The full affiliation for Author 3 is: Laboratoire Pierre Aigrain, Ecole Normale Supérieure-PSL Research University, CNRS, Université Pierre et Marie Curie-Sorbonne Universités, Université Paris Diderot-Sorbonne Paris Cité, 24 rue Lhomond, 75231 Paris.

Stability of the wobbling motion in the triaxially deformed odd-A nucleus

NASA Astrophysics Data System (ADS)

Tanabe, Kosai; Sugawara-Tanabe, Kazuko

2017-12-01

In order to analyze the content of the exact solutions for particle-rotor models with both the rigid and the hydrodynamical moments of inertia (MoI), as a theoretical probe we apply the Holstein-Primakoff (HP) boson expansion method to the total angular momentum I and the single-particle angular momentum j. We study the competition between Coriolis force and the single-particle potential by employing the different choices of the diagonal HP boson representations for the components of I and j along a common coordinate axis, and along perpendicular axes. We do not find any wobbling level sequence associated with the rotation around the principal axis with the medium MoI. The staggering in the alignments of I about the axis with the medium MoI is found in the limited range of I, while the vector R(=I-j) is confined about the axis with the largest MoI.

Role of heat equation in lap joint for welding process

NASA Astrophysics Data System (ADS)

Kumar, P.; Rohit, Sooraj

2017-07-01

Welding is predominantly used in industrial purposes and growth in their industry, which gives exact welding and more efficient. The major advantage of using this welding technique at initial stage it takes very low heat to weld the portion and gives a good result of low distortion in modules. In this context, two dissimilar metals copper and nickel are chosen for analysis in tungsten inert gas welding (TIG) in which length is 300 mm and breadth is 100 mm thickness 15 mm welded at room temperature a welded portion zone is formed simulation analysis has done on CATIA® and ANSYS®and MATLAB® code is generated for calculating temperatures at each node to calculate temperature at each node a new technique is used tri-diagonal matrix algorithm is used (TDMA) Steady state one dimension heat is calculated results compared between simulation analysis and analytical analysis temperature at each node is calculated both the temperatures are equal with error.

Steering Bell-diagonal states

PubMed Central

Quan, Quan; Zhu, Huangjun; Liu, Si-Yuan; Fei, Shao-Ming; Fan, Heng; Yang, Wen-Li

2016-01-01

We investigate the steerability of two-qubit Bell-diagonal states under projective measurements by the steering party. In the simplest nontrivial scenario of two projective measurements, we solve this problem completely by virtue of the connection between the steering problem and the joint-measurement problem. A necessary and sufficient criterion is derived together with a simple geometrical interpretation. Our study shows that a Bell-diagonal state is steerable by two projective measurements iff it violates the Clauser-Horne-Shimony-Holt (CHSH) inequality, in sharp contrast with the strict hierarchy expected between steering and Bell nonlocality. We also introduce a steering measure and clarify its connections with concurrence and the volume of the steering ellipsoid. In particular, we determine the maximal concurrence and ellipsoid volume of Bell-diagonal states that are not steerable by two projective measurements. Finally, we explore the steerability of Bell-diagonal states under three projective measurements. A simple sufficient criterion is derived, which can detect the steerability of many states that are not steerable by two projective measurements. Our study offers valuable insight on steering of Bell-diagonal states as well as the connections between entanglement, steering, and Bell nonlocality. PMID:26911250

Fetal ECG extraction using independent component analysis by Jade approach

NASA Astrophysics Data System (ADS)

Giraldo-Guzmán, Jader; Contreras-Ortiz, Sonia H.; Lasprilla, Gloria Isabel Bautista; Kotas, Marian

2017-11-01

Fetal ECG monitoring is a useful method to assess the fetus health and detect abnormal conditions. In this paper we propose an approach to extract fetal ECG from abdomen and chest signals using independent component analysis based on the joint approximate diagonalization of eigenmatrices approach. The JADE approach avoids redundancy, what reduces matrix dimension and computational costs. Signals were filtered with a high pass filter to eliminate low frequency noise. Several levels of decomposition were tested until the fetal ECG was recognized in one of the separated sources output. The proposed method shows fast and good performance.

Similarity-transformed equation-of-motion vibrational coupled-cluster theory.

PubMed

Faucheaux, Jacob A; Nooijen, Marcel; Hirata, So

2018-02-07

A similarity-transformed equation-of-motion vibrational coupled-cluster (STEOM-XVCC) method is introduced as a one-mode theory with an effective vibrational Hamiltonian, which is similarity transformed twice so that its lower-order operators are dressed with higher-order anharmonic effects. The first transformation uses an exponential excitation operator, defining the equation-of-motion vibrational coupled-cluster (EOM-XVCC) method, and the second uses an exponential excitation-deexcitation operator. From diagonalization of this doubly similarity-transformed Hamiltonian in the small one-mode excitation space, the method simultaneously computes accurate anharmonic vibrational frequencies of all fundamentals, which have unique significance in vibrational analyses. We establish a diagrammatic method of deriving the working equations of STEOM-XVCC and prove their connectedness and thus size-consistency as well as the exact equality of its frequencies with the corresponding roots of EOM-XVCC. We furthermore elucidate the similarities and differences between electronic and vibrational STEOM methods and between STEOM-XVCC and vibrational many-body Green's function theory based on the Dyson equation, which is also an anharmonic one-mode theory. The latter comparison inspires three approximate STEOM-XVCC methods utilizing the common approximations made in the Dyson equation: the diagonal approximation, a perturbative expansion of the Dyson self-energy, and the frequency-independent approximation. The STEOM-XVCC method including up to the simultaneous four-mode excitation operator in a quartic force field and its three approximate variants are formulated and implemented in computer codes with the aid of computer algebra, and they are applied to small test cases with varied degrees of anharmonicity.

A problem with inverse time for a singularly perturbed integro-differential equation with diagonal degeneration of the kernel of high order

NASA Astrophysics Data System (ADS)

Bobodzhanov, A. A.; Safonov, V. F.

2016-04-01

We consider an algorithm for constructing asymptotic solutions regularized in the sense of Lomov (see [1], [2]). We show that such problems can be reduced to integro-differential equations with inverse time. But in contrast to known papers devoted to this topic (see, for example, [3]), in this paper we study a fundamentally new case, which is characterized by the absence, in the differential part, of a linear operator that isolates, in the asymptotics of the solution, constituents described by boundary functions and by the fact that the integral operator has kernel with diagonal degeneration of high order. Furthermore, the spectrum of the regularization operator A(t) (see below) may contain purely imaginary eigenvalues, which causes difficulties in the application of the methods of construction of asymptotic solutions proposed in the monograph [3]. Based on an analysis of the principal term of the asymptotics, we isolate a class of inhomogeneities and initial data for which the exact solution of the original problem tends to the limit solution (as \\varepsilon\\to+0) on the entire time interval under consideration, also including a boundary-layer zone (that is, we solve the so-called initialization problem). The paper is of a theoretical nature and is designed to lead to a greater understanding of the problems in the theory of singular perturbations. There may be applications in various applied areas where models described by integro-differential equations are used (for example, in elasticity theory, the theory of electrical circuits, and so on).

Similarity-transformed equation-of-motion vibrational coupled-cluster theory

NASA Astrophysics Data System (ADS)

Faucheaux, Jacob A.; Nooijen, Marcel; Hirata, So

2018-02-01

A similarity-transformed equation-of-motion vibrational coupled-cluster (STEOM-XVCC) method is introduced as a one-mode theory with an effective vibrational Hamiltonian, which is similarity transformed twice so that its lower-order operators are dressed with higher-order anharmonic effects. The first transformation uses an exponential excitation operator, defining the equation-of-motion vibrational coupled-cluster (EOM-XVCC) method, and the second uses an exponential excitation-deexcitation operator. From diagonalization of this doubly similarity-transformed Hamiltonian in the small one-mode excitation space, the method simultaneously computes accurate anharmonic vibrational frequencies of all fundamentals, which have unique significance in vibrational analyses. We establish a diagrammatic method of deriving the working equations of STEOM-XVCC and prove their connectedness and thus size-consistency as well as the exact equality of its frequencies with the corresponding roots of EOM-XVCC. We furthermore elucidate the similarities and differences between electronic and vibrational STEOM methods and between STEOM-XVCC and vibrational many-body Green's function theory based on the Dyson equation, which is also an anharmonic one-mode theory. The latter comparison inspires three approximate STEOM-XVCC methods utilizing the common approximations made in the Dyson equation: the diagonal approximation, a perturbative expansion of the Dyson self-energy, and the frequency-independent approximation. The STEOM-XVCC method including up to the simultaneous four-mode excitation operator in a quartic force field and its three approximate variants are formulated and implemented in computer codes with the aid of computer algebra, and they are applied to small test cases with varied degrees of anharmonicity.

Separability of three qubit Greenberger-Horne-Zeilinger diagonal states

NASA Astrophysics Data System (ADS)

Han, Kyung Hoon; Kye, Seung-Hyeok

2017-04-01

We characterize the separability of three qubit GHZ diagonal states in terms of entries. This enables us to check separability of GHZ diagonal states without decomposition into the sum of pure product states. In the course of discussion, we show that the necessary criterion of Gühne (2011 Entanglement criteria and full separability of multi-qubit quantum states Phys. Lett. A 375 406-10) for (full) separability of three qubit GHZ diagonal states is sufficient with a simpler formula. The main tool is to use entanglement witnesses which are tri-partite Choi matrices of positive bi-linear maps.

High-Order Coupled Cluster Method (CCM) Calculations for Quantum Magnets with Valence-Bond Ground States

NASA Astrophysics Data System (ADS)

Farnell, D. J. J.; Richter, J.; Zinke, R.; Bishop, R. F.

2009-04-01

In this article, we prove that exact representations of dimer and plaquette valence-bond ket ground states for quantum Heisenberg antiferromagnets may be formed via the usual coupled cluster method (CCM) from independent-spin product (e.g. Néel) model states. We show that we are able to provide good results for both the ground-state energy and the sublattice magnetization for dimer and plaquette valence-bond phases within the CCM. As a first example, we investigate the spin-half J 1- J 2 model for the linear chain, and we show that we are able to reproduce exactly the dimerized ground (ket) state at J 2/ J 1=0.5. The dimerized phase is stable over a range of values for J 2/ J 1 around 0.5, and results for the ground-state energies are in good agreement with the results of exact diagonalizations of finite-length chains in this regime. We present evidence of symmetry breaking by considering the ket- and bra-state correlation coefficients as a function of J 2/ J 1. A radical change is also observed in the behavior of the CCM sublattice magnetization as we enter the dimerized phase. We then consider the Shastry-Sutherland model and demonstrate that the CCM can span the correct ground states in both the Néel and the dimerized phases. Once again, very good results for the ground-state energies are obtained. We find CCM critical points of the bra-state equations that are in agreement with the known phase transition point for this model. The results for the sublattice magnetization remain near to the "true" value of zero over much of the dimerized regime, although they diverge exactly at the critical point. Finally, we consider a spin-half system with nearest-neighbor bonds for an underlying lattice corresponding to the magnetic material CaV4O9 (CAVO). We show that we are able to provide excellent results for the ground-state energy in each of the plaquette-ordered, Néel-ordered, and dimerized regimes of this model. The exact plaquette and dimer ground states are reproduced by the CCM ket state in their relevant limits. Furthermore, we estimate the range over which the Néel order is stable, and we find the CCM result is in reasonable agreement with the results obtained by other methods. Our new approach has the dual advantages that it is simple to implement and that existing CCM codes for independent-spin product model states may be used from the outset. Furthermore, it also greatly extends the range of applicability to which the CCM may be applied. We believe that the CCM now provides an excellent choice of method for the study of systems with valence-bond quantum ground states.

Non-linear homogenized and heterogeneous FE models for FRCM reinforced masonry walls in diagonal compression

NASA Astrophysics Data System (ADS)

Bertolesi, Elisa; Milani, Gabriele; Poggi, Carlo

2016-12-01

Two FE modeling techniques are presented and critically discussed for the non-linear analysis of tuff masonry panels reinforced with FRCM and subjected to standard diagonal compression tests. The specimens, tested at the University of Naples (Italy), are unreinforced and FRCM retrofitted walls. The extensive characterization of the constituent materials allowed adopting here very sophisticated numerical modeling techniques. In particular, here the results obtained by means of a micro-modeling strategy and homogenization approach are compared. The first modeling technique is a tridimensional heterogeneous micro-modeling where constituent materials (bricks, joints, reinforcing mortar and reinforcing grid) are modeled separately. The second approach is based on a two-step homogenization procedure, previously developed by the authors, where the elementary cell is discretized by means of three-noded plane stress elements and non-linear interfaces. The non-linear structural analyses are performed replacing the homogenized orthotropic continuum with a rigid element and non-linear spring assemblage (RBSM). All the simulations here presented are performed using the commercial software Abaqus. Pros and cons of the two approaches are herein discussed with reference to their reliability in reproducing global force-displacement curves and crack patterns, as well as to the rather different computational effort required by the two strategies.

Thinking Differently in Global Health in Oncology Using a Diagonal Approach: Harnessing Similarities, Improving Education, and Empowering an Alternative Oncology Workforce.

PubMed

Rodriguez, Natalia M; Brant, Jeannine M; Pendharkar, Dinesh; Arreola-Ornelas, Hector; Bhadelia, Afsan; de Lima Lopes, Gilberto; Knaul, Felicia M

2017-01-01

Cancer is a leading global cause of death, and diverse and minority populations suffer worse outcomes compared with white people from Western societies. Within the United States, African Americans and other blacks, Hispanics, Asians, and American Indians have lower cancer survival rates than whites. In the rest of the world, those from low- and middle-income countries have the greatest disparities, but even those from non-Western high-income countries such as Oman and the United Arab Emirates are diagnosed with cancer at later stages and suffer increased mortality. Although considerable differences exist among these populations, similarities and synergies are also apparent. Challenges can be very similar in reaching these populations effectively for cancer control to improve outcomes, and innovative strategies are needed to effectively make change. In this review, the authors discuss new approaches to the prevention and early detection of cancer as well as the implementation of programs in global oncology and put in evidence cultural similarities and challenges of different populations, highlighting strategies to improve cancer survival and quality care around the world through innovations in training and education, empowerment of an alternative workforce, and a diagonal approach to cancer care using case studies drawn from the authors' work and experience.

Diagonalization and Jordan Normal Form--Motivation through "Maple"[R

ERIC Educational Resources Information Center

Glaister, P.

2009-01-01

Following an introduction to the diagonalization of matrices, one of the more difficult topics for students to grasp in linear algebra is the concept of Jordan normal form. In this note, we show how the important notions of diagonalization and Jordan normal form can be introduced and developed through the use of the computer algebra package…

The 'diagonal' approach to Global Fund financing: a cure for the broader malaise of health systems?

PubMed Central

Ooms, Gorik; Van Damme, Wim; Baker, Brook K; Zeitz, Paul; Schrecker, Ted

2008-01-01

Background The potentially destructive polarisation between 'vertical' financing (aiming for disease-specific results) and 'horizontal' financing (aiming for improved health systems) of health services in developing countries has found its way to the pages of Foreign Affairs and the Financial Times. The opportunity offered by 'diagonal' financing (aiming for disease-specific results through improved health systems) seems to be obscured in this polarisation. In April 2007, the board of the Global Fund to fight AIDS, Tuberculosis and Malaria agreed to consider comprehensive country health programmes for financing. The new International Health Partnership Plus, launched in September 2007, will help low-income countries to develop such programmes. The combination could lead the Global Fund to fight AIDS, Tuberculosis and Malaria to a much broader financing scope. Discussion This evolution might be critical for the future of AIDS treatment in low-income countries, yet it is proposed at a time when the Global Fund to fight AIDS, Tuberculosis and Malaria is starved for resources. It might be unable to meet the needs of much broader and more expensive proposals. Furthermore, it might lose some of its exceptional features in the process: its aim for international sustainability, rather than in-country sustainability, and its capacity to circumvent spending restrictions imposed by the International Monetary Fund. Summary The authors believe that a transformation of the Global Fund to fight AIDS, Tuberculosis and Malaria into a Global Health Fund is feasible, but only if accompanied by a substantial increase of donor commitments to the Global Fund. The transformation of the Global Fund into a 'diagonal' and ultimately perhaps 'horizontal' financing approach should happen gradually and carefully, and be accompanied by measures to safeguard its exceptional features. PMID:18364048

A Seamless Approach to Transitioning Cane Skills from the Diagonal to the Two-Point Touch Technique

ERIC Educational Resources Information Center

Penrod, William M.

2012-01-01

The profession of orientation and mobility (O&M) is replete with literature describing specific cane techniques, strategies for teaching O&M to specific populations and age groups, rationales, and appropriate settings. These strategies and techniques are also addressed in many university preparation programs. In this article, the author discusses…

Developing Multidimensional Likert Scales Using Item Factor Analysis: The Case of Four-Point Items

ERIC Educational Resources Information Center

Asún, Rodrigo A.; Rdz-Navarro, Karina; Alvarado, Jesús M.

2016-01-01

This study compares the performance of two approaches in analysing four-point Likert rating scales with a factorial model: the classical factor analysis (FA) and the item factor analysis (IFA). For FA, maximum likelihood and weighted least squares estimations using Pearson correlation matrices among items are compared. For IFA, diagonally weighted…

Automated enzyme-based diagonal capillary electrophoresis: application to phosphopeptide characterization

PubMed Central

Wojcik, Roza; Vannatta, Michael

2010-01-01

Diagonal capillary electrophoresis is a form of two-dimensional capillary electrophoresis that employs identical separation modes in each dimension. The distal end of the first capillary incorporates an enzyme-based microreactor. Analytes that are not modified by the reactor will have identical migration times in the two capillaries and will generate spots that fall on the diagonal in a reconstructed two-dimensional electropherogram. Analytes that undergo enzymatic modification in the reactor will have a different migration time in the second capillary and will generate spots that fall off the diagonal in the electropherogram. We demonstrate the system with immobilized alkaline phosphatase to monitor the phosphorylation status of a mixture of peptides. This enzyme-based diagonal capillary electrophoresis assay appears to be generalizable; any post-translational modification can be detected as long as an immobilized enzyme is available that reacts with the modification under electrophoretic conditions. PMID:20099889

Loads imposed on intermediate frames of stiffened shells

NASA Technical Reports Server (NTRS)

Kuhn, Paul

1939-01-01

The loads imposed on intermediate frames by the curvature of the longitudinal and by the diagonal-tension effects are treated. A new empirical method is proposed for analyzing diagonal-tension effects. The basic formulas of the pure diagonal-tension theory are used, and the part of the total shear S carried by diagonal tension is assumed to be given the expression S (sub DT) = S (1-tau sub o/tau)(sup n) where tau (sub o) is the critical shear stress, tau the total (nominal shear stress), and n = 3 - sigma/tau where sigma is the stress in the intermediate frame. Numerical examples illustrate all cases treated.

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).

Nonequilibrium self-energy functional theory

NASA Astrophysics Data System (ADS)

Hofmann, Felix; Eckstein, Martin; Arrigoni, Enrico; Potthoff, Michael

2013-10-01

The self-energy functional theory (SFT) is generalized to describe the real-time dynamics of correlated lattice-fermion models far from thermal equilibrium. This is achieved by starting from a reformulation of the original equilibrium theory in terms of double-time Green's functions on the Keldysh-Matsubara contour. With the help of a generalized Luttinger-Ward functional, we construct a functional Ω̂[Σ] which is stationary at the physical (nonequilibrium) self-energy Σ and which yields the grand potential of the initial thermal state Ω at the physical point. Nonperturbative approximations can be defined by specifying a reference system that serves to generate trial self-energies. These self-energies are varied by varying the reference system's one-particle parameters on the Keldysh-Matsubara contour. In the case of thermal equilibrium, this approach reduces to the conventional SFT. Contrary to the equilibrium theory, however, “unphysical” variations, i.e., variations that are different on the upper and the lower branches of the Keldysh contour, must be considered to fix the time dependence of the optimal physical parameters via the variational principle. Functional derivatives in the nonequilibrium SFT Euler equation are carried out analytically to derive conditional equations for the variational parameters that are accessible to a numerical evaluation via a time-propagation scheme. Approximations constructed by means of the nonequilibrium SFT are shown to be inherently causal, internally consistent, and to respect macroscopic conservation laws resulting from gauge symmetries of the Hamiltonian. This comprises the nonequilibrium dynamical mean-field theory but also dynamical-impurity and variational-cluster approximations that are specified by reference systems with a finite number of degrees of freedom. In this way, nonperturbative and consistent approximations can be set up, the numerical evaluation of which is accessible to an exact-diagonalization approach.

