Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Density matrix methods”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 271 records · Page 15
All sourcesNASA NTRSDOE OSTI
DOE OSTI2014

Exact solution of the thermodynamics and size parameters of a polymer confined to a lattice of finite size: Large chain limit

We extend the exact solutions of the Di Marzio-Rubin matrix method for the thermodynamic properties, including chain density, of a linear polymer molecule confined to walk on a lattice of finite size. Our extensions enable (a) the use of higher dimensions (explicit 2D and 3D lattices), (b) lattice boundaries of arbitrary shape, and (c) the flexibility to allow each monomer to have its own energy of attraction for each lattice site. In the case of the large chain limit, we demonstrate how periodic boundary conditions can also be employed to reduce computation time. Advantages to this method include easy definition of chemical and physical structure (or surface roughness) of the lattice and site-specific monomer-specific energetics, and straightforward relatively fast computations. We show the usefulness and ease of implementation of this extension by examining the effect of energy variation along the lattice walls of an infinite rectangular cylinder with the idea of studying the changes in properties caused by chemical inhomogeneities on the surface of the box. Herein, we look particularly at the polymer density profile as a function of temperature in the confined region for very long polymers. One particularly striking result is the shift in the critical condition for adsorption due to surface energy inhomogeneities and the length scale of the inhomogeneities; an observation that could have important implications for polymer chromatography. Our method should have applications to both copolymers and biopolymers of arbitrary molar mass.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

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

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

36 MATERIALS SCIENCE↗
DOE OSTI2020

Microscopic calculations of nuclear level densities with the Lanczos method

A new method for computing the density of states in nuclei making use of an extrapolated form of the tridiagonal matrix obtained from the Lanczos method is presented. It will be shown that the global, average properties of the entire Lanczos matrix can be predicted from just four Lanczos iterations. The extrapolated Lanczos matrix (ELM) approach provides for an accurate computation of the density of states described within the configuration space, which, in some cases, is sufficient to accurately calculate the density of states at, or near, the neutron separation energy. Comparisons between theory and experiment are shown for $^{57}Fe$, $^{74}Ge$, and $^6Ge$. In addition, we show results for the J -dependence of moments and the level density for these three nuclei.

Shell model↗
DOE OSTI2023

Multi-site reaction dynamics through multi-fragment density matrix embedding

The practical description of disordered chemical reactions, where the reactions involve multiple species at multiple sites, is presently a challenge using correlated electronic structure methods due to their high computational cost and steep scaling. Here, we describe the gradient theory of multi-fragment density matrix embedding theory, which potentially provides a minimal computational framework to model such processes at the correlated electron level. We present the derivation and implementation of the gradient theory, its validation on model systems and chemical reactions using density matrix embedding, and its application to a molecular dynamics simulation of proton transport in a small water cluster, a simple example of multi-site reaction dynamics.

Chemistry↗
DOE OSTI2019

Nonadiabatic molecular dynamics with decoherence and detailed balance under a density matrix ensemble formalism

The mixed quantum-classical nonadiabatic molecular dynamics (NAMD) is a powerful tool to study many phenomena, especially ultrafast carrier transport and cooling. Carrier decoherence and detailed balance are two major issues in NAMD. So far, there is no computationally inexpensive approach to incorporate both effects. While the decoherence effect can be easily included in the state density matrix formalism and the detailed balance can be included in surface hopping or the wave function collapse approach, it is difficult to include both of them in a unified formalism. In this work we introduce a state density matrix formalism (referred to as P-matrix) including both the decoherence and detailed balance effects for NAMD. This method is able to explicitly treat the decoherence between different pairs of adiabatic states. Moreover, the off-diagonal density matrix elements are divided into two parts, corresponding to energy-increasing and energy-decreasing transitions. The detailed balance is then enforced by a Boltzmann factor applied to the energy-increasing transition part. The P-matrix formalism is applied to study hot-hole cooling and transfer processes in Si quantum dot (QD) systems. The calculated hot-carrier relaxation time is consistent with experiments. In a QD-pair system, the hot-hole cooling time shows weak dependence on the QD spacing. However, the hot-carrier transfer rate from one QD to another is found to decrease exponentially with the QD-QD distance. When the QD spacing is small ( ~ 1 nm), the hot-carrier transfer can be very efficient. It is also shown that the explicit treatment of decoherence time is important in order to treat this hot-carrier transfer correctly.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2016

