Two-Fluid Hydrodynamics for a Trapped Weakly-Interacting Bose Gas

TL;DR

This paper derives coupled two-fluid hydrodynamic equations for a trapped weakly-interacting Bose gas at finite temperatures, providing a microscopic foundation for collective modes including second sound.

Contribution

It presents a derivation of two-fluid equations for trapped Bose gases using the Hartree-Fock-Popov approximation, extending Landau's theory to inhomogeneous systems.

Findings

Derivation of coupled equations of motion for condensate and non-condensate.

Identification of collective modes including second sound in trapped gases.

Microscopic basis for two-fluid hydrodynamics in inhomogeneous Bose systems.

Abstract

We derive the coupled equations of motion for the condensate (superfluid) and non-condensate (normal fluid) degrees of freedom in a trapped Bose gas at finite temperatures. Our results are based on the Hartree-Fock-Popov approximation for the time-dependent condensate wavefunction and an assumption of local equilibrium for the non-condensate atoms. In the case of a uniform weakly-interacting gas, our formalism gives a microscopic derivation of the well-known two-fluid equations of Landau. The collective modes in a parabolically trapped Bose gas include the analogue of the out-of-phase second sound mode in uniform systems.