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At least 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
DOE OSTI2013

On optimizing Jacobi–Davidson method for calculating eigenvalues in low dimensional structures using eight band k · p model

The paper presents two ways of improving the Jacobi–Davidson method for calculating the eigenvalues and eigenvectors described by eight-band k · p model for quantum dots and other low dimensional structures. First, the method is extended by the application of time reversal symmetry operator. This extension allows efficient calculations of the twofold degeneracy present in the multiband k · p model and other interior eigenvalues. Second, the preconditioner for the indefinite matrix which comes from the discretization of the eight band k · p Hamiltonian is presented. The construction of this preconditioner is based on physical considerations about energy band structure in the k · p model. On the basis of two real examples, it is shown that the preconditioner can significantly shorten the time needed to calculate the interior eigenvalues, despite the fact that the memory usage of the preconditioner and Hamiltionian is comparable. Finally, some technical details for implementing the eight band k · p Hamiltonian and the eigensolver are provided.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2015

Iterative stability analysis of spatial domain decomposition based on block Jacobi algorithm for the diamond-difference scheme

Here, we study convergence of the integral transport matrix method (ITMM) based on a parallel block Jacobi (PBJ) iterative strategy for solving particle transport problems. The ITMM is a spatial domain decomposition method proposed for massively parallel computations. AFourier analysis of the PBJ-based iterations applied to SN diamond-difference equations in 1D slab and 2D Cartesian geometries is performed. It is carried out for infinite-medium problems with homogeneous material properties. To analyze the performance of the ITMM with the PBJ algorithm and evaluate its potential in scalability we consider a limiting case of one spatial cell per subdomain. The analysis shows that in such limit the spectral radius of the iteration method is one without regard to values of the scattering ratio and optical thickness of the spatial cells. This implies lack of convergence in infinite medium. Numerical results of finite-medium problems are presented. They demonstrate effects of finite size of spatial domain on the performance of the iteration algorithm as well as its asymptotic behavior when the extent of the spatial domain increases. Finally, these numerical experiments also show that for finite domains iterative convergence to a finite criterion is achievable in a multiple of the sum of number of cells in each dimension.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2013

Rational extension and Jacobi-type X{sub m} solutions of a quantum nonlinear oscillator

We construct a rational extension of a recently studied nonlinear quantum oscillator model. Our extended model is shown to retain exact solvability, admitting a discrete spectrum and corresponding closed-form solutions that are expressed through Jacobi-type X{sub m} exceptional orthogonal polynomials.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Full-dimensional vibrational calculations of five-atom molecules using a combination of Radau and Jacobi coordinates: Applications to methane and fluoromethane

Full quantum mechanical calculations of vibrational energies of methane and fluoromethane are carried out using a polyspherical description combining Radau and Jacobi coordinates. The Hamiltonian is built in a potential-optimized discrete variable representation, and vibrational energies are solved using an iterative eigensolver. This new approach can be applied to a large variety of molecules. In particular, we show that it is able to accurately and efficiently compute eigenstates for four different molecules : CH{sub 4}, CHD{sub 3}, CH{sub 2}D{sub 2}, and CH{sub 3}F. Very good agreement is obtained with the results reported previously in the literature with different approaches and with experimental data.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2013

An exact Jacobi map in the geodesic light-cone gauge

The remarkable properties of the recently proposed geodesic light-cone (GLC) gauge allow to explicitly solve the geodesic-deviation equation, and thus to derive an exact expression for the Jacobi map J{sup A}{sub B}(s,o) connecting a generic source s to a geodesic observer o in a generic space time. In this gauge J{sup A}{sub B} factorizes into the product of a local quantity at s times one at o, implying similarly factorized expressions for the area and luminosity distance. In any other coordinate system J{sup A}{sub B} is simply given by expressing the GLC quantities in terms of the corresponding ones in the new coordinates. This is explicitly done, at first and second order, respectively, for the synchronous and Poisson gauge-fixing of a perturbed, spatially-flat cosmological background, and the consistency of the two outcomes is checked. Our results slightly amend previous calculations of the luminosity-redshift relation and suggest a possible non-perturbative way for computing the effects of inhomogeneities on observations based on light-like signals.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2019

Analog of Hamilton-Jacobi theory for the time-evolution operator

In this paper we develop an analog of Hamilton-Jacobi theory for the time-evolution operator of a quantum many-particle system. The theory offers a useful approach to develop approximations to the time-evolution operator, and also provides a unified framework and starting point for many well-known approximations to the time-evolution operator. In the important special case of periodically driven systems at stroboscopic times, we find relatively simple equations for the coupling constants of the Floquet Hamiltonian, where a straightforward truncation of the couplings leads to a powerful class of approximations. Using our theory, we construct a flow chart that illustrates the connection between various common approximations, which also highlights some missing connections and associated approximation schemes. These missing connections turn out to imply an analytically accessible approximation that is the “inverse” of a rotating frame approximation and thus has a range of validity complementary to it. Here, we numerically test the various methods on the one-dimensional Ising model to confirm the ranges of validity that one would expect from the approximations used. The theory provides a map of the relations between the growing number of approximations for the time-evolution operator. We describe these relations in a table showing the limitations and advantages of many common approximations, as well as the approximations introduced in this paper.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
NASA NTRS1980

Shaped reflector antenna analysis using the Jacobi-Bessel series

A vector radiation integral is derived for an offset shaped reflector illuminated by an arbitrarily located and oriented source. A procedure for expressing the integral in terms of a series of the Fourier transforms of an effective aperture distribution is discussed. The Jacobi-Bessel series is used to evaluate the Fourier transforms. Numerical results are presented for different reflector configurations and source locations.

Rahmat-Samii, Y.↗