Optimal laser wavelength for efficient laser power converter operation over temperature

A temperature dependent modeling study is conducted on a GaAs laser power converter to identify the optimal incident laser wavelength for optical power transmission. Furthermore, the respective temperature dependent maximal conversion efficiencies in the radiative limit as well as in a practically achievable limit are presented. The model is based on the transfer matrix method coupled to a two-diode model, and is calibrated to experimental data of a GaAs photovoltaic device over laser irradiance and temperature. Since the laser wavelength does not strongly influence the open circuit voltage of the laser power converter, the optimal laser wavelength is determined to be in the range where the external quantum efficiency is maximal, but weighted by the photon flux of the laser.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Analytical Methods of Approximating the Fisher Information Matrix for the Lognormal Distribution

Modelling the matter density in the universe through time has become one of the most important open problems in cosmology. One distribution that works particularly well is the lognormal distribution, where if Y follows a lognormal distribution, ln Y follows a normal distribution. In many cases, we want to know how much information a variable carries about some unknown parameter; this can be accomplished by calculating the Fisher information matrix. However, for the lognormal distribution, the Fisher matrix is much more complicated to evaluate in closed form. In this paper, we will look at some analytical methods to evaluate the Fisher matrix.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Topological and magnetic properties of the interacting Bernevig-Hughes-Zhang model

We investigate the effects of electronic correlations on the Bernevig-Hughes-Zhang model using the real-space density matrix renormalization group (DMRG) algorithm. We introduce a method to probe topological phase transitions in systems with strong correlations using DMRG, substantiated by an unsupervised machine learning methodology that analyzes the orbital structure of the real-space edges. Including the full multi-orbital Hubbard interaction term, we construct a phase diagram as a function of a gap parameter (m) and the Hubbard interaction strength (U) via exact DMRG simulations on N×4 cylinders. Our analysis confirms that the topological phase persists in the presence of interactions, consistent with previous studies, but it also reveals an intriguing phase transition from a paramagnetic to a stripey antiferromagnetic topological insulator. The combination of the magnetic structure factor, strength of magnetic moments, and the orbitally resolved density, provides real-space information on both topology and magnetism in a strongly correlated system.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2016

Self-consistent second-order Green’s function perturbation theory for periodic systems

Despite recent advances, systematic quantitative treatment of the electron correlation problem in extended systems remains a formidable task. Systematically improvable Green’s function methods capable of quantitatively describing weak and at least qualitatively strong correlations appear as promising candidates for computational treatment of periodic systems. We present a periodic implementation of temperature-dependent self-consistent 2nd-order Green’s function (GF2) method, where the self-energy is evaluated in the basis of atomic orbitals. Evaluating the real-space self-energy in atomic orbitals and solving the Dyson equation in k-space are the key components of a computationally feasible algorithm. We apply this technique to the one-dimensional hydrogen lattice — a prototypical crystalline system with a realistic Hamiltonian. By analyzing the behavior of the spectral functions, natural occupations, and self-energies, we claim that GF2 is able to recover metallic, band insulating, and at least qualitatively Mott regimes. We observe that the iterative nature of GF2 is essential to the emergence of the metallic and Mott phases.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Magnon interactions in the quantum paramagnetic phase of CoNb 2 O 6

In this work, we study effects of magnon interactions in the excitation spectrum of CoNb 2 O 6 in the quantum paramagnetic phase in transverse field, where the 1/S spin-wave theory exhibits unphysical divergences at the critical field. We propose a self-consistent Hartree-Fock approach that eliminates such unphysical singularities while preserving the integrity of the singular threshold phenomena of magnon decay and spectrum renormalization that are present in both theory and experiment. With the microscopic parameters adopted from previous studies, this method yields a close quantitative agreement with the available experimental data for CoNb 2 O 6 in the relevant regime. Furthermore, insights into the general structure of the spin-anisotropic model of CoNb 2 O 6 and related zigzag chain materials are also provided and a discussion of the effects of additional longitudinal field on the spectrum is given.

