Hybridization of first and second sound in a weakly-interacting Bose gas

TL;DR

This paper explores the hybridization of first and second sound modes in a weakly-interacting Bose gas across various temperatures, combining hydrodynamic theory with thermodynamic calculations to analyze sound velocity behaviors near the hybridization point.

Contribution

It introduces a comprehensive analysis of sound mode hybridization in a Bose gas using Landau's two-fluid hydrodynamics combined with thermodynamic functions from Bogoliubov and Beliaev theories.

Findings

Identification of hybridization between first and second sound at low temperatures.

Detailed behavior of sound velocities near the hybridization point.

Temperature dependence of superfluid density and sound modes.

Abstract

Using Landau's theory of two-fluid hydrodynamics we investigate the sound modes propagating in a uniform weakly-interacting superfluid Bose gas for values of temperature, up to the critical point. In order to evaluate the relevant thermodynamic functions needed to solve the hydrodynamic equations, including the temperature dependence of the superfluid density, we use Bogoliubov theory at low temperatures and the results of a perturbative approach based on Beliaev diagrammatic technique at higher temperatures. Special focus is given on the hybridization phenomenon between first and second sound which occurs at low temperatures of the order of the interaction energy and we discuss explicitly the behavior of the two sound velocities near the hybridization point.