Dynamics of a trapped Fermi gas in the BCS phase

TL;DR

This paper develops semiclassical transport equations for a trapped Fermi gas in the BCS phase, bridging superfluid hydrodynamics and Vlasov dynamics, and analyzes collective excitations with analytical and numerical methods.

Contribution

It introduces a unified semiclassical framework for Fermi gases in the BCS phase, applicable across temperature regimes, and demonstrates its effectiveness through analytical solutions and a proposed numerical approach.

Findings

Reproduces qualitative features of quantum calculations

Identifies temperature-dependent quadrupole mode frequencies

Shows strong Landau damping at intermediate temperatures

Abstract

We derive semiclassical transport equations for a trapped atomic Fermi gas in the BCS phase at temperatures between zero and the superfluid transition temperature. These equations interpolate between the two well-known limiting cases of superfluid hydrodynamics at zero temperature and the Vlasov equation at the critical one. The linearized version of these equations, valid for small deviations from equilibrium, is worked out and applied to two simple examples where analytical solutions can be found: a sound wave in a uniform medium and the quadrupole excitation in a spherical harmonic trap. In spite of some simplifying approximations, the main qualitative results of quantum mechanical calculations are reproduced, which are the different frequencies of the quadrupole mode at zero and the critical temperature and strong Landau damping at intermediate temperatures. In addition we suggest a numerical method for solving the semiclassical equations without further approximations.