1-dimensional spin chains↗
DOE OSTI2017

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

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

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2014

SS{sub p}G: A strongly orthogonal geminal method with relaxed strong orthogonality

Strong orthogonality is an important constraint placed on geminal wavefunctions in order to make variational minimization tractable. However, strong orthogonality prevents certain, possibly important, excited configurations from contributing to the ground state description of chemical systems. The presented method lifts strong orthogonality constraint from geminal wavefunction by computing a perturbative-like correction to each geminal independently from the corrections to all other geminals. The method is applied to the Singlet-type Strongly orthogonal Geminals variant of the geminal wavefunction. Comparisons of this new SS{sub p}G method are made to the non-orthogonal AP1roG and the unconstrained Geminal Mean-Field Configuration Interaction method using small atomic and molecular systems. The correction is also compared to Density Matrix Renormalization Group calculations performed on long polyene chains in order to assess its scalability and applicability to large strongly correlated systems. The results of these comparisons demonstrate that although the perturbative correction is small, it may be a necessary first step in the systematic improvement of any strongly orthogonal geminal method.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2015

Effect of Na substitution on electronic and optical properties of CuInS{sub 2} chalcopyrite semiconductor

Electronic & optical properties of Na substituted CuNaIn{sub 2}S{sub 4} chalcopyrite semiconductors are significantly modified due to Na substitution in the Cu deficient CuInS{sub 2} semiconductor. These properties are obtained form first principle calculation using density functional theory based tight binding Linear muffin tin orbital method. The presence of Na alters the structural distortion and enhances strengths of Cu d and S p hybridization in CuNaIn{sub 2}S{sub 4}. This effect reduces band gap, in agreement with experimental observations and modify other properties significantly. Calculations of optical matrix elements (OME) and joint density of states (JDOS) show that effects of Na substitution on optical properties come through p–d hybridization and structural distortion. OME contribution is prominent near band edge. Both systems show anisotropic optical properties. - Graphical abstract: The figure shows the band structure and total density of states of CuNaIn{sub 2}S{sub 4}. It illustrates energy bands at various symmetry points, band gap and contribution of various orbitals.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Practical considerations for measuring global spin density matrix elements of vector mesons in heavy-ion collisions

The STAR Collaboration has reported a significant 𝜙-meson global spin alignment (𝜌 00 ) signal in Au+Au collisions at $\sqrt{s_{NN}}$ ≤ 62 GeV by measuring the polar angle distribution of 𝜙-meson daughters with respect to the orbital angular momentum direction of the collision system. Here, in this paper, a new method is explored for studying vector-meson global spin alignment in heavy-ion collisions by examining the two-dimensional (2D) polar and azimuthal angle distribution. This method allows simultaneous extraction of 𝜌 00 and off-diagonal spin density matrix elements (SDMEs), providing unique access to local quark-antiquark spin correlations and spin hydrodynamics in quark-gluon plasma. The new 2D method also removes potential biases from nonzero off-diagonal SDMEs on 𝜌 00 with the 1D method. A detailed procedure to correct for detector acceptance and resolution effects is also presented and validated by simulation studies.

