Density-matrix methods and time dependence of order parameter in superconductors.
Time dependent differential equation for order parameter in superconductors near critical temperature derived from density matrix equations
Di Castro, C.↗
SEARCH · Search NASA
Results for “Density matrix method”
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.
Subbarrier absorption in a stationary superlattice
The calculation of the interband absorption coefficient was carried out in the classical case, when the frequency of light was assumed to bind two miniband subbarrier states of different bands. The influence of two dimensional Mott excitons on this absorption was studied and a comparison was made with the experiment. All of these considerations were done taking into account the photon wave vector (the phase spatial heterogeneity). The basic traits of the energy spectra of superlattice semiconductors, their kinetic and optical properties, and possible means of electromagnetic wave intensification were examined. By the density matrix method, a theory of electrical and electromagnetic properties of superlattices was suggested.
Arutyunyan, G. M.↗
Comparison of Conjugate Gradient Density Matrix Search and Chebyshev Expansion Methods for Avoiding Diagonalization in Large-Scale Electronic Structure Calculations
We report a comparison of two linear-scaling methods which avoid the diagonalization bottleneck of traditional electronic structure algorithms. The Chebyshev expansion method (CEM) is implemented for carbon tight-binding calculations of large systems and its memory and timing requirements compared to those of our previously implemented conjugate gradient density matrix search (CG-DMS). Benchmark calculations are carried out on icosahedral fullerenes from C60 to C8640 and the linear scaling memory and CPU requirements of the CEM demonstrated. We show that the CPU requisites of the CEM and CG-DMS are similar for calculations with comparable accuracy.
Bates, Kevin R.↗
A systematic method of calculating reduced matrix elements of single-particle operators
Inelastic transition density method for calculating reduced matrix elements of single particle operators
Braley, R. C.↗
A validation of the method of amplitude density functions in computing the S-matrix for a scattering problem.
S matrix elements for diatomic molecule rotational excitation by scattered atom computed by Amplitude Density Functions method
Bernstein, R. B.↗
Phase Diagram of the Two-Chain Hubbard Model
We have calculated the charge gap and spin gap for the two-chain Hubbard model as a function of the on-site Coulomb interaction and the interchain hopping amplitude. We used the density matrix renormalization group method and developed a method to calculate separately the gaps numerically for the symmetric and antisymmetric modes with respect to the exchange of the chain indices. We have found very different behaviors for the weak and strong interaction cases. Our calculated phase diagram is compared to the one obtained by Balents and Fisher using the weak coupling renormalization group technique.
Park, Youngho↗
Charge and Spin Dynamics of the Hubbard Chains
We calculate the local correlation functions of charge and spin for the one-chain and two-chain Hubbard model using density matrix renormalization group method and the recursion technique. Keeping only finite number of states we get good accuracy for the low energy excitations. We study the charge and spin gaps, bandwidths and weights of the spectra for various values of the on-site Coulomb interaction U and the electron filling. In the low energy part, the local correlation functions are different for the charge and spin. The bandwidths are proportional to t for the charge and J for the spin respectively.
Park, Youngho↗
What is the Best Alternative to Diagonalization of the Hamiltonian in Large Scale Semiempirical Calculations?
Recently, several linear scaling approaches have been introduced which replace the time dominating diagonalization step in semiempirical methods, enabling practical calculations to be performed, on very large molecules. This paper compares the accuracy and performance of pseudodiagonalization (PD), conjugate gradient density matrix search (CG-DMS), the Chebyshev polynomial expansion method (CEM), and purification of the density matrix (PDM) as linear scaling substitutions for diagonalization. The scaling, speed, and reliability of these methods are compared for AMI single point energy calculations on polyglycine chains (up to 20,000 atoms), water clusters (up to 12,300 atoms), and nucleic acids (up to 6300 atoms).
Daniels, Andrew D.↗
Kinematics of finite, rigid-body displacements.
Rigid body kinematics for finite displacements, proving several theorems analytically by matrix algebraic methods using mass density description
Thurnauer, P. G.↗
On Digital Simulation of Multicorrelated Random Processes and Its Applications
Two methods are described to simulate, on a digital computer, a set of correlated, stationary, and Gaussian time series with zero mean from the given matrix of power spectral densities and cross spectral densities. The first method is based upon trigonometric series with random amplitudes and deterministic phase angles. The random amplitudes are generated by using a standard random number generator subroutine. An example is given which corresponds to three components of wind velocities at two different spatial locations for a total of six correlated time series. In the second method, the whole process is carried out using the Fast Fourier Transform approach. This method gives more accurate results and works about twenty times faster for a set of six correlated time series.
