Mean-field equations for cigar- and disk-shaped Bose and Fermi superfluids
Abstract
Starting from the three-dimensional (3D) time-dependent nonlinear Gross-Pitaevskii equation for a Bose-Einstein condensate (BEC) and density functional (DF) equation for a Fermi superfluid at the unitarity and Bardeen-Cooper-Schrieffer (BCS) limits, we derive effective one- (1D) and two-dimensional (2D) mean-field equations, respectively, for the dynamics of a trapped cigar- and disk-shaped BEC and Fermi superfluid by using the adiabatic approximation. The reduced 1D and 2D equations for a cigar- and disk-shaped Fermi superfluid have simple analytic nonlinear terms and at unitarity produce results for stationary properties and non-stationary breathing oscillation and free expansion in excellent agreement with the solution of the full 3D equation.
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Cite
@article{arxiv.0909.5380,
title = {Mean-field equations for cigar- and disk-shaped Bose and Fermi superfluids},
author = {Camilo A. G. Buitrago and S. K. Adhikari},
journal= {arXiv preprint arXiv:0909.5380},
year = {2009}
}
Comments
13 pages