602 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 Annual report, 1969

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

### 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

### 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

### A naked singularity stable under scalar field perturbations

We prove the stability of a spacetime with a naked singularity under scalar
field perturbations, where the perturbations are regular at the singularity.
This spacetime, found by Janis, Newman and Winicour, and independently by
Wyman, is sourced by a massless scalar field and also arises as a certain limit
of a class of charged dilatonic solutions in string theory. This stability
result opens up specific questions for investigation related to the cosmic
censorship conjecture and the mechanism by which it is implemented in nature.Comment: 19 pages, version to appear in IJMPD, references adde

### Low-energy expansion formula for one-dimensional Fokker-Planck and Schr\"odinger equations with periodic potentials

We study the low-energy behavior of the Green function for one-dimensional
Fokker-Planck and Schr\"odinger equations with periodic potentials. We derive a
formula for the power series expansion of reflection coefficients in terms of
the wave number, and apply it to the low-energy expansion of the Green
function

### Optical Frequency Comb Generation based on Erbium Fiber Lasers

Citation: Droste, S., Ycas, G., Washburn, B. R., Coddington, I., & Newbury, N. R. (2016). Optical Frequency Comb Generation based on Erbium Fiber Lasers. Nanophotonics, 5(2), 196-213. doi:10.1515/nanoph-2016-0019Optical frequency combs have revolutionized optical frequency metrology and are being actively investigated in a number of applications outside of pure optical frequency metrology. For reasons of cost, robustness, performance, and flexibility, the erbium fiber laser frequency comb has emerged as the most commonly used frequency comb system and many different designs of erbium fiber frequency combs have been demonstrated. We review the different approaches taken in the design of erbium fiber frequency combs, including the major building blocks of the underlying mode-locked laser, amplifier, supercontinuum generation and actuators for stabilization of the frequency comb

### The type II phase resetting curve is optimal for stochastic synchrony

The phase-resetting curve (PRC) describes the response of a neural oscillator
to small perturbations in membrane potential. Its usefulness for predicting the
dynamics of weakly coupled deterministic networks has been well characterized.
However, the inputs to real neurons may often be more accurately described as
barrages of synaptic noise. Effective connectivity between cells may thus arise
in the form of correlations between the noisy input streams. We use constrained
optimization and perturbation methods to prove that PRC shape determines
susceptibility to synchrony among otherwise uncoupled noise-driven neural
oscillators. PRCs can be placed into two general categories: Type I PRCs are
non-negative while Type II PRCs have a large negative region. Here we show that
oscillators with Type II PRCs receiving common noisy input sychronize more
readily than those with Type I PRCs.Comment: 10 pages, 4 figures, submitted to Physical Review

### Critical sets of nonlinear Sturm-Liouville operators of Ambrosetti-Prodi type

The critical set C of the operator F:H^2_D([0,pi]) -> L^2([0,pi]) defined by
F(u)=-u''+f(u) is studied. Here X:=H^2_D([0,pi]) stands for the set of
functions that satisfy the Dirichlet boundary conditions and whose derivatives
are in L^2([0,pi]). For generic nonlinearities f, C=\cup C_k decomposes into
manifolds of codimension 1 in X. If f''0, the set C_j is shown to be
non-empty if, and only if, -j^2 (the j-th eigenvalue of u -> u'') is in the
range of f'. The critical components C_k are (topological) hyperplanes.Comment: 6 pages, no figure

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