First and second sound in a uniform Bose gas

TL;DR

This paper analyzes first and second sound modes in a uniform Bose gas using derived two-fluid hydrodynamic equations, confirming their consistency with Landau's theory and linking second sound to superfluid oscillations.

Contribution

It introduces two-fluid hydrodynamic equations for a trapped Bose gas and applies them to a uniform case, connecting second sound to superfluid oscillations and Goldstone mode.

Findings

Second sound corresponds to superfluid oscillations.

Results agree with Landau's two-fluid theory.

Second sound is linked to Goldstone-Bogoliubov mode.

Abstract

We have recently derived two-fluid hydrodynamic equations for a trapped weakly-interacting Bose gas. In this paper, we use these equations to discuss first and second sound in a uniform Bose gas. These results are shown to agree with the predictions of the usual two-fluid equations of Landau when the thermodynamic functions are evaluated for a weakly-interacting gas. In a uniform gas, second sound mainly corresponds to an oscillation of the superfluid (the condensate) and is the low frequency continuation of the Goldstone-Bogoliubov symmetry-breaking mode.