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

TL;DR

This paper derives effective 1D and 2D mean-field equations for cigar- and disk-shaped Bose and Fermi superfluids from 3D equations, accurately capturing their dynamics and stationary properties.

Contribution

It introduces simplified mean-field equations for anisotropic superfluids, enabling efficient analysis of their behavior with high accuracy compared to full 3D models.

Findings

Derived analytic nonlinear terms for reduced equations.

Achieved excellent agreement with 3D solutions for stationary and dynamic properties.

Validated equations through comparison with full 3D simulations.

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.