First and second sound in a uniform Bose gas

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 Bogoliubov-Goldstone symmetry-breaking mode.