Sinha, A. K.↗
Effects of correlation on the structure of impurity bands
Electron-electron interaction effects on electronic states density in electron gas impurity bands, using matrix method
Bambakidis, G.↗
Collisional redistribution of radiation. I - The density matrix
As a first step in deriving accurate, calculable expressions for collisional redistribution of radiation, valid outside the impact regime a method for calculating an accurate binary-collision density operator for an atom in the presence of a driving field and perturbers is presented. Projection-operator techniques to establish first the precise validity of the Markoff approximation for radiative relaxation are used. Using the same techniques, it is shown how the collisional-relaxation problem may be analyzed in a practical manner outside the Markoff approximation. The effect of correlations between radiative and collisional events is included in a consistent way and the physical implications of these correlation effects are demonstrated for a simple example, the two-level atom with nondegenerate levels.
Burnett, K.↗
Pulse-echo probe of rock permeability near oil wells
Processing method involves sequential insonifications of borehole wall at number of different frequencies. Return signals are normalized in amplitude, and root-mean-square (rms) value of each signal is determined. Values can be processed to yield information on size and number density of microfractures at various depths in rock matrix by using averaging methods developed for pulse-echo technique.
Narasimhan, K. Y.↗
A systematic method for calculating reduced matrix elements
Matrix elements systematic calculation method in terms of inelastic transition densities to evaluate nuclear properties
Braley, R. C.↗
Quantum theory of an optical maser. VI - Transient behavior.
The transient behavior of a laser is discussed using the quantum theory as did Scully and Lamb. The formal solution of the density-matrix equation is expressed in terms of exponentially decaying eigenmodes. Some of the lower decay constants are obtained numerically. The equations for the moments of the density matrix are then derived and solved by a truncation method. The equations of motion are integrated numerically for the case where the average number of photons in a laser cavity has the realistically large value 1.3 x 100,000. An alternative Fokker-Planck-equation approach is discussed.
Wang, Y. K.↗
An efficient formulation and implementation of the analytic energy gradient method to the single and double excitation coupled-cluster wave function - Application to Cl2O2
The analytic energy gradient for the single and double excitation coupled-cluster (CCSD) wave function has been reformulated and implemented in a new set of programs. The reformulated set of gradient equations have a smaller computational cost than any previously published. The iterative solution of the linear equations and the construction of the effective density matrices are fully vectorized, being based on matrix multiplications. The new method has been used to investigate the Cl2O2 molecule, which has recently been postulated as an important intermediate in the destruction of ozone in the stratosphere. In addition to reporting computational timings, the CCSD equilibrium geometries, harmonic vibrational frequencies, infrared intensities, and relative energetics of three isomers of Cl2O2 are presented.
Rendell, Alistair P.↗
Mars Optimal Aerobrake Maneuver Estimation
Mars science satellites often perform orbit changes to obtain different measurements, ground tracks or relay operations. Large reductions in semi-major axis and eccentricity can be done efficiently using the atmospheric drag, a.k.a aerobrake. Aerobraking is one of the most challenging planetary orbit maneuvers in terms of planning and operations. The most important consideration for aerobraking is maintaining the spacecraft's periapsis within an allocated atmospheric density corridor, which is accomplished by raising or lowering periapsis through one or a series of very small and short maneuvers. These maneuvers must be performed as efficiently as possible due to propellant constraints. Work herein details a fast and accurate method to calculate the required impulsive velocity changes in the orbit to guarantee that the spacecraft remains in a prescribed density corridor. The method makes use of the orbit's state transition matrix to map the solution space around the reference orbit. It evaluates the most efficient maneuver epochs to target a given periapsis change with a linear optimal control for single or multiple maneuvers. A fast calculation of the maneuver allows for a more comprehensive evaluation of the trade space, and the selected maneuver may be re-targeted later with a higher- fidelity model. Comparisons against fully propagated models and direct method optimizations demonstrate the new method's performance.
Sarli, Bruno V.↗
Radiative transfer theory for active remote sensing of a layer of nonspherical particles
The radiative transfer theory is applied to calculate the scattering by a layer of randomly positioned and oriented nonspherical particles. The scattering amplitude functions of each individual particle are calculated with Waterman's T matrix method, which utilizes vector spherical wave functions for expansion of incident, scattered, and surface fields. The orientation of the particles is described by a probability density function of the Eulerian angles of rotation. A rotation matrix is used to relate the T matrix of the principal frame to that of the natural frame of the particle. The extinction matrix and phase matrix of the radiative transfer equations are expressed in terms of the T matrix elements. The extinction matrix for nonspherical particles is generally nondiagonal. There are only two attenuation rates in a specified direction of propagation. The radiative transfer equations are solved by an iterative method to first order in albedo. Numerical results are illustrated as functions of incidence angle and frequency with applications to active remote sensing.
Tsang, L.↗