1,037 research outputs found

### 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 Quarterly report, 1 Jul. - 30 Sep. 1969

Research activities in technology transfer progra

### 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

### A Robust Inverse Scattering Transform for the Focusing Nonlinear Schrödinger Equation

We propose a modification of the standard inverse scattering transform for the focusing nonlinear Schrödinger equation (also other equations by natural generalization) formulated with nonzero boundary conditions at infinity. The purpose is to deal with arbitrary‐order poles and potentially severe spectral singularities in a simple and unified way. As an application, we use the modified transform to place the Peregrine solution and related higher‐order “rogue wave” solutions in an inverse‐scattering context for the first time. This allows one to directly study properties of these solutions such as their dynamical or structural stability, or their asymptotic behavior in the limit of high order. The modified transform method also allows rogue waves to be generated on top of other structures by elementary Darboux transformations rather than the generalized Darboux transformations in the literature or other related limit processes. © 2019 Wiley Periodicals, Inc.Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/149759/1/cpa21819.pd

### High-Precision Numerical Determination of Eigenvalues for a Double-Well Potential Related to the Zinn-Justin Conjecture

A numerical method of high precision is used to calculate the energy
eigenvalues and eigenfunctions for a symmetric double-well potential. The
method is based on enclosing the system within two infinite walls with a large
but finite separation and developing a power series solution for the
Schr$\ddot{o}$dinger equation. The obtained numerical results are compared with
those obtained on the basis of the Zinn-Justin conjecture and found to be in an
excellent agreement.Comment: Substantial changes including the title and the content of the paper
8 pages, 2 figures, 3 table

### Experimental studies of equilibrium vortex properties in a Bose-condensed gas

We characterize several equilibrium vortex effects in a rotating
Bose-Einstein condensate. Specifically we attempt precision measurements of
vortex lattice spacing and the vortex core size over a range of condensate
densities and rotation rates. These measurements are supplemented by numerical
simulations, and both experimental and numerical data are compared to theory
predictions of Sheehy and Radzihovsky [17] (cond-mat/0402637) and Baym and
Pethick [25] (cond-mat/0308325). Finally, we study the effect of the
centrifugal weakening of the trapping spring constants on the critical
temperature for quantum degeneracy and the effects of finite temperature on
vortex contrast.Comment: Fixed minor notational inconsistencies in figures. 12 pages, 8
figure

### 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

### Convergence of expansions in Schr\"odinger and Dirac eigenfunctions, with an application to the R-matrix theory

Expansion of a wave function in a basis of eigenfunctions of a differential
eigenvalue problem lies at the heart of the R-matrix methods for both the
Schr\"odinger and Dirac particles. A central issue that should be carefully
analyzed when functional series are applied is their convergence. In the
present paper, we study the properties of the eigenfunction expansions
appearing in nonrelativistic and relativistic $R$-matrix theories. In
particular, we confirm the findings of Rosenthal [J. Phys. G: Nucl. Phys. 13,
491 (1987)] and Szmytkowski and Hinze [J. Phys. B: At. Mol. Opt. Phys. 29, 761
(1996); J. Phys. A: Math. Gen. 29, 6125 (1996)] that in the most popular
formulation of the R-matrix theory for Dirac particles, the functional series
fails to converge to a claimed limit.Comment: Revised version, accepted for publication in Journal of Mathematical
Physics, 21 pages, 1 figur

### 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

### Potentials for which the Radial Schr\"odinger Equation can be solved

In a previous paper$^1$, submitted to Journal of Physics A -- we presented an
infinite class of potentials for which the radial Schr\"odinger equation at
zero energy can be solved explicitely. For part of them, the angular momentum
must be zero, but for the other part (also infinite), one can have any angular
momentum. In the present paper, we study a simple subclass (also infinite) of
the whole class for which the solution of the Schr\"odinger equation is simpler
than in the general case. This subclass is obtained by combining another
approach together with the general approach of the previous paper. Once this is
achieved, one can then see that one can in fact combine the two approaches in
full generality, and obtain a much larger class of potentials than the class
found in ref. $^1$ We mention here that our results are explicit, and when
exhibited, one can check in a straightforward manner their validity

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