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

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

2009-09-29

arxiv.org/abs/0909.5380v1

J. Phys. B 42 (2009) 215306

Physics

Condensed Matter

Quantum Gases

13 pages

Scientific paper

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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