Time-dependent current density functional theory on a lattice

A rigorous formulation of time-dependent current density functional theory (TDCDFT) on a lattice is presented. The density-to-potential mapping and the ${\cal V}$-representability problems are reduced to a solution of a certain nonlinear lattice Schr\"odinger equation, to which the standard existence and uniqueness results for nonliner differential equations are applicable. For two versions of the lattice TDCDFT we prove that any continuous in time current density is locally ${\cal V}$-representable (both interacting and noninteracting), provided in the initial state the local kinetic energy is nonzero everywhere. In most cases of physical interest the ${\cal V}$-representability should also hold globally in time. These results put the application of TDCDFT to any lattice model on a firm ground, and open a way for studying exact properties of exchange correlation potentials.Comment: revtex4, 9 page

Project for the analysis of technology transfer Annual report, 1969

Technology utilization of NASA programs and other research and development programs in Federal Government - project analysis results of technology transfe

Project for the analysis of technology transfer Quarterly evaluation report, 1 Jan. - 31 Mar. 1969

Technology transfer analysis project studying nonspace applications of NASA and AEC generated technolog

Project for the analysis of technology transfer Quarterly report, 1 Jul. - 30 Sep. 1969

Research activities in technology transfer progra

Sharp eigenvalue enclosures for the perturbed angular Kerr-Newman Dirac operator

A certified strategy for determining sharp intervals of enclosure for the eigenvalues of matrix differential operators with singular coefficients is examined. The strategy relies on computing the second order spectrum relative to subspaces of continuous piecewise linear functions. For smooth perturbations of the angular Kerr-Newman Dirac operator, explicit rates of convergence due to regularity of the eigenfunctions are established. Existing benchmarks are validated and sharpened by several orders of magnitude in the unperturbed setting.Comment: 27 pages, 2 figures, 5 tables. Some errors fixe

Project for the analysis of technology transfer Quarterly report, 1 Oct. - 31 Dec. 1969

Analysis of Tech Brief-Technical Support Package progra

Nonequilibrium effects of anisotropic compression applied to vortex lattices in Bose-Einstein condensates

We have studied the dynamics of large vortex lattices in a dilute-gas Bose-Einstein condensate. While undisturbed lattices have a regular hexagonal structure, large-amplitude quadrupolar shape oscillations of the condensate are shown to induce a wealth of nonequilibrium lattice dynamics. When exciting an m = -2 mode, we observe shifting of lattice planes, changes of lattice structure, and sheet-like structures in which individual vortices appear to have merged. Excitation of an m = +2 mode dissolves the regular lattice, leading to randomly arranged but still strictly parallel vortex lines.Comment: 5 pages, 6 figure

Linear relaxation to planar Travelling Waves in Inertial Confinement Fusion

We study linear stability of planar travelling waves for a scalar reaction-diffusion equation with non-linear anisotropic diffusion. The mathematical model is derived from the full thermo-hydrodynamical model describing the process of Inertial Confinement Fusion. We show that solutions of the Cauchy problem with physically relevant initial data become planar exponentially fast with rate s(\eps',k)>0, where \eps'=\frac{T_{min}}{T_{max}}\ll 1 is a small temperature ratio and $k\gg 1$ the transversal wrinkling wavenumber of perturbations. We rigorously recover in some particular limit (\eps',k)\rightarrow (0,+\infty) a dispersion relation s(\eps',k)\sim \gamma_0 k^{\alpha} previously computed heuristically and numerically in some physical models of Inertial Confinement Fusion

The Kuramoto model with distributed shear

We uncover a solvable generalization of the Kuramoto model in which shears (or nonisochronicities) and natural frequencies are distributed and statistically dependent. We show that the strength and sign of this dependence greatly alter synchronization and yield qualitatively different phase diagrams. The Ott-Antonsen ansatz allows us to obtain analytical results for a specific family of joint distributions. We also derive, using linear stability analysis, general formulae for the stability border of incoherence.Comment: 6 page