Collisionless dynamics of dilute Bose gases: Role of quantum and thermal fluctuations

TL;DR

This paper investigates the effects of quantum and thermal fluctuations on the collective oscillations of dilute Bose gases at finite temperature, extending mean-field theory to include fluctuation corrections and analyzing mode behaviors.

Contribution

It introduces a second-order perturbative approach to include quantum and thermal fluctuations in the dynamics of dilute Bose gases, extending the finite-temperature Beliaev approximation.

Findings

Calculated temperature dependence of zero sound velocity and damping rate.

Determined frequency shifts of low-energy modes in trapped systems.

Extended mean-field theory to include fluctuation effects.

Abstract

We study the low-energy collective oscillations of a dilute Bose gas at finite temperature in the collisionless regime. By using a time-dependent mean-field scheme we derive for the dynamics of the condensate and noncondensate components a set of coupled equations, which we solve perturbatively to second order in the interaction coupling constant. This approach is equivalent to the finite-temperature extension of the Beliaev approximation and includes corrections to the Gross-Pitaevskii theory due both to quantum and thermal fluctuations. For a homogeneous system we explicitly calculate the temperature dependence of the velocity of propagation and damping rate of zero sound. In the case of harmonically trapped systems in the thermodynamic limit, we calculate, as a function of temperature, the frequency shift of the low-energy compressional and surface modes.