Variational self-consistent theory for trapped Bose gases at finite temperature

TL;DR

This paper develops a variational self-consistent theoretical framework for trapped Bose gases at finite temperature, providing insights into density distributions and many-body effects with good experimental agreement.

Contribution

It introduces a time-dependent variational approach to derive coupled equations for condensate, thermal cloud, and anomalous densities in trapped Bose gases.

Findings

Qualitative agreement with recent experimental data

Analysis of density profiles as functions of temperature

Discussion of anomalous density behavior at low temperatures

Abstract

We apply the time-dependent variational principle of Balian-V\'en\'eroni to a system of self-interacting trapped bosons at finite temperature. The method leads to a set of coupled non-linear time dependent equations for the condensate density, the thermal cloud and the anomalous density. We solve numerically these equations in the static case for a harmonic trap. We analyze the various densities as functions of the radial distance and the temperature. We find an overall good qualitative agreement with recent experiments as well as with the results of many theoretical groups. We also discuss the behavior of the anomalous density at low temperatures owing to its importance to account for many-body effects.