Quantitative test of mean-field description of a trapped two-dimensional Bose gas

TL;DR

This paper evaluates the accuracy of two mean-field theories in predicting the properties of a trapped two-dimensional Bose gas, comparing them with non-perturbative classical field calculations across various parameters.

Contribution

It provides a quantitative assessment of mean-field theories' accuracy in describing 2D Bose gases near the transition region, validated against non-perturbative methods.

Findings

Mean-field theories show varying accuracy depending on parameters.

Density profiles are well-predicted in certain regimes.

Transition temperature predictions have notable deviations.

Abstract

We investigate the accuracy of two mean-field theories of the trapped two-dimensional Bose gas at predicting transition region properties by comparison to non-perturbative classical field calculations. To make these comparisons we examine the density profiles and the predictions for the Berezinskii-Kosterlitz-Thouless superfluid transition temperature over a parameter range in which the degree of thermal activation in the tightly trapped direction varies considerably. These results present an important test of these mean-field theories, and provide a characterization of their typical accuracy.