Theory of excitations of the condensate and non-condensate at finite temperatures

TL;DR

This paper reviews the theoretical understanding of collective excitations in trapped atomic Bose gases at finite temperatures, emphasizing the dynamics of both condensate and non-condensate components using quantum field methods.

Contribution

It provides a comprehensive overview of the current theoretical framework, including quantum field formulation and hydrodynamic equations, for excitations in Bose-condensed gases at finite temperatures.

Findings

Analysis of collective modes in the collisionless regime

Application of Beliaev second-order approximation

Derivation of two-fluid hydrodynamic equations

Abstract

We give an overview of the current theory of collective modes in trapped atomic gases at finite temperatures, when the dynamics of the condensate and non-condensate must both be considered. A simple introduction is given to the quantum field formulation of the dynamics of an interacting Bose-condensed system, based on equations of motion for the condensate wavefunction and single-particle Green's functions for the non-condensate atoms. We discuss the nature of excitations in the mean-field collisionless region, including the Beliaev second-order approximation for the self-energies. We also sketch the derivation of coupled two-fluid hydrodynamic equations using a simple kinetic equation which includes collisions between condensate and non-condensate atoms.