Investigation of the spectral properties and magnetism of BiFeO3 by dynamical mean-field theory

NASA Astrophysics Data System (ADS)

Paul, Souvik; Iuşan, Diana; Thunström, Patrik; Kvashnin, Yaroslav O.; Hellsvik, Johan; Pereiro, Manuel; Delin, Anna; Knut, Ronny; Phuyal, Dibya; Lindblad, Andreas; Karis, Olof; Sanyal, Biplab; Eriksson, Olle

2018-03-01

Using the local density approximation plus dynamical mean-field theory (LDA+DMFT), we have computed the valence-band photoelectron spectra and magnetic excitation spectra of BiFeO3, one of the most studied multiferroics. Within the DMFT approach, the local impurity problem is tackled by the exact diagonalization solver. The solution of the impurity problem within the LDA+DMFT method for the paramagnetic and magnetically ordered phases produces result in agreement with the experimental data on electronic and magnetic structures. For comparison, we also present results obtained by the LDA +U approach which is commonly used to compute the physical properties of this compound. Our LDA+DMFT derived electronic spectra match adequately with the experimental hard x-ray photoelectron spectroscopy and resonant photoelectron spectroscopy for Fe 3 d states, whereas the LDA +U method fails to capture the general features of the measured spectra. This indicates the importance of accurately incorporating the dynamical aspect of electronic correlation among Fe 3 d orbitals to reproduce the experimental excitation spectra. Specifically, the LDA+DMFT derived density of states exhibits a significant amount of Fe 3 d states at the position of Bi lone pairs, implying that the latter are not alone in the spectral scenario. This fact might modify our interpretation about the origin of ferroelectric polarization in this material. Our study demonstrates that the combination of orbital cross sections for the constituent elements and broadening schemes for the spectral functions are crucial to explain the detailed structures of the experimental electronic spectra. Our magnetic excitation spectra computed from the LDA+DMFT result conform well with the inelastic neutron scattering data.

A Wave Chaotic Study of Quantum Graphs with Microwave Networks

NASA Astrophysics Data System (ADS)

Fu, Ziyuan

Quantum graphs provide a setting to test the hypothesis that all ray-chaotic systems show universal wave chaotic properties. I study the quantum graphs with a wave chaotic approach. Here, an experimental setup consisting of a microwave coaxial cable network is used to simulate quantum graphs. Some basic features and the distributions of impedance statistics are analyzed from experimental data on an ensemble of tetrahedral networks. The random coupling model (RCM) is applied in an attempt to uncover the universal statistical properties of the system. Deviations from RCM predictions have been observed in that the statistics of diagonal and off-diagonal impedance elements are different. Waves trapped due to multiple reflections on bonds between nodes in the graph most likely cause the deviations from universal behavior in the finite-size realization of a quantum graph. In addition, I have done some investigations on the Random Coupling Model, which are useful for further research.

Symmetric tridiagonal structure preserving finite element model updating problem for the quadratic model

NASA Astrophysics Data System (ADS)

Rakshit, Suman; Khare, Swanand R.; Datta, Biswa Nath

2018-07-01

One of the most important yet difficult aspect of the Finite Element Model Updating Problem is to preserve the finite element inherited structures in the updated model. Finite element matrices are in general symmetric, positive definite (or semi-definite) and banded (tridiagonal, diagonal, penta-diagonal, etc.). Though a large number of papers have been published in recent years on various aspects of solutions of this problem, papers dealing with structure preservation almost do not exist. A novel optimization based approach that preserves the symmetric tridiagonal structures of the stiffness and damping matrices is proposed in this paper. An analytical expression for the global minimum solution of the associated optimization problem along with the results of numerical experiments obtained by both the analytical expressions and by an appropriate numerical optimization algorithm are presented. The results of numerical experiments support the validity of the proposed method.

Long-Range Adiabatic Corrections to the Ground Molecular State of Alkali-Metal Dimers.

NASA Astrophysics Data System (ADS)

Marinescu, M.; Dalgarno, A.

1997-04-01

The structure of the long-range limit of the diagonal adiabatic corrections to the ground molecular state of diatomic molecules, may be expressed as a series of inverse powers of internuclear distance, R. The coefficients of this expansion are proportional to the inverse of the nuclear mass. Thus, they may be interpreted as a nuclear mass-dependent corrections to the dispersion coefficients. Using perturbation theory we have calculated the long-range coefficients of the diagonal adiabatic corrections up to the order of R-10. The final expressions are in terms of integrals over imaginary frequencies of products of atomic matrix elements involving Green's functions of complex energy. Thus, in our approach the molecular problem is reduced to an atomic one. Numerical evaluations have been done for all alkali-metal dimers. We acknowledge the support of the U.S. Dept. of Energy.

Quantum Field Theory in Two Dimensions: Light-front Versus Space-like Solutions

NASA Astrophysics Data System (ADS)

Martinovic̆, L'ubomír

2017-07-01

A few non-perturbative topics of quantum field theory in D=1+1 are studied in both the conventional (SL) and light-front (LF) versions. First, we give a concise review of the recently proposed quantization of the two-dimensional massless LF fields. The LF version of bosonization follows in a simple and natural way including the bosonized form of the Thirring model. As a further application, we demonstrate the closeness of the 2D massless LF quantum fields to conformal field theory (CFT). We calculate several correlation functions including those between the components of the LF energy-momentum tensor and derive the LF version of the Virasoro algebra. Using the Euclidean time variable, we can immediately transform calculated quantities to the (anti)holomorphic form. The results found are in agreement with those from CFT. Finally, we show that the proposed framework provides us with the elements needed for an independent LF study of exactly solvable models. We compute the non-perturbative correlation functions from the exact operator solution of the LF Thirring model and compare it to the analogous results in the SL theory. While the vacuum effects are automatically taken into account in the LF case, the non-trivial vacuum structure has to be incorported by an explicit diagonalization of the SL Hamiltonians, to obtain the equivalently complete solution.

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.

Ramp and periodic dynamics across non-Ising critical points

NASA Astrophysics Data System (ADS)

Ghosh, Roopayan; Sen, Arnab; Sengupta, K.

2018-01-01

We study ramp and periodic dynamics of ultracold bosons in an one-dimensional (1D) optical lattice which supports quantum critical points separating a uniform and a Z3 or Z4 symmetry broken density-wave ground state. Our protocol involves both linear and periodic drives which takes the system from the uniform state to the quantum critical point (for linear drive protocol) or to the ordered state and back (for periodic drive protocols) via controlled variation of a parameter of the system Hamiltonian. We provide exact numerical computation, for finite-size boson chains with L ≤24 using exact diagonalization (ED), of the excitation density D , the wave function overlap F , and the excess energy Q at the end of the drive protocol. For the linear ramp protocol, we identify the range of ramp speeds for which D and Q show Kibble-Zurek scaling. We find, based on numerical analysis with L ≤24 , that such scaling is consistent with that expected from critical exponents of the q -state Potts universality class with q =3 ,4 . For the periodic protocol, we show that the model displays near-perfect dynamical freezing at specific frequencies; at these frequencies D ,Q →0 and |F |→1 . We provide a semi-analytic explanation of such freezing behavior and relate this phenomenon to a many-body version of Stuckelberg interference. We suggest experiments which can test our theory.

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.

Abelian and non-Abelian states in ν = 2 / 3 bilayer fractional quantum Hall systems

NASA Astrophysics Data System (ADS)

Peterson, Michael; Wu, Yang-Le; Cheng, Meng; Barkeshli, Maissam; Wang, Zhenghan

There are several possible theoretically allowed non-Abelian fractional quantum Hall (FQH) states that could potentially be realized in one- and two-component FQH systems at total filling fraction ν = n + 2 / 3 , for integer n. Some of these states even possess quasiparticles with non-Abelian statistics that are powerful enough for universal topological quantum computation, and are thus of particular interest. Here we initiate a systematic numerical study, using both exact diagonalization and variational Monte Carlo, to investigate the phase diagram of FQH systems at total filling fraction ν = n + 2 / 3 , including in particular the possibility of the non-Abelian Z4 parafermion state. In ν = 2 / 3 bilayers we determine the phase diagram as a function of interlayer tunneling and repulsion, finding only three competing Abelian states, without the Z4 state. On the other hand, in single-component systems at ν = 8 / 3 , we find that the Z4 parafermion state has significantly higher overlap with the exact ground state than the Laughlin state, together with a larger gap, suggesting that the experimentally observed ν = 8 / 3 state may be non-Abelian. Our results from the two complementary numerical techniques agree well with each other qualitatively. We acknowledge the Office of Research and Sponsored Programs at California State University Long Beach and Microsoft Station Q.

Direct reconstruction of cardiac PET kinetic parametric images using a preconditioned conjugate gradient approach

PubMed Central

Rakvongthai, Yothin; Ouyang, Jinsong; Guerin, Bastien; Li, Quanzheng; Alpert, Nathaniel M.; El Fakhri, Georges

2013-01-01

Purpose: Our research goal is to develop an algorithm to reconstruct cardiac positron emission tomography (PET) kinetic parametric images directly from sinograms and compare its performance with the conventional indirect approach. Methods: Time activity curves of a NCAT phantom were computed according to a one-tissue compartmental kinetic model with realistic kinetic parameters. The sinograms at each time frame were simulated using the activity distribution for the time frame. The authors reconstructed the parametric images directly from the sinograms by optimizing a cost function, which included the Poisson log-likelihood and a spatial regularization terms, using the preconditioned conjugate gradient (PCG) algorithm with the proposed preconditioner. The proposed preconditioner is a diagonal matrix whose diagonal entries are the ratio of the parameter and the sensitivity of the radioactivity associated with parameter. The authors compared the reconstructed parametric images using the direct approach with those reconstructed using the conventional indirect approach. Results: At the same bias, the direct approach yielded significant relative reduction in standard deviation by 12%–29% and 32%–70% for 50 × 106 and 10 × 106 detected coincidences counts, respectively. Also, the PCG method effectively reached a constant value after only 10 iterations (with numerical convergence achieved after 40–50 iterations), while more than 500 iterations were needed for CG. Conclusions: The authors have developed a novel approach based on the PCG algorithm to directly reconstruct cardiac PET parametric images from sinograms, and yield better estimation of kinetic parameters than the conventional indirect approach, i.e., curve fitting of reconstructed images. The PCG method increases the convergence rate of reconstruction significantly as compared to the conventional CG method. PMID:24089922

Direct reconstruction of cardiac PET kinetic parametric images using a preconditioned conjugate gradient approach.

PubMed

Rakvongthai, Yothin; Ouyang, Jinsong; Guerin, Bastien; Li, Quanzheng; Alpert, Nathaniel M; El Fakhri, Georges

2013-10-01

Our research goal is to develop an algorithm to reconstruct cardiac positron emission tomography (PET) kinetic parametric images directly from sinograms and compare its performance with the conventional indirect approach. Time activity curves of a NCAT phantom were computed according to a one-tissue compartmental kinetic model with realistic kinetic parameters. The sinograms at each time frame were simulated using the activity distribution for the time frame. The authors reconstructed the parametric images directly from the sinograms by optimizing a cost function, which included the Poisson log-likelihood and a spatial regularization terms, using the preconditioned conjugate gradient (PCG) algorithm with the proposed preconditioner. The proposed preconditioner is a diagonal matrix whose diagonal entries are the ratio of the parameter and the sensitivity of the radioactivity associated with parameter. The authors compared the reconstructed parametric images using the direct approach with those reconstructed using the conventional indirect approach. At the same bias, the direct approach yielded significant relative reduction in standard deviation by 12%-29% and 32%-70% for 50 × 10(6) and 10 × 10(6) detected coincidences counts, respectively. Also, the PCG method effectively reached a constant value after only 10 iterations (with numerical convergence achieved after 40-50 iterations), while more than 500 iterations were needed for CG. The authors have developed a novel approach based on the PCG algorithm to directly reconstruct cardiac PET parametric images from sinograms, and yield better estimation of kinetic parameters than the conventional indirect approach, i.e., curve fitting of reconstructed images. The PCG method increases the convergence rate of reconstruction significantly as compared to the conventional CG method.

Exact Exchange calculations for periodic systems: a real space approach

NASA Astrophysics Data System (ADS)

Natan, Amir; Marom, Noa; Makmal, Adi; Kronik, Leeor; Kuemmel, Stephan

2011-03-01

We present a real-space method for exact-exchange Kohn-Sham calculations of periodic systems. The method is based on self-consistent solutions of the optimized effective potential (OEP) equation on a three-dimensional non-orthogonal grid, using norm conserving pseudopotentials. These solutions can be either exact, using the S-iteration approach, or approximate, using the Krieger, Li, and Iafrate (KLI) approach. We demonstrate, using a variety of systems, the importance of singularity corrections and use of appropriate pseudopotentials.

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

Miller, William H., E-mail: millerwh@berkeley.edu; Cotton, Stephen J., E-mail: StephenJCotton47@gmail.com

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

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

Miller, William H.; Cotton, Stephen J.

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

The Hartree product and the description of local and global quantities in atomic systems: A study within Kohn-Sham theory

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

Garza, Jorge; Nichols, Jeffrey A.; Dixon, David A.

2000-01-15

The Hartree product is analyzed in the context of Kohn-Sham theory. The differential equations that emerge from this theory are solved with the optimized effective potential using the Krieger, Li, and Iafrate approximation, in order to get a local potential as required by the ordinary Kohn-Sham procedure. Because the diagonal terms of the exact exchange energy are included in Hartree theory, it is self-interaction free and the exchange potential has the proper asymptotic behavior. We have examined the impact of this correct asymptotic behavior on local and global properties using this simple model to approximate the exchange energy. Local quantities,more » such as the exchange potential and the average local electrostatic potential are used to examine whether the shell structure in an atom is revealed by this theory. Global quantities, such as the highest occupied orbital energy (related to the ionization potential) and the exchange energy are also calculated. These quantities are contrasted with those obtained from calculations with the local density approximation, the generalized gradient approximation, and the self-interaction correction approach proposed by Perdew and Zunger. We conclude that the main characteristics in an atomic system are preserved with the Hartree theory. In particular, the behavior of the exchange potential obtained in this theory is similar to those obtained within other Kohn-Sham approximations. (c) 2000 American Institute of Physics.« less

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

DOE PAGES

Miller, William H.; Cotton, Stephen J.

2016-08-28

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

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

PubMed

Miller, William H; Cotton, Stephen J

2016-08-28

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

186 K Operation of Terahertz Quantum-Cascade Lasers Based on a Diagonal Design

NASA Technical Reports Server (NTRS)

Kumar, Sushil; Hu, Qing; Reno, John L.

2009-01-01

Resonant-phonon terahertz quantum-cascade lasers operating up to a heat-sink temperature of 186 K are demonstrated. This record temperature performance is achieved based on a diagonal design, with the objective to increase the upper-state lifetime and therefore the gain at elevated temperatures. The increased diagonality also lowers the operating current densities by limiting the flow of parasitic leakage current. Quantitatively, the diagonality is characterized by a radiative oscillator strength that is smaller by a factor of two from the least of any previously published designs. At the lasing frequency of 3.9 THz, 63 mW of peak optical power was measured at 5 K, and approximately 5 mW could still be detected at 180 K.

Robust determination of the chemical potential in the pole expansion and selected inversion method for solving Kohn-Sham density functional theory

NASA Astrophysics Data System (ADS)

Jia, Weile; Lin, Lin

2017-10-01

Fermi operator expansion (FOE) methods are powerful alternatives to diagonalization type methods for solving Kohn-Sham density functional theory (KSDFT). One example is the pole expansion and selected inversion (PEXSI) method, which approximates the Fermi operator by rational matrix functions and reduces the computational complexity to at most quadratic scaling for solving KSDFT. Unlike diagonalization type methods, the chemical potential often cannot be directly read off from the result of a single step of evaluation of the Fermi operator. Hence multiple evaluations are needed to be sequentially performed to compute the chemical potential to ensure the correct number of electrons within a given tolerance. This hinders the performance of FOE methods in practice. In this paper, we develop an efficient and robust strategy to determine the chemical potential in the context of the PEXSI method. The main idea of the new method is not to find the exact chemical potential at each self-consistent-field (SCF) iteration but to dynamically and rigorously update the upper and lower bounds for the true chemical potential, so that the chemical potential reaches its convergence along the SCF iteration. Instead of evaluating the Fermi operator for multiple times sequentially, our method uses a two-level strategy that evaluates the Fermi operators in parallel. In the regime of full parallelization, the wall clock time of each SCF iteration is always close to the time for one single evaluation of the Fermi operator, even when the initial guess is far away from the converged solution. We demonstrate the effectiveness of the new method using examples with metallic and insulating characters, as well as results from ab initio molecular dynamics.

FOB-SH: Fragment orbital-based surface hopping for charge carrier transport in organic and biological molecules and materials

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

Spencer, J.; Gajdos, F.; Blumberger, J., E-mail: j.blumberger@ucl.ac.uk

2016-08-14

We introduce a fragment orbital-based fewest switches surface hopping method, FOB-SH, designed to efficiently simulate charge carrier transport in strongly fluctuating condensed phase systems such as organic semiconductors and biomolecules. The charge carrier wavefunction is expanded and the electronic Hamiltonian constructed in a set of singly occupied molecular orbitals of the molecular sites that mediate the charge transfer. Diagonal elements of the electronic Hamiltonian (site energies) are obtained from a force field, whereas the off-diagonal or electronic coupling matrix elements are obtained using our recently developed analytic overlap method. We derive a general expression for the exact forces on themore » adiabatic ground and excited electronic state surfaces from the nuclear gradients of the charge localized electronic states. Applications to electron hole transfer in a model ethylene dimer and through a chain of ten model ethylenes validate our implementation and demonstrate its computational efficiency. On the larger system, we calculate the qualitative behaviour of charge mobility with change in temperature T for different regimes of the intermolecular electronic coupling. For small couplings, FOB-SH predicts a crossover from a thermally activated regime at low temperatures to a band-like transport regime at higher temperatures. For higher electronic couplings, the thermally activated regime disappears and the mobility decreases according to a power law. This is interpreted by a gradual loss in probability for resonance between the sites as the temperature increases. The polaron hopping model solved for the same system gives a qualitatively different result and underestimates the mobility decay at higher temperatures. Taken together, the FOB-SH methodology introduced here shows promise for a realistic investigation of charge carrier transport in complex organic, aqueous, and biological systems.« less

Robust determination of the chemical potential in the pole expansion and selected inversion method for solving Kohn-Sham density functional theory.

PubMed

Jia, Weile; Lin, Lin

2017-10-14

Fermi operator expansion (FOE) methods are powerful alternatives to diagonalization type methods for solving Kohn-Sham density functional theory (KSDFT). One example is the pole expansion and selected inversion (PEXSI) method, which approximates the Fermi operator by rational matrix functions and reduces the computational complexity to at most quadratic scaling for solving KSDFT. Unlike diagonalization type methods, the chemical potential often cannot be directly read off from the result of a single step of evaluation of the Fermi operator. Hence multiple evaluations are needed to be sequentially performed to compute the chemical potential to ensure the correct number of electrons within a given tolerance. This hinders the performance of FOE methods in practice. In this paper, we develop an efficient and robust strategy to determine the chemical potential in the context of the PEXSI method. The main idea of the new method is not to find the exact chemical potential at each self-consistent-field (SCF) iteration but to dynamically and rigorously update the upper and lower bounds for the true chemical potential, so that the chemical potential reaches its convergence along the SCF iteration. Instead of evaluating the Fermi operator for multiple times sequentially, our method uses a two-level strategy that evaluates the Fermi operators in parallel. In the regime of full parallelization, the wall clock time of each SCF iteration is always close to the time for one single evaluation of the Fermi operator, even when the initial guess is far away from the converged solution. We demonstrate the effectiveness of the new method using examples with metallic and insulating characters, as well as results from ab initio molecular dynamics.

Effective model with strong Kitaev interactions for α -RuCl3

NASA Astrophysics Data System (ADS)

Suzuki, Takafumi; Suga, Sei-ichiro

2018-04-01

We use an exact numerical diagonalization method to calculate the dynamical spin structure factors of three ab initio models and one ab initio guided model for a honeycomb-lattice magnet α -RuCl3 . We also use thermal pure quantum states to calculate the temperature dependence of the heat capacity, the nearest-neighbor spin-spin correlation function, and the static spin structure factor. From the results obtained from these four effective models, we find that, even when the magnetic order is stabilized at low temperature, the intensity at the Γ point in the dynamical spin structure factors increases with increasing nearest-neighbor spin correlation. In addition, we find that the four models fail to explain heat-capacity measurements whereas two of the four models succeed in explaining inelastic-neutron-scattering experiments. In the four models, when temperature decreases, the heat capacity shows a prominent peak at a high temperature where the nearest-neighbor spin-spin correlation function increases. However, the peak temperature in heat capacity is too low in comparison with that observed experimentally. To address these discrepancies, we propose an effective model that includes strong ferromagnetic Kitaev coupling, and we show that this model quantitatively reproduces both inelastic-neutron-scattering experiments and heat-capacity measurements. To further examine the adequacy of the proposed model, we calculate the field dependence of the polarized terahertz spectra, which reproduces the experimental results: the spin-gapped excitation survives up to an onset field where the magnetic order disappears and the response in the high-field region is almost linear. Based on these numerical results, we argue that the low-energy magnetic excitation in α -RuCl3 is mainly characterized by interactions such as off-diagonal interactions and weak Heisenberg interactions between nearest-neighbor pairs, rather than by the strong Kitaev interactions.

