31,483 research outputs found
Extension of the Thomas-Fermi approximation for trapped Bose-Einstein condensates with an arbitrary number of atoms
By incorporating the zero-point energy contribution we derive simple and
accurate extensions of the usual Thomas-Fermi (TF) expressions for the
ground-state properties of trapped Bose-Einstein condensates that remain valid
for an arbitrary number of atoms in the mean-field regime. Specifically, we
obtain approximate analytical expressions for the ground-state properties of
spherical, cigar-shaped, and disk-shaped condensates that reduce to the correct
analytical formulas in both the TF and the perturbative regimes, and remain
valid and accurate in between these two limiting cases. Mean-field quasi-1D and
-2D condensates appear as simple particular cases of our formulation. The
validity of our results is corroborated by an independent numerical computation
based on the 3D Gross-Pitaevskii equation.Comment: 5 pages, 3 figures. Final version published in Phys. Rev.
Almost sharp nonlinear scattering in one-dimensional Born-Infeld equations arising in nonlinear Electrodynamics
We study decay of small solutions of the Born-Infeld equation in 1+1
dimensions, a quasilinear scalar field equation modeling nonlinear
electromagnetism, as well as branes in String theory and minimal surfaces in
Minkowski space-times. From the work of Whitham, it is well-known that there is
no decay because of arbitrary solutions traveling to the speed of light just as
linear wave equation. However, even if there is no global decay in 1+1
dimensions, we are able to show that all globally small ,
solutions do decay to the zero background state in space, inside a
strictly proper subset of the light cone. We prove this result by constructing
a Virial identity related to a momentum law, in the spirit of works
\cite{KMM,KMM1}, as well as a Lyapunov functional that controls the energy.Comment: 12 pages; This is version 2. Some typos corrected and sections
organized differently for ease readin
Three-dimensional gap solitons in Bose-Einstein condensates supported by one-dimensional optical lattices
We study fundamental and compound gap solitons (GSs) of matter waves in
one-dimensional (1D) optical lattices (OLs) in a three-dimensional (3D)
weak-radial-confinement regime, which corresponds to realistic experimental
conditions in Bose-Einstein condensates (BECs). In this regime GSs exhibit
nontrivial radial structures. Associated with each 3D linear spectral band
exists a family of fundamental gap solitons that share a similar transverse
structure with the Bloch waves of the corresponding linear band. GSs with
embedded vorticity may exist \emph{inside} bands corresponding to other
values of . Stable GSs, both fundamental and compound ones (including vortex
solitons), are those which originate from the bands with lowest axial and
radial quantum numbers. These findings suggest a scenario for the experimental
generation of robust GSs in 3D settings.Comment: 5 pages, 5 figures; v2: matches published versio
Constraining the Minimum Mass of High-Redshift Galaxies and Their Contribution to the Ionization State of the IGM
We model the latest HST WFPC3/IR observations of > 100 galaxies at redshifts
z=7-8 in terms of a hierarchical galaxy formation model with starburst
activity. Our model provides a distribution of UV luminosities per dark matter
halo of a given mass and a natural explanation for the fraction of halos
hosting galaxies. The observed luminosity function is best fit with a minimum
halo mass per galaxy of 10^{9.4+0.3-0.9} Msun, corresponding to a virial
temperature of 10^{4.9+0.2-0.7} K. Extrapolating to faint, undetected galaxies,
the total production rate of ionizing radiation depends critically on this
minimum mass. Future measurements with JWST should determine whether the entire
galaxy population can comfortably account for the UV background required to
keep the intergalactic medium ionized.Comment: 9 pages, 6 figures, submitted to ApJ, comments welcom
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