Wilks, Gavin [University of Illinois, Chicago, IL ↗
DOE OSTI2019

Microscopic calculations of nuclear level densities with the Lanczos method

A new method for computing the density of states in nuclei making use of an extrapolated form of the tri-diagonal matrix obtained from the Lanczos method is presented. It will be shown that the global, average properties of the entire Lanczos matrix can be predicted from just four Lanczos iterations. The extrapolated Lanczos matrix (ELM) approach provides far an accurate computation of the density of states described within the configuration space, which, in many cases, is sufficient to accurately calculate the density of states at, or near, the neutron separation energy. Comparisons between theory and experiment are shown for 57 Fe. In addition, we show results for the J-dependence of the level density in 57 Fe.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2014

Iterative image-domain decomposition for dual-energy CT

Purpose: Dual energy CT (DECT) imaging plays an important role in advanced imaging applications due to its capability of material decomposition. Direct decomposition via matrix inversion suffers from significant degradation of image signal-to-noise ratios, which reduces clinical values of DECT. Existing denoising algorithms achieve suboptimal performance since they suppress image noise either before or after the decomposition and do not fully explore the noise statistical properties of the decomposition process. In this work, the authors propose an iterative image-domain decomposition method for noise suppression in DECT, using the full variance-covariance matrix of the decomposed images. Methods: The proposed algorithm is formulated in the form of least-square estimation with smoothness regularization. Based on the design principles of a best linear unbiased estimator, the authors include the inverse of the estimated variance-covariance matrix of the decomposed images as the penalty weight in the least-square term. The regularization term enforces the image smoothness by calculating the square sum of neighboring pixel value differences. To retain the boundary sharpness of the decomposed images, the authors detect the edges in the CT images before decomposition. These edge pixels have small weights in the calculation of the regularization term. Distinct from the existing denoising algorithms applied on the images before or after decomposition, the method has an iterative process for noise suppression, with decomposition performed in each iteration. The authors implement the proposed algorithm using a standard conjugate gradient algorithm. The method performance is evaluated using an evaluation phantom (Catphan©600) and an anthropomorphic head phantom. The results are compared with those generated using direct matrix inversion with no noise suppression, a denoising method applied on the decomposed images, and an existing algorithm with similar formulation as the proposed method but with an edge-preserving regularization term. Results: On the Catphan phantom, the method maintains the same spatial resolution on the decomposed images as that of the CT images before decomposition (8 pairs/cm) while significantly reducing their noise standard deviation. Compared to that obtained by the direct matrix inversion, the noise standard deviation in the images decomposed by the proposed algorithm is reduced by over 98%. Without considering the noise correlation properties in the formulation, the denoising scheme degrades the spatial resolution to 6 pairs/cm for the same level of noise suppression. Compared to the edge-preserving algorithm, the method achieves better low-contrast detectability. A quantitative study is performed on the contrast-rod slice of Catphan phantom. The proposed method achieves lower electron density measurement error as compared to that by the direct matrix inversion, and significantly reduces the error variation by over 97%. On the head phantom, the method reduces the noise standard deviation of decomposed images by over 97% without blurring the sinus structures. Conclusions: The authors propose an iterative image-domain decomposition method for DECT. The method combines noise suppression and material decomposition into an iterative process and achieves both goals simultaneously. By exploring the full variance-covariance properties of the decomposed images and utilizing the edge predetection, the proposed algorithm shows superior performance on noise suppression with high image spatial resolution and low-contrast detectability.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2019

Multisliced gausslet basis sets for electronic structure

We introduce highly local basis sets for electronic structure which are very efficient for correlation calculations near the complete basis set limit. Our approach is based on gausslets, recently introduced waveletlike smooth orthogonal functions. We adapt the gausslets to particular systems using one-dimensional (1D) coordinate transformations, putting more basis functions near the nuclei, while maintaining orthogonality. Furthermore, three-dimensional basis functions are composed out of products of the 1D functions in an efficient way called multislicing. We demonstrate these bases with both Hartree-Fock and density matrix renormalization group calculations on hydrogen chain systems. With both methods, we can go to higher accuracy in the complete basis set limit than is practical for conventional Gaussian basis sets, with errors near 0.1 mH per atom.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