FOB-SH: Fragment orbital-based surface hopping for charge carrier transport in organic and biological molecules and materials

NASA Astrophysics Data System (ADS)

Spencer, J.; Gajdos, F.; Blumberger, J.

2016-08-01

We introduce a fragment orbital-based fewest switches surface hopping method, FOB-SH, designed to efficiently simulate charge carrier transport in strongly fluctuating condensed phase systems such as organic semiconductors and biomolecules. The charge carrier wavefunction is expanded and the electronic Hamiltonian constructed in a set of singly occupied molecular orbitals of the molecular sites that mediate the charge transfer. Diagonal elements of the electronic Hamiltonian (site energies) are obtained from a force field, whereas the off-diagonal or electronic coupling matrix elements are obtained using our recently developed analytic overlap method. We derive a general expression for the exact forces on the adiabatic ground and excited electronic state surfaces from the nuclear gradients of the charge localized electronic states. Applications to electron hole transfer in a model ethylene dimer and through a chain of ten model ethylenes validate our implementation and demonstrate its computational efficiency. On the larger system, we calculate the qualitative behaviour of charge mobility with change in temperature T for different regimes of the intermolecular electronic coupling. For small couplings, FOB-SH predicts a crossover from a thermally activated regime at low temperatures to a band-like transport regime at higher temperatures. For higher electronic couplings, the thermally activated regime disappears and the mobility decreases according to a power law. This is interpreted by a gradual loss in probability for resonance between the sites as the temperature increases. The polaron hopping model solved for the same system gives a qualitatively different result and underestimates the mobility decay at higher temperatures. Taken together, the FOB-SH methodology introduced here shows promise for a realistic investigation of charge carrier transport in complex organic, aqueous, and biological systems.

Kids in Communities Study (KiCS) study protocol: a cross-sectional mixed-methods approach to measuring community-level factors influencing early child development in Australia.

PubMed

Goldfeld, Sharon; Villanueva, Karen; Tanton, Robert; Katz, Ilan; Brinkman, Sally; Woolcock, Geoffrey; Giles-Corti, Billie

2017-03-13

Healthy childhood development in the early years is critical for later adult health and well-being. Early childhood development (ECD) research has focused primarily on individual, family and school factors, but largely ignored community factors. The Kids in Communities Study (KiCS) will test and investigate community-level influences on child development across Australia. Cross-sectional mixed-methods study exploring community-level effects in 25 Australian local communities; selection based on community socioeconomic status (SES) and ECD using the Australian Early Development Census (AEDC), a population measure of child development, to create a local community 'diagonality type', that is, those performing better or worse (off-diagonal), or as expected (on-diagonal) on the AEDC relative to their SES. Data collection includes stakeholder interviews, parent and service provider focus groups, and surveys with general community residents and service providers, mapping of neighbourhood design and local amenities and services, analysis of policy documents, and the use of existing sociodemographic and early childhood education and care data. Quantitative data will be used to test associations between local community diagonality type, and ECD based on AEDC scores. Qualitative data will provide complementary and deeper exploration of these same associations. The Royal Children's Hospital Human Research Ethics Committee approved the study protocol (#30016). Further ethics approvals were obtained from State Education and Health departments and Catholic archdioceses where required. ECD community-level indicators will eventually be derived and made publically available. Findings will be published in peer-reviewed journals, community reports, websites and policy briefs to disseminate results to researchers, and key stakeholders including policymakers, practitioners and (most importantly) the communities involved. Published by the BMJ Publishing Group Limited. For permission to use (where not already granted under a licence) please go to http://www.bmj.com/company/products-services/rights-and-licensing/.

A decoupled approach to filter design for stochastic systems

NASA Astrophysics Data System (ADS)

Barbata, A.; Zasadzinski, M.; Ali, H. Souley; Messaoud, H.

2016-08-01

This paper presents a new theorem to guarantee the almost sure exponential stability for a class of stochastic triangular systems by studying only the stability of each diagonal subsystems. This result allows to solve the filtering problem of the stochastic systems with multiplicative noises by using the almost sure exponential stability concept. Two kinds of observers are treated: the full-order and reduced-order cases.

LSMS

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

Eisenbach, Markus; Li, Ying Wai; Liu, Xianglin

2017-12-01

LSMS is a first principles, Density Functional theory based, electronic structure code targeted mainly at materials applications. LSMS calculates the local spin density approximation to the diagonal part of the electron Green's function. The electron/spin density and energy are easily determined once the Green's function is known. Linear scaling with system size is achieved in the LSMS by using several unique properties of the real space multiple scattering approach to the Green's function.

The accurate solution of Poisson's equation by expansion in Chebyshev polynomials

NASA Technical Reports Server (NTRS)

Haidvogel, D. B.; Zang, T.

1979-01-01

A Chebyshev expansion technique is applied to Poisson's equation on a square with homogeneous Dirichlet boundary conditions. The spectral equations are solved in two ways - by alternating direction and by matrix diagonalization methods. Solutions are sought to both oscillatory and mildly singular problems. The accuracy and efficiency of the Chebyshev approach compare favorably with those of standard second- and fourth-order finite-difference methods.

Exact Mapping from Many-Spin Hamiltonians to Giant-Spin Hamiltonians.

PubMed

Ghassemi Tabrizi, Shadan; Arbuznikov, Alexei V; Kaupp, Martin

2018-03-26

Thermodynamic and spectroscopic data of exchange-coupled molecular spin clusters (e.g. single-molecule magnets) are routinely interpreted in terms of two different models: the many-spin Hamiltonian (MSH) explicitly considers couplings between individual spin centers, while the giant-spin Hamiltonian (GSH) treats the system as a single collective spin. When isotropic exchange coupling is weak, the physical compatibility between both spin Hamiltonian models becomes a serious concern, due to mixing of spin multiplets by local zero-field splitting (ZFS) interactions ('S-mixing'). Until now, this effect, which makes the mapping MSH→GSH ('spin projection') non-trivial, had only been treated perturbationally (up to third order), with obvious limitations. Here, based on exact diagonalization of the MSH, canonical effective Hamiltonian theory is applied to construct a GSH that exactly matches the energies of the relevant (2S+1) states comprising an effective spin multiplet. For comparison, a recently developed strategy for the unique derivation of effective ('pseudospin') Hamiltonians, now routinely employed in ab initio calculations of mononuclear systems, is adapted to the problem of spin projection. Expansion of the zero-field Hamiltonian and the magnetic moment in terms of irreducible tensor operators (or Stevens operators) yields terms of all ranks k (up to k=2S) in the effective spin. Calculations employing published MSH parameters illustrate exact spin projection for the well-investigated [Ni(hmp)(dmb)Cl] 4 ('Ni 4 ') single-molecule magnet, which displays weak isotropic exchange (dmb=3,3-dimethyl-1-butanol, hmp - is the anion of 2-hydroxymethylpyridine). The performance of the resulting GSH in finite field is assessed in terms of EPR resonances and diabolical points. The large tunnel splitting in the M=± 4 ground doublet of the S=4 multiplet, responsible for fast tunneling in Ni 4 , is attributed to a Stevens operator with eightfold rotational symmetry, marking the first quantification of a k=8 term in a spin cluster. The unique and exact mapping MSH→GSH should be of general importance for weakly-coupled systems; it represents a mandatory ultimate step for comparing theoretical predictions (e.g. from quantum-chemical calculations) to ZFS, hyperfine or g-tensors from spectral fittings. © 2018 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.

Robotic Compliant Motion Control for Aircraft Refueling Applications

DTIC Science & Technology

1988-12-01

J. DUVALL 29 SEP 88 C-26 SUBROUTINE IMPCONST(CONST,MINV, BMAT ) Abstract: This subroutine calculates the 25 constants used by the Fortran subroutine...mass with center of gravity along the joint 6 axis. The desired mass and the damping ( BMAT ) matrices are assumed to be diagonal. Joints angles 4,5...constants. MINV -- A 2x2 matrix containing the elements of the inverse desired mass matrix (diagonal). BMAT -- A 2x2 matrix of damping coefficents (diagonal

Implementation of a finite-amplitude method in a relativistic meson-exchange model

NASA Astrophysics Data System (ADS)

Sun, Xuwei; Lu, Dinghui

2017-08-01

The finite-amplitude method is a feasible numerical approach to large scale random phase approximation calculations. It avoids the storage and calculation of residual interaction elements as well as the diagonalization of the RPA matrix, which will be prohibitive when the configuration space is huge. In this work we finished the implementation of a finite-amplitude method in a relativistic meson exchange mean field model with axial symmetry. The direct variation approach makes our FAM scheme capable of being extended to the multipole excitation case.

High-performance implementation of Chebyshev filter diagonalization for interior eigenvalue computations

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

Pieper, Andreas; Kreutzer, Moritz; Alvermann, Andreas, E-mail: alvermann@physik.uni-greifswald.de

2016-11-15

We study Chebyshev filter diagonalization as a tool for the computation of many interior eigenvalues of very large sparse symmetric matrices. In this technique the subspace projection onto the target space of wanted eigenvectors is approximated with filter polynomials obtained from Chebyshev expansions of window functions. After the discussion of the conceptual foundations of Chebyshev filter diagonalization we analyze the impact of the choice of the damping kernel, search space size, and filter polynomial degree on the computational accuracy and effort, before we describe the necessary steps towards a parallel high-performance implementation. Because Chebyshev filter diagonalization avoids the need formore » matrix inversion it can deal with matrices and problem sizes that are presently not accessible with rational function methods based on direct or iterative linear solvers. To demonstrate the potential of Chebyshev filter diagonalization for large-scale problems of this kind we include as an example the computation of the 10{sup 2} innermost eigenpairs of a topological insulator matrix with dimension 10{sup 9} derived from quantum physics applications.« less

Improving stochastic estimates with inference methods: calculating matrix diagonals.

PubMed

Selig, Marco; Oppermann, Niels; Ensslin, Torsten A

2012-02-01

Estimating the diagonal entries of a matrix, that is not directly accessible but only available as a linear operator in the form of a computer routine, is a common necessity in many computational applications, especially in image reconstruction and statistical inference. Here, methods of statistical inference are used to improve the accuracy or the computational costs of matrix probing methods to estimate matrix diagonals. In particular, the generalized Wiener filter methodology, as developed within information field theory, is shown to significantly improve estimates based on only a few sampling probes, in cases in which some form of continuity of the solution can be assumed. The strength, length scale, and precise functional form of the exploited autocorrelation function of the matrix diagonal is determined from the probes themselves. The developed algorithm is successfully applied to mock and real world problems. These performance tests show that, in situations where a matrix diagonal has to be calculated from only a small number of computationally expensive probes, a speedup by a factor of 2 to 10 is possible with the proposed method. © 2012 American Physical Society

23. INCLINED END POST / VERTICAL / DIAGONAL / PORTAL ...

Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

23. INCLINED END POST / VERTICAL / DIAGONAL / PORTAL BRACING DETAIL. VIEW TO SOUTHEAST. - Abraham Lincoln Memorial Bridge, Spanning Missouri River on Highway 30 between Nebraska & Iowa, Blair, Washington County, NE

Entropy of isolated quantum systems after a quench.

PubMed

Santos, Lea F; Polkovnikov, Anatoli; Rigol, Marcos

2011-07-22

A diagonal entropy, which depends only on the diagonal elements of the system's density matrix in the energy representation, has been recently introduced as the proper definition of thermodynamic entropy in out-of-equilibrium quantum systems. We study this quantity after an interaction quench in lattice hard-core bosons and spinless fermions, and after a local chemical potential quench in a system of hard-core bosons in a superlattice potential. The former systems have a chaotic regime, where the diagonal entropy becomes equivalent to the equilibrium microcanonical entropy, coinciding with the onset of thermalization. The latter system is integrable. We show that its diagonal entropy is additive and different from the entropy of a generalized Gibbs ensemble, which has been introduced to account for the effects of conserved quantities at integrability.

Confidence bounds for normal and lognormal distribution coefficients of variation

Treesearch

Steve Verrill

2003-01-01

This paper compares the so-called exact approach for obtaining confidence intervals on normal distribution coefficients of variation to approximate methods. Approximate approaches were found to perform less well than the exact approach for large coefficients of variation and small sample sizes. Web-based computer programs are described for calculating confidence...

Error due to unresolved scales in estimation problems for atmospheric data assimilation

NASA Astrophysics Data System (ADS)

Janjic, Tijana

The error arising due to unresolved scales in data assimilation procedures is examined. The problem of estimating the projection of the state of a passive scalar undergoing advection at a sequence of times is considered. The projection belongs to a finite- dimensional function space and is defined on the continuum. Using the continuum projection of the state of a passive scalar, a mathematical definition is obtained for the error arising due to the presence, in the continuum system, of scales unresolved by the discrete dynamical model. This error affects the estimation procedure through point observations that include the unresolved scales. In this work, two approximate methods for taking into account the error due to unresolved scales and the resulting correlations are developed and employed in the estimation procedure. The resulting formulas resemble the Schmidt-Kalman filter and the usual discrete Kalman filter, respectively. For this reason, the newly developed filters are called the Schmidt-Kalman filter and the traditional filter. In order to test the assimilation methods, a two- dimensional advection model with nonstationary spectrum was developed for passive scalar transport in the atmosphere. An analytical solution on the sphere was found depicting the model dynamics evolution. Using this analytical solution the model error is avoided, and the error due to unresolved scales is the only error left in the estimation problem. It is demonstrated that the traditional and the Schmidt- Kalman filter work well provided the exact covariance function of the unresolved scales is known. However, this requirement is not satisfied in practice, and the covariance function must be modeled. The Schmidt-Kalman filter cannot be computed in practice without further approximations. Therefore, the traditional filter is better suited for practical use. Also, the traditional filter does not require modeling of the full covariance function of the unresolved scales, but only modeling of the covariance matrix obtained by evaluating the covariance function at the observation points. We first assumed that this covariance matrix is stationary and that the unresolved scales are not correlated between the observation points, i.e., the matrix is diagonal, and that the values along the diagonal are constant. Tests with these assumptions were unsuccessful, indicating that a more sophisticated model of the covariance is needed for assimilation of data with nonstationary spectrum. A new method for modeling the covariance matrix based on an extended set of modeling assumptions is proposed. First, it is assumed that the covariance matrix is diagonal, that is, that the unresolved scales are not correlated between the observation points. It is postulated that the values on the diagonal depend on a wavenumber that is characteristic for the unresolved part of the spectrum. It is further postulated that this characteristic wavenumber can be diagnosed from the observations and from the estimate of the projection of the state that is being estimated. It is demonstrated that the new method successfully overcomes previously encountered difficulties.

Quantum transport and the Wigner distribution function for Bloch electrons in spatially homogeneous electric and magnetic fields

NASA Astrophysics Data System (ADS)

Iafrate, G. J.; Sokolov, V. N.; Krieger, J. B.

2017-10-01

The theory of Bloch electron dynamics for carriers in homogeneous electric and magnetic fields of arbitrary time dependence is developed in the framework of the Liouville equation. The Wigner distribution function (WDF) is determined from the single-particle density matrix in the ballistic regime, i.e., collision effects are excluded. In the theory, the single-particle transport equation is established with the electric field described in the vector potential gauge, and the magnetic field is treated in the symmetric gauge. No specific assumptions are made concerning the form of the initial distribution in momentum or configuration space. The general approach is to employ the accelerated Bloch state representation (ABR) as a basis so that the dependence upon the electric field, including multiband Zener tunneling, is treated exactly. Further, in the formulation of the WDF, we transform to a new set of variables so that the final WDF is gauge invariant and is expressed explicitly in terms of the position, kinetic momentum, and time. The methodology for developing the WDF is illustrated by deriving the exact WDF equation for free electrons in homogeneous electric and magnetic fields resulting in the same form as given by the collisionless Boltzmann transport equation (BTE). The methodology is then extended to the case of electrons described by an effective Hamiltonian corresponding to an arbitrary energy band function; the exact WDF equation results for the effective Hamiltonian case are shown to approximate the free electron results when taken to second order in the magnetic field. As a corollary, in these cases, it is shown that if the WDF is a wave packet, then the time rate of change of the electron quasimomentum is given by the Lorentz force. In treating the problem of Bloch electrons in a periodic potential in the presence of homogeneous electric and magnetic fields, the methodology for deriving the WDF reveals a multiband character due to the inherent nature of the Bloch states. The K0 representation of the Bloch envelope functions is employed to express the multiband WDF in a useful form. In examining the single-band WDF, it is found that the collisionless WDF equation matches the equivalent BTE to first order in the magnetic field. These results are necessarily extended to second order in the magnetic field by employing a unitary transformation that diagonalizes the Hamiltonian using the ABR to second order. The unitary transformation process includes a discussion of the multiband WDF transport analysis and the identification of the combined Zener-magnetic-field induced tunneling.

Nonequilibrium thermo-chemical calculations using a diagonal implicit scheme

NASA Technical Reports Server (NTRS)

Imlay, Scott T.; Roberts, Donald W.; Soetrisno, Moeljo; Eberhardt, Scott

1991-01-01

A recently developed computer program for hypersonic vehicle flow analysis is described. The program uses a diagonal implicit algorithm to solve the equations of viscous flow for a gas in thermochemical nonequilibrium. The diagonal scheme eliminates the expense of inverting large block matrices that arise when species conservation equations are introduced. The program uses multiple zones of grids patched together and includes radiation wall and rarefied gas boundary conditions. Solutions are presented for hypersonic flows of air and hydrogen air mixtures.

Fluctuating hydrodynamics, current fluctuations, and hyperuniformity in boundary-driven open quantum chains

NASA Astrophysics Data System (ADS)

Carollo, Federico; Garrahan, Juan P.; Lesanovsky, Igor; Pérez-Espigares, Carlos

2017-11-01

We consider a class of either fermionic or bosonic noninteracting open quantum chains driven by dissipative interactions at the boundaries and study the interplay of coherent transport and dissipative processes, such as bulk dephasing and diffusion. Starting from the microscopic formulation, we show that the dynamics on large scales can be described in terms of fluctuating hydrodynamics. This is an important simplification as it allows us to apply the methods of macroscopic fluctuation theory to compute the large deviation (LD) statistics of time-integrated currents. In particular, this permits us to show that fermionic open chains display a third-order dynamical phase transition in LD functions. We show that this transition is manifested in a singular change in the structure of trajectories: while typical trajectories are diffusive, rare trajectories associated with atypical currents are ballistic and hyperuniform in their spatial structure. We confirm these results by numerically simulating ensembles of rare trajectories via the cloning method, and by exact numerical diagonalization of the microscopic quantum generator.

Fluctuating hydrodynamics, current fluctuations, and hyperuniformity in boundary-driven open quantum chains.

PubMed

Carollo, Federico; Garrahan, Juan P; Lesanovsky, Igor; Pérez-Espigares, Carlos

2017-11-01

We consider a class of either fermionic or bosonic noninteracting open quantum chains driven by dissipative interactions at the boundaries and study the interplay of coherent transport and dissipative processes, such as bulk dephasing and diffusion. Starting from the microscopic formulation, we show that the dynamics on large scales can be described in terms of fluctuating hydrodynamics. This is an important simplification as it allows us to apply the methods of macroscopic fluctuation theory to compute the large deviation (LD) statistics of time-integrated currents. In particular, this permits us to show that fermionic open chains display a third-order dynamical phase transition in LD functions. We show that this transition is manifested in a singular change in the structure of trajectories: while typical trajectories are diffusive, rare trajectories associated with atypical currents are ballistic and hyperuniform in their spatial structure. We confirm these results by numerically simulating ensembles of rare trajectories via the cloning method, and by exact numerical diagonalization of the microscopic quantum generator.

