Mean-field equations for cigar- and disk-shaped Bose and Fermi superfluids

Camilo A. G. Buitrago; S. K. Adhikari

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arXiv · 0909.5380

Mean-field equations for cigar- and disk-shaped Bose and Fermi superfluids

Camilo A. G. Buitrago·S. K. Adhikari

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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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Camilo A. G. Buitrago, S. K. Adhikari. 2009-09-29. Mean-field equations for cigar- and disk-shaped Bose and Fermi superfluids. https://arxiv.org/abs/0909.5380

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