Accuracy of the microcanonical Lanczos method to compute real-frequency dynamical spectral functions of quantum models at finite temperatures

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

Okamoto, Satoshi; Alvarez, Gonzalo; Dagotto, Elbio

We examine the accuracy of the microcanonical Lanczos method (MCLM) developed by Long et al. [Phys. Rev. B 68, 235106 (2003)] to compute dynamical spectral functions of interacting quantum models at finite temperatures. The MCLM is based on the microcanonical ensemble, which becomes exact in the thermodynamic limit. To apply the microcanonical ensemble at a fixed temperature, one has to find energy eigenstates with the energy eigenvalue corresponding to the internal energy in the canonical ensemble. Here in this paper, we propose to use thermal pure quantum state methods by Sugiura and Shimizu [Phys. Rev. Lett. 111, 010401 (2013)] tomore » obtain the internal energy. After obtaining the energy eigenstates using the Lanczos diagonalization method, dynamical quantities are computed via a continued fraction expansion, a standard procedure for Lanczos-based numerical methods. Using one-dimensional antiferromagnetic Heisenberg chains with S = 1/2, we demonstrate that the proposed procedure is reasonably accurate, even for relatively small systems.« less

Characterizing the three-orbital Hubbard model with determinant quantum Monte Carlo

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

Kung, Y. F.; Chen, C. -C.; Wang, Yao

Here, we characterize the three-orbital Hubbard model using state-of-the-art determinant quantum Monte Carlo (DQMC) simulations with parameters relevant to the cuprate high-temperature superconductors. The simulations find that doped holes preferentially reside on oxygen orbitals and that the (π,π) antiferromagnetic ordering vector dominates in the vicinity of the undoped system, as known from experiments. The orbitally-resolved spectral functions agree well with photoemission spectroscopy studies and enable identification of orbital content in the bands. A comparison of DQMC results with exact diagonalization and cluster perturbation theory studies elucidates how these different numerical techniques complement one another to produce a more complete understandingmore » of the model and the cuprates. Interestingly, our DQMC simulations predict a charge-transfer gap that is significantly smaller than the direct (optical) gap measured in experiment. Most likely, it corresponds to the indirect gap that has recently been suggested to be on the order of 0.8 eV, and demonstrates the subtlety in identifying charge gaps.« less

Characterizing the three-orbital Hubbard model with determinant quantum Monte Carlo

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

Kung, Y. F.; Chen, C. -C.; Wang, Yao

We characterize the three-orbital Hubbard model using state-of-the-art determinant quantum Monte Carlo (DQMC) simulations with parameters relevant to the cuprate high-temperature superconductors. The simulations find that doped holes preferentially reside on oxygen orbitals and that the (π,π) antiferromagnetic ordering vector dominates in the vicinity of the undoped system, as known from experiments. The orbitally-resolved spectral functions agree well with photoemission spectroscopy studies and enable identification of orbital content in the bands. A comparison of DQMC results with exact diagonalization and cluster perturbation theory studies elucidates how these different numerical techniques complement one another to produce a more complete understanding ofmore » the model and the cuprates. Interestingly, our DQMC simulations predict a charge-transfer gap that is significantly smaller than the direct (optical) gap measured in experiment. Most likely, it corresponds to the indirect gap that has recently been suggested to be on the order of 0.8 eV, and demonstrates the subtlety in identifying charge gaps.« less

Accuracy of the microcanonical Lanczos method to compute real-frequency dynamical spectral functions of quantum models at finite temperatures

DOE PAGES

Okamoto, Satoshi; Alvarez, Gonzalo; Dagotto, Elbio; ...

2018-04-20

We examine the accuracy of the microcanonical Lanczos method (MCLM) developed by Long et al. [Phys. Rev. B 68, 235106 (2003)] to compute dynamical spectral functions of interacting quantum models at finite temperatures. The MCLM is based on the microcanonical ensemble, which becomes exact in the thermodynamic limit. To apply the microcanonical ensemble at a fixed temperature, one has to find energy eigenstates with the energy eigenvalue corresponding to the internal energy in the canonical ensemble. Here in this paper, we propose to use thermal pure quantum state methods by Sugiura and Shimizu [Phys. Rev. Lett. 111, 010401 (2013)] tomore » obtain the internal energy. After obtaining the energy eigenstates using the Lanczos diagonalization method, dynamical quantities are computed via a continued fraction expansion, a standard procedure for Lanczos-based numerical methods. Using one-dimensional antiferromagnetic Heisenberg chains with S = 1/2, we demonstrate that the proposed procedure is reasonably accurate, even for relatively small systems.« 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.

Emergent Chiral Spin State in the Mott Phase of a Bosonic Kane-Mele-Hubbard Model

NASA Astrophysics Data System (ADS)

Plekhanov, Kirill; Vasić, Ivana; Petrescu, Alexandru; Nirwan, Rajbir; Roux, Guillaume; Hofstetter, Walter; Le Hur, Karyn

2018-04-01

Recently, the frustrated X Y model for spins 1 /2 on the honeycomb lattice has attracted a lot of attention in relation with the possibility to realize a chiral spin liquid state. This model is relevant to the physics of some quantum magnets. Using the flexibility of ultracold atom setups, we propose an alternative way to realize this model through the Mott regime of the bosonic Kane-Mele-Hubbard model. The phase diagram of this model is derived using bosonic dynamical mean-field theory. Focusing on the Mott phase, we investigate its magnetic properties as a function of frustration. We do find an emergent chiral spin state in the intermediate frustration regime. Using exact diagonalization we study more closely the physics of the effective frustrated X Y model and the properties of the chiral spin state. This gapped phase displays a chiral order, breaking time-reversal and parity symmetry, but is not topologically ordered (the Chern number is zero).

Probing α -RuCl3 Beyond Magnetic Order: Effects of Temperature and Magnetic Field

NASA Astrophysics Data System (ADS)

Winter, Stephen M.; Riedl, Kira; Kaib, David; Coldea, Radu; Valentí, Roser

2018-02-01

Recent studies have brought α -RuCl3 to the forefront of experimental searches for materials realizing Kitaev spin-liquid physics. This material exhibits strongly anisotropic exchange interactions afforded by the spin-orbit coupling of the 4 d Ru centers. We investigate the dynamical response at finite temperature and magnetic field for a realistic model of the magnetic interactions in α -RuCl3 . These regimes are thought to host unconventional paramagnetic states that emerge from the suppression of magnetic order. Using exact diagonalization calculations of the quantum model complemented by semiclassical analysis, we find a very rich evolution of the spin dynamics as the applied field suppresses the zigzag order and stabilizes a quantum paramagnetic state that is adiabatically connected to the fully polarized state at high fields. At finite temperature, we observe large redistributions of spectral weight that can be attributed to the anisotropic frustration of the model. These results are compared to recent experiments and provide a road map for further studies of these regimes.

Raman and fluorescence characteristics of resonant inelastic X-ray scattering from doped superconducting cuprates

DOE PAGES

Huang, H. Y.; Jia, C. J.; Chen, Z. Y.; ...

2016-01-22

Measurements of spin excitations are essential for an understanding of spin-mediated pairing for superconductivity; and resonant inelastic X-ray scattering (RIXS) provides a considerable opportunity to probe high-energy spin excitations. However, whether RIXS correctly measures the collective spin excitations of doped superconducting cuprates remains under debate. Here we demonstrate distinct Raman- and fluorescence-like RIXS excitations of Bi1.5Pb0.6Sr1.54CaCu2O8+δ. Combining photon-energy and momentum dependent RIXS measurements with theoretical calculations using exact diagonalization provides conclusive evidence that the Raman-like RIXS excitations correspond to collective spin excitations, which are magnons in the undoped Mott insulators and evolve into paramagnons in doped superconducting compounds. In contrast,more » the fluorescence-like shifts are due primarily to the continuum of particle-hole excitations in the charge channel. Our results show that under the proper experimental conditions RIXS indeed can be used to probe paramagnons in doped high-Tc cuprate superconductors.« less

Characterizing the three-orbital Hubbard model with determinant quantum Monte Carlo

DOE PAGES

Kung, Y. F.; Chen, C. -C.; Wang, Yao; ...

2016-04-29

Here, we characterize the three-orbital Hubbard model using state-of-the-art determinant quantum Monte Carlo (DQMC) simulations with parameters relevant to the cuprate high-temperature superconductors. The simulations find that doped holes preferentially reside on oxygen orbitals and that the (π,π) antiferromagnetic ordering vector dominates in the vicinity of the undoped system, as known from experiments. The orbitally-resolved spectral functions agree well with photoemission spectroscopy studies and enable identification of orbital content in the bands. A comparison of DQMC results with exact diagonalization and cluster perturbation theory studies elucidates how these different numerical techniques complement one another to produce a more complete understandingmore » of the model and the cuprates. Interestingly, our DQMC simulations predict a charge-transfer gap that is significantly smaller than the direct (optical) gap measured in experiment. Most likely, it corresponds to the indirect gap that has recently been suggested to be on the order of 0.8 eV, and demonstrates the subtlety in identifying charge gaps.« less

Stress Transmission in Granular Packings: Localization and Cooperative Response

NASA Astrophysics Data System (ADS)

Ramola, Kabir

We develop a framework for stress transmission in two dimensional granular media that respects vector force balance at the microscopic level. For a packing of grains interacting via pairwise contact forces, we introduce local gauge degrees of freedom that determine the response of the system to external perturbations. This allows us to construct unique force-balanced solutions that determine the change in contact forces as a response to external stress. By mapping this response to diffusion in the underlying contact network, we show that this naturally leads to spatial localization of forces. We present numerical evidence for stress localization using exact diagonalization studies of network Laplacians associated with soft disk packings. We use this formalism to characterize the deviation from elastic behaviour as the amount of disorder in the underlying network is varied. We discuss generalizations to systems with large friction between grains and other networks that display topological disorder. This work has been supported by NSF-DMR 1409093 and the W. M. Keck Foundation.

Characterizing the three-orbital Hubbard model with determinant quantum Monte Carlo

NASA Astrophysics Data System (ADS)

Kung, Y. F.; Chen, C.-C.; Wang, Yao; Huang, E. W.; Nowadnick, E. A.; Moritz, B.; Scalettar, R. T.; Johnston, S.; Devereaux, T. P.

2016-04-01

We characterize the three-orbital Hubbard model using state-of-the-art determinant quantum Monte Carlo (DQMC) simulations with parameters relevant to the cuprate high-temperature superconductors. The simulations find that doped holes preferentially reside on oxygen orbitals and that the (π ,π ) antiferromagnetic ordering vector dominates in the vicinity of the undoped system, as known from experiments. The orbitally-resolved spectral functions agree well with photoemission spectroscopy studies and enable identification of orbital content in the bands. A comparison of DQMC results with exact diagonalization and cluster perturbation theory studies elucidates how these different numerical techniques complement one another to produce a more complete understanding of the model and the cuprates. Interestingly, our DQMC simulations predict a charge-transfer gap that is significantly smaller than the direct (optical) gap measured in experiment. Most likely, it corresponds to the indirect gap that has recently been suggested to be on the order of 0.8 eV, and demonstrates the subtlety in identifying charge gaps.

Quantifying and tuning entanglement for quantum systems

NASA Astrophysics Data System (ADS)

Xu, Qing

A 2D Ising model with transverse field on a triangular lattice is studied using exact diagonalization. The quantum entanglement of the system is quantified by the entanglement of formation. The ground state property of the system is studied and the quantified entanglement is shown to be closely related to the ground state wavefunction while the singularity in the entanglement as a function of the transverse field is a reasonable indicator of the quantum phase transition. In order to tune the entanglement, one can either include an impurity in the otherwise homogeneous system whose strength is tunable, or one can vary the external transverse field as a tuner. The latter kind of tuning involves complicated dynamical properties of the system. From the study of the dynamics on a comparatively smaller system, we provide ways to tune the entanglement without triggering any decoherence. The finite temperature effect is also discussed. Besides showing above physical results, the realization of the trace-minimization method in our system is provided; the scalability of such method to larger systems is argued.

Markov-modulated Markov chains and the covarion process of molecular evolution.

PubMed

Galtier, N; Jean-Marie, A

2004-01-01

The covarion (or site specific rate variation, SSRV) process of biological sequence evolution is a process by which the evolutionary rate of a nucleotide/amino acid/codon position can change in time. In this paper, we introduce time-continuous, space-discrete, Markov-modulated Markov chains as a model for representing SSRV processes, generalizing existing theory to any model of rate change. We propose a fast algorithm for diagonalizing the generator matrix of relevant Markov-modulated Markov processes. This algorithm makes phylogeny likelihood calculation tractable even for a large number of rate classes and a large number of states, so that SSRV models become applicable to amino acid or codon sequence datasets. Using this algorithm, we investigate the accuracy of the discrete approximation to the Gamma distribution of evolutionary rates, widely used in molecular phylogeny. We show that a relatively large number of classes is required to achieve accurate approximation of the exact likelihood when the number of analyzed sequences exceeds 20, both under the SSRV and among site rate variation (ASRV) models.

Wave Function and Emergent SU(2) Symmetry in the ν_{T}=1 Quantum Hall Bilayer.

PubMed

Lian, Biao; Zhang, Shou-Cheng

2018-02-16

We propose a trial wave function for the quantum Hall bilayer system of total filling factor ν_{T}=1 at a layer distance d to magnetic length ℓ ratio d/ℓ=κ_{c1}≈1.1, where the lowest charged excitation is known to have a level crossing. The wave function has two-particle correlations, which fit well with those in previous numerical studies, and can be viewed as a Bose-Einstein condensate of free excitons formed by composite bosons and anticomposite bosons in different layers. We show the free nature of these excitons indicating an emergent SU(2) symmetry for the composite bosons at d/ℓ=κ_{c1}, which leads to the level crossing in low-lying charged excitations. We further show the overlap between the trial wave function, and the ground state of a small size exact diagonalization is peaked near d/ℓ=κ_{c1}, which supports our theory.

Thermalization threshold in models of 1D fermions

NASA Astrophysics Data System (ADS)

Mukerjee, Subroto; Modak, Ranjan; Ramswamy, Sriram

2013-03-01

The question of how isolated quantum systems thermalize is an interesting and open one. In this study we equate thermalization with non-integrability to try to answer this question. In particular, we study the effect of system size on the integrability of 1D systems of interacting fermions on a lattice. We find that for a finite-sized system, a non-zero value of an integrability breaking parameter is required to make an integrable system appear non-integrable. Using exact diagonalization and diagnostics such as energy level statistics and the Drude weight, we find that the threshold value of the integrability breaking parameter scales to zero as a power law with system size. We find the exponent to be the same for different models with its value depending on the random matrix ensemble describing the non-integrable system. We also study a simple analytical model of a non-integrable system with an integrable limit to better understand how a power law emerges.

Crystalline phases by an improved gradient expansion technique

NASA Astrophysics Data System (ADS)

Carignano, S.; Mannarelli, M.; Anzuini, F.; Benhar, O.

2018-02-01

We develop an innovative technique for studying inhomogeneous phases with a spontaneous broken symmetry. The method relies on the knowledge of the exact form of the free energy in the homogeneous phase and on a specific gradient expansion of the order parameter. We apply this method to quark matter at vanishing temperature and large chemical potential, which is expected to be relevant for astrophysical considerations. The method is remarkably reliable and fast as compared to performing the full numerical diagonalization of the quark Hamiltonian in momentum space and is designed to improve the standard Ginzburg-Landau expansion close to the phase transition points. For definiteness, we focus on inhomogeneous chiral symmetry breaking, accurately reproducing known results for one-dimensional and two-dimensional modulations and examining novel crystalline structures, as well. Consistently with previous results, we find that the energetically favored modulation is the so-called one-dimensional real-kink crystal. We propose a qualitative description of the pairing mechanism to motivate this result.

Numerical investigation of gapped edge states in fractional quantum Hall-superconductor heterostructures

NASA Astrophysics Data System (ADS)

Repellin, Cécile; Cook, Ashley M.; Neupert, Titus; Regnault, Nicolas

2018-03-01

Fractional quantum Hall-superconductor heterostructures may provide a platform towards non-abelian topological modes beyond Majoranas. However their quantitative theoretical study remains extremely challenging. We propose and implement a numerical setup for studying edge states of fractional quantum Hall droplets with a superconducting instability. The fully gapped edges carry a topological degree of freedom that can encode quantum information protected against local perturbations. We simulate such a system numerically using exact diagonalization by restricting the calculation to the quasihole-subspace of a (time-reversal symmetric) bilayer fractional quantum Hall system of Laughlin ν = 1/3 states. We show that the edge ground states are permuted by spin-dependent flux insertion and demonstrate their fractional 6π Josephson effect, evidencing their topological nature and the Cooper pairing of fractionalized quasiparticles. The versatility and efficiency of our setup make it a well suited method to tackle wider questions of edge phases and phase transitions in fractional quantum Hall systems.

Planar pyrochlore: A strong-coupling analysis

NASA Astrophysics Data System (ADS)

Brenig, Wolfram; Honecker, Andreas

2002-04-01

Recent investigations of the two-dimensional spin-1/2 checkerboard lattice favor a valence bond crystal with long-range quadrumer order [J.-B. Fouet, M. Mambrini, P. Sindzingre, and C. Lhuillier, cond-mat/0108070 (unpublished)]. Starting from the limit of isolated quadrumers, we perform a complementary analysis of the evolution of the spectrum as a function of the interquadrumer coupling j using both exact diagonalization (ED) and series expansion (SE) by continuous unitary transformation. We compute (i) the ground-state energy, (ii) the elementary triplet excitations, and (iii) singlet excitations on finite systems and find very good agreement between SE and ED. In the thermodynamic limit we find a ground-state energy substantially lower than that documented in the literature. The elementary triplet excitation is shown to be gapped and almost dispersionless, whereas the singlet sector contains strongly dispersive modes. Evidence is presented for the low energy singlet excitations in the spin gap in the vicinity of j=1 to result from a large downward renormalization of local high-energy states.

Characterizing Plasmonic Excitations of Quasi-2D Chains

NASA Astrophysics Data System (ADS)

Townsend, Emily; Bryant, Garnett

A quantum description of the optical response of nanostructures and other atomic-scale systems is desirable for modeling systems that use plasmons for quantum information transfer, or coherent transport and interference of quantum states, as well as systems small enough for electron tunneling or quantum confinement to affect the electronic states of the system. Such a quantum description is complicated by the fact that collective and single-particle excitations can have similar energies and thus will mix. We seek to better understand the excitations of nanosystems to identify which characteristics of the excitations are most relevant to modeling their behavior. In this work we use a quasi 2-dimensional linear atomic chain as a model system, and exact diagonalization of the many-body Hamiltonian to obtain its excitations. We compare this to previous work in 1-d chains which used a combination of criteria involving a many-body state's transfer dipole moment, balance, transfer charge, dynamical response, and induced-charge distribution to identify which excitations are plasmonic in character.

ESR modes in a Strong-Leg Ladder in the Tomonaga-Luttinger Liquid Phase

NASA Astrophysics Data System (ADS)

Zvyagin, S.; Ozerov, M.; Maksymenko, M.; Wosnitza, J.; Honecker, A.; Landee, C. P.; Turnbull, M.; Furuya, S. C.; Giamarchi, T.

Magnetic excitations in the strong-leg quantum spin ladder compound (C7H10N)2CuBr4 (known as DIMPY) in the field-induced Tomonaga-Luttinger spin liquid phase are studied by means of high-field electron spin resonance (ESR) spectroscopy. The presence of a gapped ESR mode with unusual non-linear frequency-field dependence is revealed experimentally. Using a combination of analytic and exact diagonalization methods, we compute the dynamical structure factor and identify this mode with longitudinal excitations in the antisymmetric channel. We argue that these excitations constitute a fingerprint of the spin dynamics in a strong-leg spin-1/2 Heisenberg antiferromagnetic ladder and owe its ESR observability to the uniform Dzyaloshinskii-Moriya interaction. This work was partially supported by the DFG and Helmholtz Gemeinschaft (Germany), Swiss SNF under Division II, and ERC synergy UQUAM project. We acknowledge the support of the HLD at HZDR, member of the European Magnetic Field Laboratory (EMFL).

Quasi-one-dimensional Hall physics in the Harper–Hofstadter–Mott model

NASA Astrophysics Data System (ADS)

Kozarski, Filip; Hügel, Dario; Pollet, Lode

2018-04-01

We study the ground-state phase diagram of the strongly interacting Harper–Hofstadter–Mott model at quarter flux on a quasi-one-dimensional lattice consisting of a single magnetic flux quantum in y-direction. In addition to superfluid phases with various density patterns, the ground-state phase diagram features quasi-one-dimensional analogs of fractional quantum Hall phases at fillings ν = 1/2 and 3/2, where the latter is only found thanks to the hopping anisotropy and the quasi-one-dimensional geometry. At integer fillings—where in the full two-dimensional system the ground-state is expected to be gapless—we observe gapped non-degenerate ground-states: at ν = 1 it shows an odd ‘fermionic’ Hall conductance, while the Hall response at ν = 2 consists of the transverse transport of a single particle–hole pair, resulting in a net zero Hall conductance. The results are obtained by exact diagonalization and in the reciprocal mean-field approximation.

RANDOM MATRIX DIAGONALIZATION--A COMPUTER PROGRAM

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

Fuchel, K.; Greibach, R.J.; Porter, C.E.

A computer prograra is described which generates random matrices, diagonalizes them and sorts appropriately the resulting eigenvalues and eigenvector components. FAP and FORTRAN listings for the IBM 7090 computer are included. (auth)

A Diagonal-Steering-Based Binaural Beamforming Algorithm Incorporating a Diagonal Speech Localizer for Persons With Bilateral Hearing Impairment.

PubMed

Lee, Jun Chang; Nam, Kyoung Won; Jang, Dong Pyo; Kim, In Young

2015-12-01

Previously suggested diagonal-steering algorithms for binaural hearing support devices have commonly assumed that the direction of the speech signal is known in advance, which is not always the case in many real circumstances. In this study, a new diagonal-steering-based binaural speech localization (BSL) algorithm is proposed, and the performances of the BSL algorithm and the binaural beamforming algorithm, which integrates the BSL and diagonal-steering algorithms, were evaluated using actual speech-in-noise signals in several simulated listening scenarios. Testing sounds were recorded in a KEMAR mannequin setup and two objective indices, improvements in signal-to-noise ratio (SNRi ) and segmental SNR (segSNRi ), were utilized for performance evaluation. Experimental results demonstrated that the accuracy of the BSL was in the 90-100% range when input SNR was -10 to +5 dB range. The average differences between the γ-adjusted and γ-fixed diagonal-steering algorithms (for -15 to +5 dB input SNR) in the talking in the restaurant scenario were 0.203-0.937 dB for SNRi and 0.052-0.437 dB for segSNRi , and in the listening while car driving scenario, the differences were 0.387-0.835 dB for SNRi and 0.259-1.175 dB for segSNRi . In addition, the average difference between the BSL-turned-on and the BSL-turned-off cases for the binaural beamforming algorithm in the listening while car driving scenario was 1.631-4.246 dB for SNRi and 0.574-2.784 dB for segSNRi . In all testing conditions, the γ-adjusted diagonal-steering and BSL algorithm improved the values of the indices more than the conventional algorithms. The binaural beamforming algorithm, which integrates the proposed BSL and diagonal-steering algorithm, is expected to improve the performance of the binaural hearing support devices in noisy situations. Copyright © 2015 International Center for Artificial Organs and Transplantation and Wiley Periodicals, Inc.

Exact finite elements for conduction and convection

NASA Technical Reports Server (NTRS)

Thornton, E. A.; Dechaumphai, P.; Tamma, K. K.

1981-01-01

An approach for developing exact one dimensional conduction-convection finite elements is presented. Exact interpolation functions are derived based on solutions to the governing differential equations by employing a nodeless parameter. Exact interpolation functions are presented for combined heat transfer in several solids of different shapes, and for combined heat transfer in a flow passage. Numerical results demonstrate that exact one dimensional elements offer advantages over elements based on approximate interpolation functions.

Diagonal ordering operation technique applied to Morse oscillator

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

Popov, Dušan, E-mail: dusan_popov@yahoo.co.uk; Dong, Shi-Hai; Popov, Miodrag

2015-11-15

We generalize the technique called as the integration within a normally ordered product (IWOP) of operators referring to the creation and annihilation operators of the harmonic oscillator coherent states to a new operatorial approach, i.e. the diagonal ordering operation technique (DOOT) about the calculations connected with the normally ordered product of generalized creation and annihilation operators that generate the generalized hypergeometric coherent states. We apply this technique to the coherent states of the Morse oscillator including the mixed (thermal) state case and get the well-known results achieved by other methods in the corresponding coherent state representation. Also, in the lastmore » section we construct the coherent states for the continuous dynamics of the Morse oscillator by using two new methods: the discrete–continuous limit, respectively by solving a finite difference equation. Finally, we construct the coherent states corresponding to the whole Morse spectrum (discrete plus continuous) and demonstrate their properties according the Klauder’s prescriptions.« less

Towards first-principles calculation of electronic excitations in the ring of the protein-bound bacteriochlorophylls

NASA Astrophysics Data System (ADS)

Polyakov, Igor V.; Khrenova, Maria G.; Moskovsky, Alexander A.; Shabanov, Boris M.; Nemukhin, Alexander V.

2018-04-01

Modeling electronic excitation of bacteriochlorophyll (BChl) molecules in light-harvesting (LH) antennae from photosynthetic centers presents a challenge for the quantum theory. We report on a quantum chemical study of the ring of 32 BChl molecules from the bacterial core complex LH1-RC. Diagonal and off-diagonal elements of the excitonic Hamiltonian matrices are estimated in quantum chemical calculations of relevant fragments using the TD-DFT and CIS approaches. The deviation of the computed excitation energy of this BChl system from the experimental data related to the Qy band maximum of this LH1-RC complex is about 0.2 eV. We demonstrate that corrections due to improvement in modeling of an individual BChl molecule and due to contributions from the protein environment are in the range of the obtained discrepancy between theory and experiment. Differences between results of the excitonic model and direct quantum chemical calculations of BChl aggregates fall in the same range.

Asymmetric color image encryption based on singular value decomposition

NASA Astrophysics Data System (ADS)

Yao, Lili; Yuan, Caojin; Qiang, Junjie; Feng, Shaotong; Nie, Shouping

2017-02-01

A novel asymmetric color image encryption approach by using singular value decomposition (SVD) is proposed. The original color image is encrypted into a ciphertext shown as an indexed image by using the proposed method. The red, green and blue components of the color image are subsequently encoded into a complex function which is then separated into U, S and V parts by SVD. The data matrix of the ciphertext is obtained by multiplying orthogonal matrices U and V while implementing phase-truncation. Diagonal entries of the three diagonal matrices of the SVD results are abstracted and scrambling combined to construct the colormap of the ciphertext. Thus, the encrypted indexed image covers less space than the original image. For decryption, the original color image cannot be recovered without private keys which are obtained from phase-truncation and the orthogonality of V. Computer simulations are presented to evaluate the performance of the proposed algorithm. We also analyze the security of the proposed system.

Effective friction of granular flows made of non-spherical particles

NASA Astrophysics Data System (ADS)

Somfai, Ellák; Nagy, Dániel B.; Claudin, Philippe; Favier, Adeline; Kálmán, Dávid; Börzsönyi, Tamás

2017-06-01

Understanding the rheology of dense granular matter is a long standing problem and is important both from the fundamental and the applied point of view. As the basic building blocks of granular materials are macroscopic particles, the nature of both the response to deformations and the dissipation is very different from that of molecular materials. In the absence of large gradients, the best approach formulates the constitutive equation as an effective friction: for sheared granular matter the ratio of the off-diagonal and the diagonal elements of the stress tensor depends only on dynamical parameters, in particular the inertial number. In this work we employ numerical simulations to extend this formalism to granular packings made of frictionless elongated particles. We measured how the shape of the particles affects the effective friction, volume fraction and first normal stress difference, and compared it to the spherical particle case. We had to introduce polydispersity in particle size in order to keep the systems of the more elongated particles disordered.

R4 terms in supergravities via T -duality constraint

NASA Astrophysics Data System (ADS)

Razaghian, Hamid; Garousi, Mohammad R.

2018-05-01

It has been speculated in the literature that the effective actions of string theories at any order of α' should be invariant under the Buscher rules plus their higher covariant-derivative corrections. This may be used as a constraint to find effective actions at any order of α', in particular, the metric, the B -field, and the dilaton couplings in supergravities at order α'3 up to an overall factor. For the simple case of zero B -field and diagonal metric in which we have done the calculations explicitly, we have found that the constraint fixes almost all of the seven independent Riemann curvature couplings. There is only one term which is not fixed, because when metric is diagonal, the reduction of two R4 terms becomes identical. The Riemann curvature couplings that the T -duality constraint produces for both type II and heterotic theories are fully consistent with the existing couplings in the literature which have been found by the S-matrix and by the sigma-model approaches.

Bending response of cross-ply laminated composite plates with diagonally perturbed localized interfacial degeneration.

PubMed

Kam, Chee Zhou; Kueh, Ahmad Beng Hong

2013-01-01

A laminated composite plate element with an interface description is developed using the finite element approach to investigate the bending performance of two-layer cross-ply laminated composite plates in presence of a diagonally perturbed localized interfacial degeneration between laminae. The stiffness of the laminate is expressed through the assembly of the stiffnesses of lamina sub-elements and interface element, the latter of which is formulated adopting the well-defined virtually zero-thickness concept. To account for the extent of both shear and axial weak bonding, a degeneration ratio is introduced in the interface formulation. The model has the advantage of simulating a localized weak bonding at arbitrary locations, with various degeneration areas and intensities, under the influence of numerous boundary conditions since the interfacial description is expressed discretely. Numerical results show that the bending behavior of laminate is significantly affected by the aforementioned parameters, the greatest effect of which is experienced by those with a localized total interface degeneration, representing the case of local delamination.

4. LOOKING SOUTHWEST AT LATTICED GUARDRAIL, DIAGONALS, ASPHALT DECK AND ...

Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

4. LOOKING SOUTHWEST AT LATTICED GUARDRAIL, DIAGONALS, ASPHALT DECK AND LACED ANGLES ON VERTICALS - Wayne County Bridge No. 122, Spanning West Fork Whitewater River at Main Street, Milton, Wayne County, IN

Detail view of turnbuckle in diagonal member, with kodachrome film ...

Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

Detail view of turnbuckle in diagonal member, with kodachrome film box on right turnbuckle for scale. - Pennsylvania Railroad, Whitford Bridge, Spanning Amtrak tracks at Whitford Road, Whitford, Chester County, PA

Detail of inclined end post, diagonal tension rods, and vertical ...

Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

Detail of inclined end post, diagonal tension rods, and vertical members with concrete encased lower chord. - Mowersville Road Bridge, Mowersville Road (Township Route 644) spanning Paxton Run, Mowersville, Franklin County, PA

16. DIAGONAL VIEW TO NORTHWEST OF 1895 ENGINE/PUMP HOUSE SHOWING ...

Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

16. DIAGONAL VIEW TO NORTHWEST OF 1895 ENGINE/PUMP HOUSE SHOWING REPLACEMENT DIESEL ENGINE LOCATIONS AND ASSOCIATED COOLING EQUIPMENT WITH PIPING - Deer Island Pumping Station, Boston, Suffolk County, MA

30. BEARING SHOE / VERTICAL / DIAGONAL / UPPER AND ...

Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

30. BEARING SHOE / VERTICAL / DIAGONAL / UPPER AND LOWER CHORD DETAIL OF DECK TRUSS. VIEW TO NORTHEAST. - Abraham Lincoln Memorial Bridge, Spanning Missouri River on Highway 30 between Nebraska & Iowa, Blair, Washington County, NE

A theoretical study of the dissociative recombination of SH+ with electrons through the 2Π states of SH.

PubMed

Kashinski, D O; Talbi, D; Hickman, A P; Di Nallo, O E; Colboc, F; Chakrabarti, K; Schneider, I F; Mezei, J Zs

2017-05-28

A quantitative theoretical study of the dissociative recombination of SH + with electrons has been carried out. Multireference, configuration interaction calculations were used to determine accurate potential energy curves for SH + and SH. The block diagonalization method was used to disentangle strongly interacting SH valence and Rydberg states and to construct a diabatic Hamiltonian whose diagonal matrix elements provide the diabatic potential energy curves. The off-diagonal elements are related to the electronic valence-Rydberg couplings. Cross sections and rate coefficients for the dissociative recombination reaction were calculated with a stepwise version of the multichannel quantum defect theory, using the molecular data provided by the block diagonalization method. The calculated rates are compared with the most recent measurements performed on the ion Test Storage Ring (TSR) in Heidelberg, Germany.

Diagonal chromatography to study plant protein modifications.

PubMed

Walton, Alan; Tsiatsiani, Liana; Jacques, Silke; Stes, Elisabeth; Messens, Joris; Van Breusegem, Frank; Goormachtig, Sofie; Gevaert, Kris

2016-08-01

An interesting asset of diagonal chromatography, which we have introduced for contemporary proteome research, is its high versatility concerning proteomic applications. Indeed, the peptide modification or sorting step that is required between consecutive peptide separations can easily be altered and thereby allows for the enrichment of specific, though different types of peptides. Here, we focus on the application of diagonal chromatography for the study of modifications of plant proteins. In particular, we show how diagonal chromatography allows for studying proteins processed by proteases, protein ubiquitination, and the oxidation of protein-bound methionines. We discuss the actual sorting steps needed for each of these applications and the obtained results. This article is part of a Special Issue entitled: Plant Proteomics--a bridge between fundamental processes and crop production, edited by Dr. Hans-Peter Mock. Copyright © 2016 Elsevier B.V. All rights reserved.

Calculation of electronic coupling matrix elements for ground and excited state electron transfer reactions: Comparison of the generalized Mulliken-Hush and block diagonalization methods

NASA Astrophysics Data System (ADS)

Cave, Robert J.; Newton, Marshall D.

1997-06-01

Two independent methods are presented for the nonperturbative calculation of the electronic coupling matrix element (Hab) for electron transfer reactions using ab initio electronic structure theory. The first is based on the generalized Mulliken-Hush (GMH) model, a multistate generalization of the Mulliken Hush formalism for the electronic coupling. The second is based on the block diagonalization (BD) approach of Cederbaum, Domcke, and co-workers. Detailed quantitative comparisons of the two methods are carried out based on results for (a) several states of the system Zn2OH2+ and (b) the low-lying states of the benzene-Cl atom complex and its contact ion pair. Generally good agreement between the two methods is obtained over a range of geometries. Either method can be applied at an arbitrary nuclear geometry and, as a result, may be used to test the validity of the Condon approximation. Examples of nonmonotonic behavior of the electronic coupling as a function of nuclear coordinates are observed for Zn2OH2+. Both methods also yield a natural definition of the effective distance (rDA) between donor (D) and acceptor (A) sites, in contrast to earlier approaches which required independent estimates of rDA, generally based on molecular structure data.

Phylogeography of Partamona rustica (Hymenoptera, Apidae), an Endemic Stingless Bee from the Neotropical Dry Forest Diagonal.

PubMed

Miranda, Elder Assis; Batalha-Filho, Henrique; Congrains, Carlos; Carvalho, Antônio Freire; Ferreira, Kátia Maria; Del Lama, Marco Antonio

2016-01-01

The South America encompasses the highest levels of biodiversity found anywhere in the world and its rich biota is distributed among many different biogeographical regions. However, many regions of South America are still poorly studied, including its xeric environments, such as the threatened Caatinga and Cerrado phytogeographical domains. In particular, the effects of Quaternary climatic events on the demography of endemic species from xeric habitats are poorly understood. The present study uses an integrative approach to reconstruct the evolutionary history of Partamona rustica, an endemic stingless bee from dry forest diagonal in Brazil, in a spatial-temporal framework. In this sense, we sequenced four mitochondrial genes and genotyped eight microsatellite loci. Our results identified two population groups: one to the west and the other to the east of the São Francisco River Valley (SFRV). These groups split in the late Pleistocene, and the Approximate Bayesian Computation approach and phylogenetic reconstruction indicated that P. rustica originated in the west of the SFRV, subsequently colonising eastern region. Our tests of migration detected reduced gene flow between these groups. Finally, our results also indicated that the inferences both from the genetic data analyses and from the spatial distribution modelling are compatible with historical demographic stability.

Analysis of superimposed ultrasonic guided waves in long bones by the joint approximate diagonalization of eigen-matrices algorithm.

PubMed

Song, Xiaojun; Ta, Dean; Wang, Weiqi

2011-10-01

The parameters of ultrasonic guided waves (GWs) are very sensitive to mechanical and structural changes in long cortical bones. However, it is a challenge to obtain the group velocity and other parameters of GWs because of the presence of mixed multiple modes. This paper proposes a blind identification algorithm using the joint approximate diagonalization of eigen-matrices (JADE) and applies it to the separation of superimposed GWs in long bones. For the simulation case, the velocity of the single mode was calculated after separation. A strong agreement was obtained between the estimated velocity and the theoretical expectation. For the experiments in bovine long bones, by using the calculated velocity and a theoretical model, the cortical thickness (CTh) was obtained. For comparison with the JADE approach, an adaptive Gaussian chirplet time-frequency (ACGTF) method was also used to estimate the CTh. The results showed that the mean error of the CTh acquired by the JADE approach was 4.3%, which was smaller than that of the ACGTF method (13.6%). This suggested that the JADE algorithm may be used to separate the superimposed GWs and that the JADE algorithm could potentially be used to evaluate long bones. Copyright © 2011 World Federation for Ultrasound in Medicine & Biology. Published by Elsevier Inc. All rights reserved.

Phylogeography of Partamona rustica (Hymenoptera, Apidae), an Endemic Stingless Bee from the Neotropical Dry Forest Diagonal

PubMed Central

Batalha-Filho, Henrique; Congrains, Carlos; Carvalho, Antônio Freire; Ferreira, Kátia Maria; Del Lama, Marco Antonio

2016-01-01

The South America encompasses the highest levels of biodiversity found anywhere in the world and its rich biota is distributed among many different biogeographical regions. However, many regions of South America are still poorly studied, including its xeric environments, such as the threatened Caatinga and Cerrado phytogeographical domains. In particular, the effects of Quaternary climatic events on the demography of endemic species from xeric habitats are poorly understood. The present study uses an integrative approach to reconstruct the evolutionary history of Partamona rustica, an endemic stingless bee from dry forest diagonal in Brazil, in a spatial-temporal framework. In this sense, we sequenced four mitochondrial genes and genotyped eight microsatellite loci. Our results identified two population groups: one to the west and the other to the east of the São Francisco River Valley (SFRV). These groups split in the late Pleistocene, and the Approximate Bayesian Computation approach and phylogenetic reconstruction indicated that P. rustica originated in the west of the SFRV, subsequently colonising eastern region. Our tests of migration detected reduced gene flow between these groups. Finally, our results also indicated that the inferences both from the genetic data analyses and from the spatial distribution modelling are compatible with historical demographic stability. PMID:27723778

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.

Gravitoelectromagnetic analogy based on tidal tensors

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

Costa, L. Filipe O.; Herdeiro, Carlos A. R.

2008-07-15

We propose a new approach to a physical analogy between general relativity and electromagnetism, based on tidal tensors of both theories. Using this approach we write a covariant form for the gravitational analogues of the Maxwell equations, which makes transparent both the similarities and key differences between the two interactions. The following realizations of the analogy are given. The first one matches linearized gravitational tidal tensors to exact electromagnetic tidal tensors in Minkowski spacetime. The second one matches exact magnetic gravitational tidal tensors for ultrastationary metrics to exact magnetic tidal tensors of electromagnetism in curved spaces. In the third wemore » show that our approach leads to a two-step exact derivation of Papapetrou's equation describing the force exerted on a spinning test particle. Analogous scalar invariants built from tidal tensors of both theories are also discussed.« less

An efficient sparse matrix multiplication scheme for the CYBER 205 computer

NASA Technical Reports Server (NTRS)

Lambiotte, Jules J., Jr.

1988-01-01

This paper describes the development of an efficient algorithm for computing the product of a matrix and vector on a CYBER 205 vector computer. The desire to provide software which allows the user to choose between the often conflicting goals of minimizing central processing unit (CPU) time or storage requirements has led to a diagonal-based algorithm in which one of four types of storage is selected for each diagonal. The candidate storage types employed were chosen to be efficient on the CYBER 205 for diagonals which have nonzero structure which is dense, moderately sparse, very sparse and short, or very sparse and long; however, for many densities, no diagonal type is most efficient with respect to both resource requirements, and a trade-off must be made. For each diagonal, an initialization subroutine estimates the CPU time and storage required for each storage type based on results from previously performed numerical experimentation. These requirements are adjusted by weights provided by the user which reflect the relative importance the user places on the two resources. The adjusted resource requirements are then compared to select the most efficient storage and computational scheme.

Virial expansion for almost diagonal random matrices

NASA Astrophysics Data System (ADS)

Yevtushenko, Oleg; Kravtsov, Vladimir E.

2003-08-01

Energy level statistics of Hermitian random matrices hat H with Gaussian independent random entries Higeqj is studied for a generic ensemble of almost diagonal random matrices with langle|Hii|2rangle ~ 1 and langle|Hi\

Diagonalizing the Hamiltonian of λϕ4 theory in 2 space-time dimensions

NASA Astrophysics Data System (ADS)

Christensen, Neil

2018-01-01

We propose a new non-perturbative technique for calculating the scattering amplitudes of field-theory directly from the eigenstates of the Hamiltonian. Our method involves a discretized momentum space and a momentum cutoff, thereby truncating the Hilbert space and making numerical diagonalization of the Hamiltonian achievable. We show how to do this in the context of a simplified λϕ4 theory in two space-time dimensions. We present the results of our diagonalization, its dependence on time, its dependence on the parameters of the theory and its renormalization.

Algebraic techniques for diagonalization of a split quaternion matrix in split quaternionic mechanics

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

Jiang, Tongsong, E-mail: jiangtongsong@sina.com; Department of Mathematics, Heze University, Heze, Shandong 274015; Jiang, Ziwu

In the study of the relation between complexified classical and non-Hermitian quantum mechanics, physicists found that there are links to quaternionic and split quaternionic mechanics, and this leads to the possibility of employing algebraic techniques of split quaternions to tackle some problems in complexified classical and quantum mechanics. This paper, by means of real representation of a split quaternion matrix, studies the problem of diagonalization of a split quaternion matrix and gives algebraic techniques for diagonalization of split quaternion matrices in split quaternionic mechanics.

Modeling rainfall-runoff relationship using multivariate GARCH model

NASA Astrophysics Data System (ADS)

Modarres, R.; Ouarda, T. B. M. J.

2013-08-01

The traditional hydrologic time series approaches are used for modeling, simulating and forecasting conditional mean of hydrologic variables but neglect their time varying variance or the second order moment. This paper introduces the multivariate Generalized Autoregressive Conditional Heteroscedasticity (MGARCH) modeling approach to show how the variance-covariance relationship between hydrologic variables varies in time. These approaches are also useful to estimate the dynamic conditional correlation between hydrologic variables. To illustrate the novelty and usefulness of MGARCH models in hydrology, two major types of MGARCH models, the bivariate diagonal VECH and constant conditional correlation (CCC) models are applied to show the variance-covariance structure and cdynamic correlation in a rainfall-runoff process. The bivariate diagonal VECH-GARCH(1,1) and CCC-GARCH(1,1) models indicated both short-run and long-run persistency in the conditional variance-covariance matrix of the rainfall-runoff process. The conditional variance of rainfall appears to have a stronger persistency, especially long-run persistency, than the conditional variance of streamflow which shows a short-lived drastic increasing pattern and a stronger short-run persistency. The conditional covariance and conditional correlation coefficients have different features for each bivariate rainfall-runoff process with different degrees of stationarity and dynamic nonlinearity. The spatial and temporal pattern of variance-covariance features may reflect the signature of different physical and hydrological variables such as drainage area, topography, soil moisture and ground water fluctuations on the strength, stationarity and nonlinearity of the conditional variance-covariance for a rainfall-runoff process.

Flexural anchorage performance at diagonal crack locations.

DOT National Transportation Integrated Search

2010-12-01

Large numbers of reinforced concrete deck girder bridges that were constructed during the interstate system expansion of the 1950s have developed diagonal cracking in the stems. Though compliant with design codes when constructed, many of these bridg...

Assessment methodology for diagonally cracked reinforced concrete deck girders.

DOT National Transportation Integrated Search

2004-10-01

This report details the results of a research program conducted to estimate the capacity and remaining life of 1950s : vintage conventionally reinforced concrete deck girder (RCDG) bridges with diagonal cracks. The investigation : encompassed fiel...

Is the Diagonal Part of the Self-Energy Negligible within an Isolated Vortex in Weak-Coupling Superconductors?

NASA Astrophysics Data System (ADS)

Kurosawa, Noriyuki

2018-02-01

In the weak-coupling theory of superconductivity, the diagonal self-energy term is usually disregarded so that this term is already included in the renormalized chemical potential. Using the bulk solution, we can easily see that the term vanishes in the quasiclassical level. However, the validity of this treatment is obscured in nonuniform systems, such as quantized vortices. In this paper, we study an isolated vortex both analytically and numerically using the quasiclassical theory and demonstrate that the finite magnitude of the self-energy can emerge within a vortex in some odd-parity superconductors. We also find that the existence of diagonal self-energy can induce the breaking of the axisymmetry of vortices in chiral p-wave superconductors. This implies that the diagonal self-energy is not negligible within a vortex in odd-parity superconductors in general, even in the weak-coupling limit.

Volumetric analysis of the diagonal band of Broca in patients with schizophrenia and affective disorders: A post-mortem study.

PubMed

Brisch, Ralf; Bernstein, Hans-Gert; Dobrowolny, Henrik; Krzyżanowska, Marta; Jankowski, Zbigniew; Bogerts, Bernhard; Gos, Tomasz

2016-05-01

The human diagonal band of Broca is connected to other parts of the limbic system, such as the hippocampus, that are involved in the pathology of schizophrenia. This study aimed to characterize the volume and anterior-to-posterior distance of the human diagonal band of Broca (vertical limb) from post-mortem brains obtained from three groups: healthy control subjects (N = 17), patients with schizophrenia (N = 26), and patients with affective disorders (N = 12). There were no significant differences in the volume or anterior-to-posterior distance in the patients with schizophrenia or affective disorders compared with the healthy control subjects. To date, this is the first post-mortem investigation measuring the volume and the anterior-to-posterior distance of the diagonal band of Broca (vertical limb) in patients with schizophrenia or affective disorders compared with healthy control subjects. © 2015 Wiley Periodicals, Inc.

Efficient spares matrix multiplication scheme for the CYBER 203

NASA Technical Reports Server (NTRS)

Lambiotte, J. J., Jr.

1984-01-01

This work has been directed toward the development of an efficient algorithm for performing this computation on the CYBER-203. The desire to provide software which gives the user the choice between the often conflicting goals of minimizing central processing (CPU) time or storage requirements has led to a diagonal-based algorithm in which one of three types of storage is selected for each diagonal. For each storage type, an initialization sub-routine estimates the CPU and storage requirements based upon results from previously performed numerical experimentation. These requirements are adjusted by weights provided by the user which reflect the relative importance the user places on the resources. The three storage types employed were chosen to be efficient on the CYBER-203 for diagonals which are sparse, moderately sparse, or dense; however, for many densities, no diagonal type is most efficient with respect to both resource requirements. The user-supplied weights dictate the choice.

Diagonalization of complex symmetric matrices: Generalized Householder reflections, iterative deflation and implicit shifts

NASA Astrophysics Data System (ADS)

Noble, J. H.; Lubasch, M.; Stevens, J.; Jentschura, U. D.

2017-12-01

We describe a matrix diagonalization algorithm for complex symmetric (not Hermitian) matrices, A ̲ =A̲T, which is based on a two-step algorithm involving generalized Householder reflections based on the indefinite inner product 〈 u ̲ , v ̲ 〉 ∗ =∑iuivi. This inner product is linear in both arguments and avoids complex conjugation. The complex symmetric input matrix is transformed to tridiagonal form using generalized Householder transformations (first step). An iterative, generalized QL decomposition of the tridiagonal matrix employing an implicit shift converges toward diagonal form (second step). The QL algorithm employs iterative deflation techniques when a machine-precision zero is encountered "prematurely" on the super-/sub-diagonal. The algorithm allows for a reliable and computationally efficient computation of resonance and antiresonance energies which emerge from complex-scaled Hamiltonians, and for the numerical determination of the real energy eigenvalues of pseudo-Hermitian and PT-symmetric Hamilton matrices. Numerical reference values are provided.

Alternate solution to generalized Bernoulli equations via an integrating factor: an exact differential equation approach

NASA Astrophysics Data System (ADS)

Tisdell, C. C.

2017-08-01

Solution methods to exact differential equations via integrating factors have a rich history dating back to Euler (1740) and the ideas enjoy applications to thermodynamics and electromagnetism. Recently, Azevedo and Valentino presented an analysis of the generalized Bernoulli equation, constructing a general solution by linearizing the problem through a substitution. The purpose of this note is to present an alternative approach using 'exact methods', illustrating that a substitution and linearization of the problem is unnecessary. The ideas may be seen as forming a complimentary and arguably simpler approach to Azevedo and Valentino that have the potential to be assimilated and adapted to pedagogical needs of those learning and teaching exact differential equations in schools, colleges, universities and polytechnics. We illustrate how to apply the ideas through an analysis of the Gompertz equation, which is of interest in biomathematical models of tumour growth.

Flexural anchorage performance at diagonal crack locations : final report.

DOT National Transportation Integrated Search

2010-12-01

Large numbers of reinforced concrete deck girder bridges that were constructed during the interstate system expansion of the 1950s have developed diagonal cracking in the stems. Though compliant with design codes when constructed, many of these bridg...

33. Coal Fuel Elevator (diagonal in foreground), Fuel Elevator (left), ...

Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

33. Coal Fuel Elevator (diagonal in foreground), Fuel Elevator (left), Fuel Storage Bins (center), and Power Plant (right) Photographs taken by Joseph E.B. Elliot - Huber Coal Breaker, 101 South Main Street, Ashley, Luzerne County, PA

Exact Tests for the Rasch Model via Sequential Importance Sampling

ERIC Educational Resources Information Center

Chen, Yuguo; Small, Dylan

2005-01-01

Rasch proposed an exact conditional inference approach to testing his model but never implemented it because it involves the calculation of a complicated probability. This paper furthers Rasch's approach by (1) providing an efficient Monte Carlo methodology for accurately approximating the required probability and (2) illustrating the usefulness…

Prescriptive unitarity

DOE PAGES

Bourjaily, Jacob L.; Herrmann, Enrico; Trnka, Jaroslav

2017-06-12

We introduce a prescriptive approach to generalized unitarity, resulting in a strictly-diagonal basis of loop integrands with coefficients given by specifically-tailored residues in field theory. We illustrate the power of this strategy in the case of planar, maximally supersymmetric Yang-Mills theory (SYM), where we construct closed-form representations of all (n-point N k MHV) scattering amplitudes through three loops. The prescriptive approach contrasts with the ordinary description of unitarity-based methods by avoiding any need for linear algebra to determine integrand coefficients. We describe this approach in general terms as it should have applications to many quantum field theories, including those withoutmore » planarity, supersymmetry, or massless spectra defined in any number of dimensions.« less

PLACING DIAGONALS IN CENTER PANEL. View is northnorthwest from the ...

Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

PLACING DIAGONALS IN CENTER PANEL. View is north-northwest from the old suspension bridge, looking at upstream side of new bridge - South Fork Trinity River Bridge, State Highway 299 spanning South Fork Trinity River, Salyer, Trinity County, CA

Detail of diagonal end post support bracket mounted to east ...

Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

Detail of diagonal end post support bracket mounted to east face of track girder, east span. View south - New York, New Haven & Hartford Railroad, Fort Point Channel Rolling Lift Bridge, Spanning Fort Point Channel, Boston, Suffolk County, MA

On Negations and Algebras in Fuzzy Set Theory

DTIC Science & Technology

1986-03-19

Esteva Departament de Matematiques i Estadistica ~ Universitat Politecnica de Catalunya Diagonal 649 08028 Barcelona !Spain) ABSTRACT Dual... Estadistica Universitat Politecnica de Catalunya Diagonal 649 08028 Barcelona (Spain) In Zadeh’s definition of Fuzzy Sets [1] the operations are defined

26. Typical top chord, vertical lattice, diagonal bracing and bottom ...

Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

26. Typical top chord, vertical lattice, diagonal bracing and bottom chord assembly. View is of south side of center panels of 4th span. - Cleves Bridge, Spanning Great Miami River on U.S. Highway 50, Cleves, Hamilton County, OH

Reflection matrices with U q [osp(2) (2|2m)] symmetry

NASA Astrophysics Data System (ADS)

Vieira, R. S.; Lima-Santos, A.

2017-09-01

We propose a classification of the reflection K-matrices (solutions of the boundary Yang-Baxter equation) for the Uq[osp(2)(2\\vert 2m)]=Uq[C(2)(m+1)] vertex-model. We found four families of solutions, namely, the complete solutions, in which no elements of the reflection K-matrix is null, the block-diagonal solutions, the X-shape solutions and the diagonal solutions. We highlight that these diagonal K-matrices also hold for the Uq[osp(2)(2n+2\\vert 2m)]=Uq[D(2)(n+1, m)] vertex-model.

Group Sparse Optimization by Alternating Direction Method

DTIC Science & Technology

2012-11-22

to solving the following linear system: (β1G TG+ β2A TA)x = β1G T z −GTλ1 + β2AT b+ATλ2. (3.5) Note that GTG ∈ Rn×n is a diagonal matrix whose i-th...diagonal entry is the number of repetitions of xi in x̃. When the groups form an complete cover of the solution, the diagonal entries of GTG will be...positive, so GTG is invertible. In the next subsection, we will show that an incomplete cover case can be converted to a complete cover case by

Triple collocation-based estimation of spatially correlated observation error covariance in remote sensing soil moisture data assimilation

NASA Astrophysics Data System (ADS)

Wu, Kai; Shu, Hong; Nie, Lei; Jiao, Zhenhang

2018-01-01

Spatially correlated errors are typically ignored in data assimilation, thus degenerating the observation error covariance R to a diagonal matrix. We argue that a nondiagonal R carries more observation information making assimilation results more accurate. A method, denoted TC_Cov, was proposed for soil moisture data assimilation to estimate spatially correlated observation error covariance based on triple collocation (TC). Assimilation experiments were carried out to test the performance of TC_Cov. AMSR-E soil moisture was assimilated with a diagonal R matrix computed using the TC and assimilated using a nondiagonal R matrix, as estimated by proposed TC_Cov. The ensemble Kalman filter was considered as the assimilation method. Our assimilation results were validated against climate change initiative data and ground-based soil moisture measurements using the Pearson correlation coefficient and unbiased root mean square difference metrics. These experiments confirmed that deterioration of diagonal R assimilation results occurred when model simulation is more accurate than observation data. Furthermore, nondiagonal R achieved higher correlation coefficient and lower ubRMSD values over diagonal R in experiments and demonstrated the effectiveness of TC_Cov to estimate richly structuralized R in data assimilation. In sum, compared with diagonal R, nondiagonal R may relieve the detrimental effects of assimilation when simulated model results outperform observation data.

Off-diagonal ekpyrotic scenarios and equivalence of modified, massive and/or Einstein gravity

NASA Astrophysics Data System (ADS)

Vacaru, Sergiu I.

2016-01-01

Using our anholonomic frame deformation method, we show how generic off-diagonal cosmological solutions depending, in general, on all spacetime coordinates and undergoing a phase of ultra-slow contraction can be constructed in massive gravity. In this paper, there are found and studied new classes of locally anisotropic and (in)homogeneous cosmological metrics with open and closed spatial geometries. The late time acceleration is present due to effective cosmological terms induced by nonlinear off-diagonal interactions and graviton mass. The off-diagonal cosmological metrics and related Stückelberg fields are constructed in explicit form up to nonholonomic frame transforms of the Friedmann-Lamaître-Robertson-Walker (FLRW) coordinates. We show that the solutions include matter, graviton mass and other effective sources modeling nonlinear gravitational and matter fields interactions in modified and/or massive gravity, with polarization of physical constants and deformations of metrics, which may explain certain dark energy and dark matter effects. There are stated and analyzed the conditions when such configurations mimic interesting solutions in general relativity and modifications and recast the general Painlevé-Gullstrand and FLRW metrics. Finally, we elaborate on a reconstruction procedure for a subclass of off-diagonal cosmological solutions which describe cyclic and ekpyrotic universes, with an emphasis on open issues and observable signatures.

Partition-free approach to open quantum systems in harmonic environments: An exact stochastic Liouville equation

NASA Astrophysics Data System (ADS)

McCaul, G. M. G.; Lorenz, C. D.; Kantorovich, L.

2017-03-01

We present a partition-free approach to the evolution of density matrices for open quantum systems coupled to a harmonic environment. The influence functional formalism combined with a two-time Hubbard-Stratonovich transformation allows us to derive a set of exact differential equations for the reduced density matrix of an open system, termed the extended stochastic Liouville-von Neumann equation. Our approach generalizes previous work based on Caldeira-Leggett models and a partitioned initial density matrix. This provides a simple, yet exact, closed-form description for the evolution of open systems from equilibriated initial conditions. The applicability of this model and the potential for numerical implementations are also discussed.

Laplace-Beltrami operator and exact solutions for branes

NASA Astrophysics Data System (ADS)

Zheltukhin, A. A.

2013-02-01

Proposed is a new approach to finding exact solutions of nonlinear p-brane equations in D-dimensional Minkowski space based on the use of various initial value constraints. It is shown that the constraints Δx→=0 and Δx→=-Λ(t,σr)x→ give two sets of exact solutions.

Fast iterative solution of the Bethe-Salpeter eigenvalue problem using low-rank and QTT tensor approximation

NASA Astrophysics Data System (ADS)

Benner, Peter; Dolgov, Sergey; Khoromskaia, Venera; Khoromskij, Boris N.

2017-04-01

In this paper, we propose and study two approaches to approximate the solution of the Bethe-Salpeter equation (BSE) by using structured iterative eigenvalue solvers. Both approaches are based on the reduced basis method and low-rank factorizations of the generating matrices. We also propose to represent the static screen interaction part in the BSE matrix by a small active sub-block, with a size balancing the storage for rank-structured representations of other matrix blocks. We demonstrate by various numerical tests that the combination of the diagonal plus low-rank plus reduced-block approximation exhibits higher precision with low numerical cost, providing as well a distinct two-sided error estimate for the smallest eigenvalues of the Bethe-Salpeter operator. The complexity is reduced to O (Nb2) in the size of the atomic orbitals basis set, Nb, instead of the practically intractable O (Nb6) scaling for the direct diagonalization. In the second approach, we apply the quantized-TT (QTT) tensor representation to both, the long eigenvectors and the column vectors in the rank-structured BSE matrix blocks, and combine this with the ALS-type iteration in block QTT format. The QTT-rank of the matrix entities possesses almost the same magnitude as the number of occupied orbitals in the molecular systems, No

Justifying quasiparticle self-consistent schemes via gradient optimization in Baym-Kadanoff theory.

PubMed

Ismail-Beigi, Sohrab

2017-09-27

The question of which non-interacting Green's function 'best' describes an interacting many-body electronic system is both of fundamental interest as well as of practical importance in describing electronic properties of materials in a realistic manner. Here, we study this question within the framework of Baym-Kadanoff theory, an approach where one locates the stationary point of a total energy functional of the one-particle Green's function in order to find the total ground-state energy as well as all one-particle properties such as the density matrix, chemical potential, or the quasiparticle energy spectrum and quasiparticle wave functions. For the case of the Klein functional, our basic finding is that minimizing the length of the gradient of the total energy functional over non-interacting Green's functions yields a set of self-consistent equations for quasiparticles that is identical to those of the quasiparticle self-consistent GW (QSGW) (van Schilfgaarde et al 2006 Phys. Rev. Lett. 96 226402-4) approach, thereby providing an a priori justification for such an approach to electronic structure calculations. In fact, this result is general, applies to any self-energy operator, and is not restricted to any particular approximation, e.g., the GW approximation for the self-energy. The approach also shows that, when working in the basis of quasiparticle states, solving the diagonal part of the self-consistent Dyson equation is of primary importance while the off-diagonals are of secondary importance, a common observation in the electronic structure literature of self-energy calculations. Finally, numerical tests and analytical arguments show that when the Dyson equation produces multiple quasiparticle solutions corresponding to a single non-interacting state, minimizing the length of the gradient translates into choosing the solution with largest quasiparticle weight.

35. Coal Fuel Elevator (diagonal in center), Fuel Elevator (left), ...

Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

35. Coal Fuel Elevator (diagonal in center), Fuel Elevator (left), Fuel Storage Bins (center), and Power Plant (far center), and Retail Coal Storage Bins (right) Photograph taken by George Harven - Huber Coal Breaker, 101 South Main Street, Ashley, Luzerne County, PA

34. Coal Fuel Elevator (diagonal in foreground), Fuel Elevator (left), ...

Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

34. Coal Fuel Elevator (diagonal in foreground), Fuel Elevator (left), Fuel Storage Bins (center), and Power Plant (far center), and Retail Coal Storage Bins (right) Photograph taken by George Harven - Huber Coal Breaker, 101 South Main Street, Ashley, Luzerne County, PA

Remaining life of reinforced concrete beams with diagonal-tension cracks : final report.

DOT National Transportation Integrated Search

2004-04-01

This report covers the initial efforts of a research study investigating the remaining capacity and life of cast-in-place reinforced concrete deck-girder (RCDG) bridges with diagonal tension cracks. A database of 442 bridges constructed from 1947 to ...

Remaining life of reinforced concrete beams with diagonal-tension cracks : appendix A & B.

DOT National Transportation Integrated Search

2004-04-01

The appendices belong to "Remaining life of reinforced concrete beams with diagonal-tension cracks". : This report covers the initial efforts of a research study investigating the remaining capacity and life of cast-in-place reinforced concrete deck-...

Remaining life of reinforced concrete beams with diagonal-tension cracks : appendix C & D.

DOT National Transportation Integrated Search

2004-04-01

The appendices belong to "Remaining life of reinforced concrete beams with diagonal-tension cracks". : This report covers the initial efforts of a research study investigating the remaining capacity and life of cast-in-place reinforced concrete deck-...

Computational studies of model disordered and strongly correlated electronic systems

NASA Astrophysics Data System (ADS)

Johri, Sonika

The theory of non-interacting electrons in perfect crystals was completed soon after the advent of quantum mechanics. Though capable of describing electron behaviour in most simple solid state physics systems, this approach falls woefully short of describing condensed matter systems of interest today, and designing the quantum devices of the future. The reason is that nature is never free of disorder, and emergent properties arising from interactions can be clearly seen in the pure, low-dimensional materials that can be engineered today. In this thesis, I address some salient problems in disordered and correlated electronic systems using modern numerical techniques like sparse matrix diagonalization, density matrix renormalization group (DMRG), and large disorder renormalization group (LDRG) methods. The pioneering work of P. W. Anderson, in 1958, led to an understanding of how an electron can stop diffusing and become localized in a region of space when a crystal is sufficiently disordered. Thus disorder can lead to metal-insulator transitions, for instance, in doped semiconductors. Theoretical research on the Anderson disorder model since then has mostly focused on the localization-delocalization phase transition. The localized phase in itself was not thought to exhibit any interesting physics. Our work has uncovered a new singularity in the disorder-averaged inverse participation ratio of wavefunctions within the localized phase, arising from resonant states. The effects of system size, dimension and disorder distribution on the singularity have been studied. A novel wavefunction-based LDRG technique has been designed for the Anderson model which captures the singular behaviour. While localization is well established for a single electron in a disordered potential, the situation is less clear in the case of many interacting particles. Most studies of a many-body localized phase are restricted to a system which is isolated from its environment. Such a condition cannot be achieved perfectly in experiments. A chapter of this thesis is devoted to studying signatures of incomplete localization in a disordered system with interacting particles which is coupled to a bath. . Strongly interacting particles can also give rise to topological phases of matter that have exotic emergent properties, such as quasiparticles with fractional charges and anyonic, or perhaps even non-Abelian statistics. In addition to their intrinsic novelty, these particles (e.g. Majorana fermions) may be the building blocks of future quantum computers. The third part of my thesis focuses on the best experimentally known realizations of such systems - the fractional quantum Hall effect (FQHE) which occurs in two-dimensional electron gases in a strong perpendicular magnetic field. It has been observed in systems such as semiconductor heterostructures and, more recently, graphene. I have developed software for exact diagonalization of the many-body FQHE problem on the surface of a cylinder, a hitherto unstudied type of geometry. This geometry turns out to be optimal for the DMRG algorithm. Using this new geometry, I have studied properties of various fractionally-filled states, computing the overlap between exact ground states and model wavefunctions, their edge excitations, and entanglement spectra. I have calculated the sizes and tunneling amplitudes of quasiparticles, information which is needed to design the interferometers used to experimentally measure their Aharanov-Bohm phase. I have also designed numerical probes of the recently discovered geometric degree of freedom of FQHE states.

7. Typical top chord, vertical lattice, diagonals and strut assembly ...

Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

7. Typical top chord, vertical lattice, diagonals and strut assembly for the 1st and 4th spans. View is of north side of 1st span. - Cleves Bridge, Spanning Great Miami River on U.S. Highway 50, Cleves, Hamilton County, OH

Diagonal dominance for the multivariable Nyquist array using function minimization

NASA Technical Reports Server (NTRS)

Leininger, G. G.

1977-01-01

A new technique for the design of multivariable control systems using the multivariable Nyquist array method was developed. A conjugate direction function minimization algorithm is utilized to achieve a diagonal dominant condition over the extended frequency range of the control system. The minimization is performed on the ratio of the moduli of the off-diagonal terms to the moduli of the diagonal terms of either the inverse or direct open loop transfer function matrix. Several new feedback design concepts were also developed, including: (1) dominance control parameters for each control loop; (2) compensator normalization to evaluate open loop conditions for alternative design configurations; and (3) an interaction index to determine the degree and type of system interaction when all feedback loops are closed simultaneously. This new design capability was implemented on an IBM 360/75 in a batch mode but can be easily adapted to an interactive computer facility. The method was applied to the Pratt and Whitney F100 turbofan engine.

Are we living near the center of a local void?

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

Cusin, Giulia; Pitrou, Cyril; Uzan, Jean-Philippe, E-mail: giulia.cusin@unige.ch, E-mail: pitrou@iap.fr, E-mail: uzan@iap.fr

The properties of the cosmic microwave background (CMB) temperature and polarisation anisotropies measured by a static, off-centered observer located in a local spherically symmetric void, are described. In particular in this paper we compute, together with the standard 2-point angular correlation functions, the off-diagonal correlators, which are no more vanishing by symmetry. While the energy shift induced by the off-centered position of the observer can be suppressed by a proper choice of the observer velocity, a lensing-like effect on the CMB emission point remains. This latter effect is genuinely geometrical (e.g. non-degenerate with a boost) and reflects in the structuremore » of the off-diagonal correlators. At lowest order in this effect, the temperature and polarisation correlation matrices have non-vanishing diagonal elements, as usual, and all the off-diagonal terms are excited. This particular signature of a local void model allows one, in principle, to disentangle geometrical effects from local kinematical ones in CMB observations.« less

Inertial sensor and method of use

NASA Technical Reports Server (NTRS)

Gutierrez, Roman C. (Inventor); Tang, Tony K. (Inventor)

2003-01-01

The inertial sensor of the present invention utilizes a proof mass suspended from spring structures forming a nearly degenerate resonant structure into which a perturbation is introduced, causing a split in frequency of the two modes so that the mode shape become uniquely defined, and to the first order, remains orthogonal. The resonator is provided with a mass or inertia tensor with off-diagonal elements. These off-diagonal elements are large enough to change the mode shape of the two nearly degenerate modes from the original coordinate frame. The spring tensor is then provided with a compensating off-diagonal element, such that the mode shape is again defined in the original coordinate frame. The compensating off-diagonal element in the spring tensor is provided by a biasing voltage that softens certain elements in the spring tensor. Acceleration disturbs the compensation and the mode shape again changes from the original coordinate frame. By measuring the change in the mode shape, the acceleration is measured.

A diagonal algorithm for the method of pseudocompressibility. [for steady-state solution to incompressible Navier-Stokes equation

NASA Technical Reports Server (NTRS)

Rogers, S. E.; Kwak, D.; Chang, J. L. C.

1986-01-01

The method of pseudocompressibility has been shown to be an efficient method for obtaining a steady-state solution to the incompressible Navier-Stokes equations. Recent improvements to this method include the use of a diagonal scheme for the inversion of the equations at each iteration. The necessary transformations have been derived for the pseudocompressibility equations in generalized coordinates. The diagonal algorithm reduces the computing time necessary to obtain a steady-state solution by a factor of nearly three. Implicit viscous terms are maintained in the equations, and it has become possible to use fourth-order implicit dissipation. The steady-state solution is unchanged by the approximations resulting from the diagonalization of the equations. Computed results for flow over a two-dimensional backward-facing step and a three-dimensional cylinder mounted normal to a flat plate are presented for both the old and new algorithms. The accuracy and computing efficiency of these algorithms are compared.

Microplate array diagonal gel electrophoresis (MADGE), CpG-PCR and temporal thermal ramp-MADGE (Melt-MADGE) for single nucleotide analyses in populations.

PubMed

Day, I N; O'Dell, S D; Spanakis, E; Weavind, G P

1999-02-01

Important requirements for molecular genetic epidemiological studies are economy, sample parallelism, convenience of setup and accessibility, goals inadequately met by existent approaches. We invented microplate array diagonal gel electrophoresis (MADGE) to gain simultaneously the advantages of simple setup, 96-well microplate compatibility, horizontal electrophoresis, and the resolution of polyacrylamide. At essentially no equipment cost (one simple plastic gel former), 10-100-fold savings on time for sample coding, liquid transfers, and data documentation, in addition to volume reductions and gel re-use, can be achieved. MADGE is compatible with ARMS, restriction analysis and other pattern analyses. CpG-PCR is a general PCR approach to CpG sites (10-20% of all human single base variation): both primers have 3' T, and are abutted to the CpG, forcing a TaqI restriction site if the CpG is intact. Typically, a 52 bp PCR product is then cut in half. CpG-PCR also illustrates that PAGE-MADGE readily permits analysis of 'ultrashort' PCRs. Melt-MADGE employs real-time-variable-temperature electrophoresis to examine duplex mobility during melting, achieving DGGE-like de novo, mutation scanning, but with the conveniences of arbitrary programmability, MADGE compatibility and short run time. This suite of methods enhances our capability to type or scan thousands of samples simultaneously, by 10-100-fold.

Revisiting the comparison between the Shack-Hartmann and the pyramid wavefront sensors via the Fisher information matrix.

PubMed

Plantet, C; Meimon, S; Conan, J-M; Fusco, T

2015-11-02

Exoplanet direct imaging with large ground based telescopes requires eXtreme Adaptive Optics that couples high-order adaptive optics and coronagraphy. A key element of such systems is the high-order wavefront sensor. We study here several high-order wavefront sensing approaches, and more precisely compare their sensitivity to noise. Three techniques are considered: the classical Shack-Hartmann sensor, the pyramid sensor and the recently proposed LIFTed Shack-Hartmann sensor. They are compared in a unified framework based on precise diffractive models and on the Fisher information matrix, which conveys the information present in the data whatever the estimation method. The diagonal elements of the inverse of the Fisher information matrix, which we use as a figure of merit, are similar to noise propagation coefficients. With these diagonal elements, so called "Fisher coefficients", we show that the LIFTed Shack-Hartmann and pyramid sensors outperform the classical Shack-Hartmann sensor. In photon noise regime, the LIFTed Shack-Hartmann and modulated pyramid sensors obtain a similar overall noise propagation. The LIFTed Shack-Hartmann sensor however provides attractive noise properties on high orders.

Size consistent formulations of the perturb-then-diagonalize Møller-Plesset perturbation theory correction to non-orthogonal configuration interaction

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

Yost, Shane R.; Head-Gordon, Martin, E-mail: mhg@cchem.berkeley.edu; Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720

2016-08-07

In this paper we introduce two size consistent forms of the non-orthogonal configuration interaction with second-order Møller-Plesset perturbation theory method, NOCI-MP2. We show that the original NOCI-MP2 formulation [S. R. Yost, T. Kowalczyk, and T. VanVoorh, J. Chem. Phys. 193, 174104 (2013)], which is a perturb-then-diagonalize multi-reference method, is not size consistent. We also show that this causes significant errors in large systems like the linear acenes. By contrast, the size consistent versions of the method give satisfactory results for singlet and triplet excited states when compared to other multi-reference methods that include dynamic correlation. For NOCI-MP2 however, the numbermore » of required determinants to yield similar levels of accuracy is significantly smaller. These results show the promise of the NOCI-MP2 method, though work still needs to be done in creating a more consistent black-box approach to computing the determinants that comprise the many-electron NOCI basis.« less

Influence of the sign of the coupling on the temperature dependence of optical properties of one-dimensional exciton models

NASA Astrophysics Data System (ADS)

Cruzeiro, L.

2008-10-01

A new physical cause for a temperature-dependent double peak in exciton systems is put forward within a thermal equilibrium approach for the calculation of optical properties of exciton systems. Indeed, it is found that one-dimensional exciton systems with only one molecule per unit cell can have an absorption spectrum characterized by a double peak provided that the coupling between excitations in different molecules is positive. The two peaks, whose relative intensities vary with temperature, are located around the exciton band edges, being separated by an energy of approximately 4V, where V is the average coupling between nearest neighbours. For small amounts of diagonal and off-diagonal disorder, the contributions from the intermediate states in the band are also visible as intermediate structure between the two peaks, this being enhanced for systems with periodic boundary conditions. At a qualitative level, these results correlate well with experimental observations in the molecular aggregates of the thiacarbocyanine dye THIATS and in the organic crystals of acetanilide and N-methylacetamide.

Empirical Bayes method for reducing false discovery rates of correlation matrices with block diagonal structure.

PubMed

Pacini, Clare; Ajioka, James W; Micklem, Gos

2017-04-12

Correlation matrices are important in inferring relationships and networks between regulatory or signalling elements in biological systems. With currently available technology sample sizes for experiments are typically small, meaning that these correlations can be difficult to estimate. At a genome-wide scale estimation of correlation matrices can also be computationally demanding. We develop an empirical Bayes approach to improve covariance estimates for gene expression, where we assume the covariance matrix takes a block diagonal form. Our method shows lower false discovery rates than existing methods on simulated data. Applied to a real data set from Bacillus subtilis we demonstrate it's ability to detecting known regulatory units and interactions between them. We demonstrate that, compared to existing methods, our method is able to find significant covariances and also to control false discovery rates, even when the sample size is small (n=10). The method can be used to find potential regulatory networks, and it may also be used as a pre-processing step for methods that calculate, for example, partial correlations, so enabling the inference of the causal and hierarchical structure of the networks.

Efficient conjugate gradient algorithms for computation of the manipulator forward dynamics

NASA Technical Reports Server (NTRS)

Fijany, Amir; Scheid, Robert E.

1989-01-01

The applicability of conjugate gradient algorithms for computation of the manipulator forward dynamics is investigated. The redundancies in the previously proposed conjugate gradient algorithm are analyzed. A new version is developed which, by avoiding these redundancies, achieves a significantly greater efficiency. A preconditioned conjugate gradient algorithm is also presented. A diagonal matrix whose elements are the diagonal elements of the inertia matrix is proposed as the preconditioner. In order to increase the computational efficiency, an algorithm is developed which exploits the synergism between the computation of the diagonal elements of the inertia matrix and that required by the conjugate gradient algorithm.

13. Detail, downstream side of Bridge Number 310.58, showing lower ...

Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

13. Detail, downstream side of Bridge Number 310.58, showing lower chord connection, view to southeast, 210mm lens. The riveted portion of the bottom chord is at left, joined at the pin connection to the eyebars. The vertical intermediate post is a compression member, and is attached to one end of a floor beam that spans transversely below the bridge floor. There are paired diagonals to the left of the intermediate post, with a turnbuckled counter to rising diagonally to the right. The diagonals below the floor are bottom lateral members. - Southern Pacific Railroad Shasta Route, Bridge No. 310.58, Milepost 310.58, Sims, Shasta County, CA

Discrete Fourier Transform in a Complex Vector Space

NASA Technical Reports Server (NTRS)

Dean, Bruce H. (Inventor)

2015-01-01

An image-based phase retrieval technique has been developed that can be used on board a space based iterative transformation system. Image-based wavefront sensing is computationally demanding due to the floating-point nature of the process. The discrete Fourier transform (DFT) calculation is presented in "diagonal" form. By diagonal we mean that a transformation of basis is introduced by an application of the similarity transform of linear algebra. The current method exploits the diagonal structure of the DFT in a special way, particularly when parts of the calculation do not have to be repeated at each iteration to converge to an acceptable solution in order to focus an image.

Spectral sharpening of color sensors: diagonal color constancy and beyond.

PubMed

Vazquez-Corral, Javier; Bertalmío, Marcelo

2014-02-26

It has now been 20 years since the seminal work by Finlayson et al. on the use of spectral sharpening of sensors to achieve diagonal color constancy. Spectral sharpening is still used today by numerous researchers for different goals unrelated to the original goal of diagonal color constancy e.g., multispectral processing, shadow removal, location of unique hues. This paper reviews the idea of spectral sharpening through the lens of what is known today in color constancy, describes the different methods used for obtaining a set of sharpening sensors and presents an overview of the many different uses that have been found for spectral sharpening over the years.

The Two-Capacitor Problem Revisited: A Mechanical Harmonic Oscillator Model Approach

ERIC Educational Resources Information Center

Lee, Keeyung

2009-01-01

The well-known two-capacitor problem, in which exactly half the stored energy disappears when a charged capacitor is connected to an identical capacitor, is discussed based on the mechanical harmonic oscillator model approach. In the mechanical harmonic oscillator model, it is shown first that "exactly half" the work done by a constant applied…

Mechanisms of Diagonal-Shear Failure in Reinforced Concrete Beams analyzed by AE-SiGMA

NASA Astrophysics Data System (ADS)

Ohno, Kentaro; Shimozono, Shinichiro; Sawada, Yosuke; Ohtsu, Masayasu

Serious shear failures in reinforced concrete (RC) structures were reported in the Hanshin-Awaji Earthquake. In particular, it was demonstrated that a diagonal-shear failure could lead to disastrous damage. However, mechanisms of the diagonal-shear failure in RC beams have not been completely clarified yet. In this study, the diagonal-shear failure in RC beams is investigated, applying acoustic emission (AE) method. To identify source mechanisms of AE signals, SiGMA (Simplified Green's functions for Moment tensor Analysis) procedure was applied. Prior to four-point bending tests of RC beams, theoretical waveforms were calculated to determine the optimal arrangement of AE sensors. Then, cracking mechanisms in experiments were investigated by applying the SiGMA procedure to AE waveforms. From results of the SiGMA analysis, dominant motions of micro-cracks are found to be of shear crack in all the loading stages. As the load increased, the number of tensile cracks increased and eventually the diagonal-shear failure occurred in the shear span. Prior to final failure, AE cluster of micro-cracks was intensely observed in the shear span. To classify AE sources into tensile and shear cracks, AE parameter analysis was also applied. As a result, most of AE hits are classified into tensile cracks. The difference between results obtained by the AE parameter analysis and by the SiGMA analysis is investigated and discussed.

Biomechanical pole and leg characteristics during uphill diagonal roller skiing.

PubMed

Lindinger, Stefan Josef; Göpfert, Caroline; Stöggl, Thomas; Müller, Erich; Holmberg, Hans-Christer

2009-11-01

Diagonal skiing as a major classical technique has hardly been investigated over the last two decades, although technique and racing velocities have developed substantially. The aims of the present study were to 1) analyse pole and leg kinetics and kinematics during submaximal uphill diagonal roller skiing and 2) identify biomechanical factors related to performance. Twelve elite skiers performed a time to exhaustion (performance) test on a treadmill. Joint kinematics and pole/plantar forces were recorded separately during diagonal roller skiing (9 degrees; 11 km/h). Performance was correlated to cycle length (r = 0.77; P < 0.05), relative leg swing (r = 0.71), and gliding time (r = 0.74), hip flexion range of motion (ROM) during swing (r = 0.73) and knee extension ROM during gliding (r = 0.71). Push-off demonstrated performance correlations for impulse of leg force (r = 0.84), relative duration (r= -0.76) and knee flexion (r = 0.73) and extension ROM (r = 0.74). Relative time to peak pole force was associated with performance (r = 0.73). In summary, diagonal roller skiing performance was linked to 1) longer cycle length, 2) greater impulse of force during a shorter push-off with larger flexion/extension ROMs in leg joints, 3) longer leg swing, and 4) later peak pole force, demonstrating the major key characteristics to be emphasised in training.

Prosthetic misfit of implant-supported prosthesis obtained by an alternative section method

PubMed Central

Falcão-Filho, Hilmo Barreto Leite; de Aguiar, Fábio Afrânio; Rodrigues, Renata Cristina Silveira; de Mattos, Maria da Gloria Chiarello; Ribeiro, Ricardo Faria

2012-01-01

PURPOSE Adequate passive-fitting of one-piece cast 3-element implant-supported frameworks is hard to achieve. This short communication aims to present an alternative method for section of one-piece cast frameworks and for casting implant-supported frameworks. MATERIALS AND METHODS Three-unit implant-supported nickel-chromium (Ni-Cr) frameworks were tested for vertical misfit (n = 6). The frameworks were cast as one-piece (Group A) and later transversally sectioned through a diagonal axis (Group B) and compared to frameworks that were cast diagonally separated (Group C). All separated frameworks were laser welded. Only one side of the frameworks was screwed. RESULTS The results on the tightened side were significantly lower in Group C (6.43 ± 3.24 µm) when compared to Groups A (16.50 ± 7.55 µm) and B (16.27 ± 1.71 µm) (P<.05). On the opposite side, the diagonal section of the one-piece castings for laser welding showed significant improvement in the levels of misfit of the frameworks (Group A, 58.66±14.30 µm; Group B, 39.48±12.03 µm; Group C, 23.13±8.24 µm) (P<.05). CONCLUSION Casting diagonally sectioned frameworks lowers the misfit levels. Lower misfit levels for the frameworks can be achieved by diagonally sectioning one-piece frameworks. PMID:22737313

27 CFR 9.217 - Happy Canyon of Santa Barbara.

Code of Federal Regulations, 2011 CFR

2011-04-01

... Barbara viticultural area are titled: (1) Los Olivos, CA, 1995; (2) Figueroa Mountain, CA, 1995; (3) Lake... intersection of the Santa Lucia Ranger District diagonal line and Figueroa Mountain Road, a light-duty road... diagonal line, crossing onto the Figueroa Mountain map, and continuing east to its intersection with the...

27 CFR 9.217 - Happy Canyon of Santa Barbara.

Code of Federal Regulations, 2014 CFR

2014-04-01

... Barbara viticultural area are titled: (1) Los Olivos, CA, 1995; (2) Figueroa Mountain, CA, 1995; (3) Lake... intersection of the Santa Lucia Ranger District diagonal line and Figueroa Mountain Road, a light-duty road... diagonal line, crossing onto the Figueroa Mountain map, and continuing east to its intersection with the...

27 CFR 9.217 - Happy Canyon of Santa Barbara.

Code of Federal Regulations, 2013 CFR

2013-04-01

... Barbara viticultural area are titled: (1) Los Olivos, CA, 1995; (2) Figueroa Mountain, CA, 1995; (3) Lake... intersection of the Santa Lucia Ranger District diagonal line and Figueroa Mountain Road, a light-duty road... diagonal line, crossing onto the Figueroa Mountain map, and continuing east to its intersection with the...

27 CFR 9.217 - Happy Canyon of Santa Barbara.

Code of Federal Regulations, 2010 CFR

2010-04-01

... Barbara viticultural area are titled: (1) Los Olivos, CA, 1995; (2) Figueroa Mountain, CA, 1995; (3) Lake... intersection of the Santa Lucia Ranger District diagonal line and Figueroa Mountain Road, a light-duty road... diagonal line, crossing onto the Figueroa Mountain map, and continuing east to its intersection with the...

27 CFR 9.217 - Happy Canyon of Santa Barbara.

Code of Federal Regulations, 2012 CFR

2012-04-01

... Barbara viticultural area are titled: (1) Los Olivos, CA, 1995; (2) Figueroa Mountain, CA, 1995; (3) Lake... intersection of the Santa Lucia Ranger District diagonal line and Figueroa Mountain Road, a light-duty road... diagonal line, crossing onto the Figueroa Mountain map, and continuing east to its intersection with the...

Nodeless vibrational amplitudes and quantum nonadiabatic dynamics in the nested funnel for a pseudo Jahn-Teller molecule or homodimer

NASA Astrophysics Data System (ADS)

Peters, William K.; Tiwari, Vivek; Jonas, David M.

2017-11-01

The nonadiabatic states and dynamics are investigated for a linear vibronic coupling Hamiltonian with a static electronic splitting and weak off-diagonal Jahn-Teller coupling through a single vibration with a vibrational-electronic resonance. With a transformation of the electronic basis, this Hamiltonian is also applicable to the anti-correlated vibration in a symmetric homodimer with marginally strong constant off-diagonal coupling, where the non-adiabatic states and dynamics model electronic excitation energy transfer or self-exchange electron transfer. For parameters modeling a free-base naphthalocyanine, the nonadiabatic couplings are deeply quantum mechanical and depend on wavepacket width; scalar couplings are as important as the derivative couplings that are usually interpreted to depend on vibrational velocity in semiclassical curve crossing or surface hopping theories. A colored visualization scheme that fully characterizes the non-adiabatic states using the exact factorization is developed. The nonadiabatic states in this nested funnel have nodeless vibrational factors with strongly avoided zeroes in their vibrational probability densities. Vibronic dynamics are visualized through the vibrational coordinate dependent density of the time-dependent dipole moment in free induction decay. Vibrational motion is amplified by the nonadiabatic couplings, with asymmetric and anisotropic motions that depend upon the excitation polarization in the molecular frame and can be reversed by a change in polarization. This generates a vibrational quantum beat anisotropy in excess of 2/5. The amplitude of vibrational motion can be larger than that on the uncoupled potentials, and the electronic population transfer is maximized within one vibrational period. Most of these dynamics are missed by the adiabatic approximation, and some electronic and vibrational motions are completely suppressed by the Condon approximation of a coordinate-independent transition dipole between adiabatic states. For all initial conditions investigated, the initial nonadiabatic electronic motion is driven towards the lower adiabatic state, and criteria for this directed motion are discussed.

Nodeless vibrational amplitudes and quantum nonadiabatic dynamics in the nested funnel for a pseudo Jahn-Teller molecule or homodimer.

PubMed

Peters, William K; Tiwari, Vivek; Jonas, David M

2017-11-21

The nonadiabatic states and dynamics are investigated for a linear vibronic coupling Hamiltonian with a static electronic splitting and weak off-diagonal Jahn-Teller coupling through a single vibration with a vibrational-electronic resonance. With a transformation of the electronic basis, this Hamiltonian is also applicable to the anti-correlated vibration in a symmetric homodimer with marginally strong constant off-diagonal coupling, where the non-adiabatic states and dynamics model electronic excitation energy transfer or self-exchange electron transfer. For parameters modeling a free-base naphthalocyanine, the nonadiabatic couplings are deeply quantum mechanical and depend on wavepacket width; scalar couplings are as important as the derivative couplings that are usually interpreted to depend on vibrational velocity in semiclassical curve crossing or surface hopping theories. A colored visualization scheme that fully characterizes the non-adiabatic states using the exact factorization is developed. The nonadiabatic states in this nested funnel have nodeless vibrational factors with strongly avoided zeroes in their vibrational probability densities. Vibronic dynamics are visualized through the vibrational coordinate dependent density of the time-dependent dipole moment in free induction decay. Vibrational motion is amplified by the nonadiabatic couplings, with asymmetric and anisotropic motions that depend upon the excitation polarization in the molecular frame and can be reversed by a change in polarization. This generates a vibrational quantum beat anisotropy in excess of 2/5. The amplitude of vibrational motion can be larger than that on the uncoupled potentials, and the electronic population transfer is maximized within one vibrational period. Most of these dynamics are missed by the adiabatic approximation, and some electronic and vibrational motions are completely suppressed by the Condon approximation of a coordinate-independent transition dipole between adiabatic states. For all initial conditions investigated, the initial nonadiabatic electronic motion is driven towards the lower adiabatic state, and criteria for this directed motion are discussed.

Accuracy of the microcanonical Lanczos method to compute real-frequency dynamical spectral functions of quantum models at finite temperatures.

PubMed

Okamoto, Satoshi; Alvarez, Gonzalo; Dagotto, Elbio; Tohyama, Takami

2018-04-01

We examine the accuracy of the microcanonical Lanczos method (MCLM) developed by Long et al. [Phys. Rev. B 68, 235106 (2003)PRBMDO0163-182910.1103/PhysRevB.68.235106] to compute dynamical spectral functions of interacting quantum models at finite temperatures. The MCLM is based on the microcanonical ensemble, which becomes exact in the thermodynamic limit. To apply the microcanonical ensemble at a fixed temperature, one has to find energy eigenstates with the energy eigenvalue corresponding to the internal energy in the canonical ensemble. Here, we propose to use thermal pure quantum state methods by Sugiura and Shimizu [Phys. Rev. Lett. 111, 010401 (2013)PRLTAO0031-900710.1103/PhysRevLett.111.010401] to obtain the internal energy. After obtaining the energy eigenstates using the Lanczos diagonalization method, dynamical quantities are computed via a continued fraction expansion, a standard procedure for Lanczos-based numerical methods. Using one-dimensional antiferromagnetic Heisenberg chains with S=1/2, we demonstrate that the proposed procedure is reasonably accurate, even for relatively small systems.

Frenkel-Charge-Transfer exciton intermixing theory for molecular crystals with two isolated Frenkel exciton states.

NASA Astrophysics Data System (ADS)

Bondarev, Igor; Popescu, Adrian

We develop an analytical theory for the intra-intermolecular exciton intermixing in periodic 1D chains of planar organic molecules with two isolated low-lying Frenkel exciton states, typical of copper phthalocyanine (CuPc) and other transition metal phthalocyanine molecules. We formulate the Hamiltonian and use the exact Bogoliubov diagonalization procedure to derive the eigen energy spectrum for the two lowest intramolecular Frenkel excitons coupled to the intermolecular charge transfer (CT) exciton state. By comparing our theoretical spectrum with available experimental CuPc absorption data, we obtain the parameters of the Frenkel-CT exciton intermixing in CuPc thin films. The two Frenkel exciton states here are spaced apart by 0.26 eV, and the charge transfer exciton state is 50 meV above the lowest Frenkel exciton. Both Frenkel excitons are strongly mixed with the CT exciton, showing the coupling constant 0.17 eV in agreement with earlier electron transport experiments. Our results can be used for the proper interpretation of the physical properties of crystalline phthalocyanines. DOE-DE-SC0007117 (I.B.), UNC-GA ROI Grant (A.P.).

Accuracy of the microcanonical Lanczos method to compute real-frequency dynamical spectral functions of quantum models at finite temperatures

NASA Astrophysics Data System (ADS)

Okamoto, Satoshi; Alvarez, Gonzalo; Dagotto, Elbio; Tohyama, Takami

2018-04-01

We examine the accuracy of the microcanonical Lanczos method (MCLM) developed by Long et al. [Phys. Rev. B 68, 235106 (2003), 10.1103/PhysRevB.68.235106] to compute dynamical spectral functions of interacting quantum models at finite temperatures. The MCLM is based on the microcanonical ensemble, which becomes exact in the thermodynamic limit. To apply the microcanonical ensemble at a fixed temperature, one has to find energy eigenstates with the energy eigenvalue corresponding to the internal energy in the canonical ensemble. Here, we propose to use thermal pure quantum state methods by Sugiura and Shimizu [Phys. Rev. Lett. 111, 010401 (2013), 10.1103/PhysRevLett.111.010401] to obtain the internal energy. After obtaining the energy eigenstates using the Lanczos diagonalization method, dynamical quantities are computed via a continued fraction expansion, a standard procedure for Lanczos-based numerical methods. Using one-dimensional antiferromagnetic Heisenberg chains with S =1 /2 , we demonstrate that the proposed procedure is reasonably accurate, even for relatively small systems.

Rotational symmetry breaking toward a string-valence bond solid phase in frustrated J1 -J2 transverse field Ising model

NASA Astrophysics Data System (ADS)

Sadrzadeh, M.; Langari, A.

2018-06-01

We study the effect of quantum fluctuations by means of a transverse magnetic field (Γ) on the highly degenerate ground state of antiferromagnetic J1 -J2 Ising model on the square lattice, at the limit J2 /J1 = 0.5 . We show that harmonic quantum fluctuations based on single spin flips can not lift such degeneracy, however an-harmonic quantum fluctuations based on multi spin cluster flip excitations lift the degeneracy toward a unique ground state with string-valence bond solid (VBS) nature. A cluster operator formalism has been implemented to incorporate an-harmonic quantum fluctuations. We show that cluster-type excitations of the model lead not only to lower the excitation energy compared with a single-spin flip but also to lift the extensive degeneracy in favor of a string-VBS state, which breaks lattice rotational symmetry with only two fold degeneracy. The tendency toward the broken symmetry state is justified by numerical exact diagonalization. Moreover, we introduce a map to find the relation between the present model on the checkerboard and square lattices.

Two-Dimensional Collective Hamiltonian for Chiral and Wobbling Modes

DOE PAGES

Chen, Q. B.; Zhang, S. Q.; Zhao, P. W.; ...

2016-10-03

Here, a two-dimensional collective Hamiltonian (2DCH) on both azimuth and polar motions in triaxial nuclei is proposed to investigate the chiral and wobbling modes. In the 2DCH, the collective potential and the mass parameters are determined from three-dimensional tilted axis cranking (TAC) calculations. The broken chiral and signature symmetries in the TAC solutions are restored by the 2DCH. The validity of the 2DCH is illustrated with a triaxial rotor (γ= -30°) coupling to one h 11/2 proton particle and one h 11/2 neutron hole. By diagonalizing the 2DCH, the angular momenta and energy spectra are obtained. These results agree withmore » the exact solutions of the particle rotor model (PRM) at high rotational frequencies. However, at low frequencies, the energies given by the 2DCH are larger than those by the PRM due to the underestimation of the mass parameters. In addition, with increasing angular momentum, the transitions from the chiral vibration to chiral rotation and further to longitudinal wobbling motion have been presented in the 2DCH.« less

Mass eigenstates in bimetric theory with matter coupling

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

Schmidt-May, Angnis, E-mail: angnis.schmidt-may@fysik.su.se

2015-01-01

In this paper we study the ghost-free bimetric action extended by a recently proposed coupling to matter through a composite metric. The equations of motion for this theory are derived using a method which avoids varying the square-root matrix that appears in the matter coupling. We make an ansatz for which the metrics are proportional to each other and find that it can solve the equations provided that one parameter in the action is fixed. In this case, the proportional metrics as well as the effective metric that couples to matter solve Einstein's equations of general relativity including a mattermore » source. Around these backgrounds we derive the quadratic action for perturbations and diagonalize it into generalized mass eigenstates. It turns out that matter only interacts with the massless spin-2 mode whose equation of motion has exactly the form of the linearized Einstein equations, while the field with Fierz-Pauli mass term is completely decoupled. Hence, bimetric theory, with one parameter fixed such that proportional solutions exist, is degenerate with general relativity up to linear order around these backgrounds.« less

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.

Fractional charge and inter-Landau-level states at points of singular curvature.

PubMed

Biswas, Rudro R; Son, Dam Thanh

2016-08-02

The quest for universal properties of topological phases is fundamentally important because these signatures are robust to variations in system-specific details. Aspects of the response of quantum Hall states to smooth spatial curvature are well-studied, but challenging to observe experimentally. Here we go beyond this prevailing paradigm and obtain general results for the response of quantum Hall states to points of singular curvature in real space; such points may be readily experimentally actualized. We find, using continuum analytical methods, that the point of curvature binds an excess fractional charge and sequences of quantum states split away, energetically, from the degenerate bulk Landau levels. Importantly, these inter-Landau-level states are bound to the topological singularity and have energies that are universal functions of bulk parameters and the curvature. Our exact diagonalization of lattice tight-binding models on closed manifolds demonstrates that these results continue to hold even when lattice effects are significant. An important technological implication of these results is that these inter-Landau-level states, being both energetically and spatially isolated quantum states, are promising candidates for constructing qubits for quantum computation.

Simulation of Quantum Many-Body Dynamics for Generic Strongly-Interacting Systems

NASA Astrophysics Data System (ADS)

Meyer, Gregory; Machado, Francisco; Yao, Norman

2017-04-01

Recent experimental advances have enabled the bottom-up assembly of complex, strongly interacting quantum many-body systems from individual atoms, ions, molecules and photons. These advances open the door to studying dynamics in isolated quantum systems as well as the possibility of realizing novel out-of-equilibrium phases of matter. Numerical studies provide insight into these systems; however, computational time and memory usage limit common numerical methods such as exact diagonalization to relatively small Hilbert spaces of dimension 215 . Here we present progress toward a new software package for dynamical time evolution of large generic quantum systems on massively parallel computing architectures. By projecting large sparse Hamiltonians into a much smaller Krylov subspace, we are able to compute the evolution of strongly interacting systems with Hilbert space dimension nearing 230. We discuss and benchmark different design implementations, such as matrix-free methods and GPU based calculations, using both pre-thermal time crystals and the Sachdev-Ye-Kitaev model as examples. We also include a simple symbolic language to describe generic Hamiltonians, allowing simulation of diverse quantum systems without any modification of the underlying C and Fortran code.

Inverse participation ratios in the XX spin chain

NASA Astrophysics Data System (ADS)

Tsukerman, Emmanuel

2017-03-01

We continue the study of the inverse participation ratios (IPRs) of the XXZ Heisenberg spin chain initiated by Stéphan, Furukawa, Misguich, and Pasquier (2009) and continued by Misguich, Pasquier, and Luck (2016) by focusing on the case of the XX Heisenberg spin chain. For the ground state, Stéphan et al. note that calculating the IPR is equivalent to Dyson's constant term ex-conjecture. We express the IPRs of excited states as an apparently new "discrete" Hall inner product. We analyze this inner product using the theory of symmetric functions (Jack polynomials, Schur polynomials, the standard Hall inner product, and ωq ,t) to determine some exact expressions and asymptotics for IPRs. We show that IPRs can be indexed by partitions, and asymptotically the IPR of a partition is equal to that of the conjugate partition. We relate the IPRs to two other models from physics, namely, the circular symplectic ensemble of Dyson and the Dyson-Gaudin two-dimensional Coulomb lattice gas. Finally, we provide a description of the IPRs in terms of a signed count of diagonals of permutohedra.

Two-Dimensional Collective Hamiltonian for Chiral and Wobbling Modes

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

Chen, Q. B.; Zhang, S. Q.; Zhao, P. W.

Here, a two-dimensional collective Hamiltonian (2DCH) on both azimuth and polar motions in triaxial nuclei is proposed to investigate the chiral and wobbling modes. In the 2DCH, the collective potential and the mass parameters are determined from three-dimensional tilted axis cranking (TAC) calculations. The broken chiral and signature symmetries in the TAC solutions are restored by the 2DCH. The validity of the 2DCH is illustrated with a triaxial rotor (γ= -30°) coupling to one h 11/2 proton particle and one h 11/2 neutron hole. By diagonalizing the 2DCH, the angular momenta and energy spectra are obtained. These results agree withmore » the exact solutions of the particle rotor model (PRM) at high rotational frequencies. However, at low frequencies, the energies given by the 2DCH are larger than those by the PRM due to the underestimation of the mass parameters. In addition, with increasing angular momentum, the transitions from the chiral vibration to chiral rotation and further to longitudinal wobbling motion have been presented in the 2DCH.« less

Slice-thickness evaluation in CT and MRI: an alternative computerised procedure.

PubMed

Acri, G; Tripepi, M G; Causa, F; Testagrossa, B; Novario, R; Vermiglio, G

2012-04-01

The efficient use of computed tomography (CT) and magnetic resonance imaging (MRI) equipment necessitates establishing adequate quality-control (QC) procedures. In particular, the accuracy of slice thickness (ST) requires scan exploration of phantoms containing test objects (plane, cone or spiral). To simplify such procedures, a novel phantom and a computerised LabView-based procedure have been devised, enabling determination of full width at half maximum (FWHM) in real time. The phantom consists of a polymethyl methacrylate (PMMA) box, diagonally crossed by a PMMA septum dividing the box into two sections. The phantom images were acquired and processed using the LabView-based procedure. The LabView (LV) results were compared with those obtained by processing the same phantom images with commercial software, and the Fisher exact test (F test) was conducted on the resulting data sets to validate the proposed methodology. In all cases, there was no statistically significant variation between the two different procedures and the LV procedure, which can therefore be proposed as a valuable alternative to other commonly used procedures and be reliably used on any CT and MRI scanner.

Strain distribution and band structure of InAs/GaAs quantum ring superlattice

NASA Astrophysics Data System (ADS)

Mughnetsyan, Vram; Kirakosyan, Albert

2017-12-01

The elastic strain distribution and the band structure of InAs/GaAs one-layer quantum ring superlattice with square symmetry has been considered in this work. The Green's function formalism based on the method of inclusions has been implied to calculate the components of the strain tensor, while the combination of Green's function method with the Fourier transformation to momentum space in Pikus-Bir Hamiltonian has been used for obtaining the miniband energy dispersion surfaces via the exact diagonalization procedure. The dependencies of the strain tensor components on spatial coordinates are compared with ones for single quantum ring and are in good agreement with previously obtained results for cylindrical quantum disks. It is shown that strain significantly affects the miniband structure of the superlattice and has contribution to the degeneracy lifting effect due to heavy hole-light hole coupling. The demonstrated method is simple and provides reasonable results for comparatively small Hamiltonian matrix. The obtained results may be useful for further investigation and construction of novel devices based on quantum ring superlattices.

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.

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

Diaz-Cruz, J. L.

We discuss several aspects of the flavor problem in the Supersymmetry. First, in order to quantify the SUSY flavor problem, we generate randomly the entries of the sfermion mass matrices and determine which percentage of the points are consistent with current bounds on the flavor violating transitions, for which we take as an illustration the lepton flavor violating (LFV) decays li {yields} lj{gamma}. In the first instance we apply the mass-insertion method, and study how this percentage changes as one varies the parameters of the model. It is found that for 105 points about 10% of points pass current LFVmore » bounds on {mu} {yields} e{gamma} provided the sleptons masses are {approx} 10 TeV. While bounds on {tau} {yields} {mu}{gamma}, e{gamma} are satisfied for almost 100% of points even for sleptons masses as low as 360 GeV. Then, we consider an ansatz for sfermion masses that can be diagonalized exactly, and compare the results obtained previously for {tau} {yields} {mu}{gamma}. Now, we get that 100% of points satisfy the experimental bounds but with sleptons masses larger than 460 GeV.« less

Charged excitons in a dilute two-dimensional electron gas in a high magnetic field

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

Wojs, Arkadiusz; Institute of Physics, Wroclaw University of Technology, Wroclaw 50-370,; Quinn, John J.

2000-08-15

A theory of charged excitons X{sup -} in a dilute two-dimensional (2D) electron gas in a high-magnetic field is presented. In contrast to previous calculations, three bound X{sup -} states (one singlet and two triplets) are found in a narrow and symmetric GaAs quantum well. The singlet and a ''bright'' triplet are the two optically active states observed in experiments. The bright triplet has the binding energy of about 1 meV, smaller than the singlet and a ''dark'' triplet. The interaction of bound X{sup -}'s with a dilute 2D electron gas is investigated using exact diagonalization techniques. It is foundmore » that the short-range character of the e-X{sup -} interactions effectively isolates bound X{sup -} states from a dilute e-h plasma. This results in the insensitivity of the photoluminescence spectrum to the filling factor {nu}, and a rapid decrease of the oscillator strength of the dark triplet X{sup -} as a function of {nu}{sup -1}. (c) 2000 The American Physical Society.« less

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

Electronic state and optical response in a hydrogen-bonded molecular conductor

NASA Astrophysics Data System (ADS)

Naka, Makoto; Ishihara, Sumio

2018-06-01

Motivated by recent experimental studies of hydrogen-bonded molecular conductors κ -X 3(Cat-EDT-TTF) 2[X =H , D], interplays of protons and correlated electrons, and their effects on magnetic, dielectric, and optical properties, are studied theoretically. We introduce a model Hamiltonian for κ -X 3(Cat-EDT-TTF) 2, in which molecular dimers are connected by hydrogen bonds. Ground-state phase diagram and optical conductivity spectra are examined by using the mean-field approximation and the exact diagonalization method in finite-size cluster. Three types of the competing electronic and protonic phases, charge density wave phase, polar charge-ordered phase, and antiferromagnetic dimer-Mott insulating phase are found. Observed softening of the interdimer excitation due to the electron-proton coupling implies reduction of the effective electron-electron repulsion, i.e., "Hubbard U ," due to the quantum proton motion. Contrastingly, the intradimer charge excitation is hardened due to the proton-electron coupling. Implications of the theoretical calculations to the recent experimental results in κ -X 3(Cat-EDT-TTF) 2 are discussed.