Theory of Bose-Einstein condensation for trapped atoms

TL;DR

This paper reviews the mean-field theory of Bose-Einstein condensates, highlights its limitations, and proposes a more rigorous microscopic approach along with considerations for finite-temperature extensions.

Contribution

It introduces a new microscopic formalism for Bose-Einstein condensates and discusses the development of a consistent finite-temperature mean-field theory.

Findings

Conventional mean-field theory aligns well with experiments but lacks rigor.

A new microscopic approach captures collisional dynamics more accurately.

Finite-temperature theory requires analysis beyond traditional mean-field methods.

Abstract

We outline the general features of the conventional mean-field theory for the description of Bose-Einstein condensates at near zero temperatures. This approach, based on a phenomenological model, appears to give excellent agreement with experimental data. We argue, however, that such an approach is not rigorous and cannot contain the full effect of collisional dynamics due to the presence of the mean-field. We thus discuss an alternative microscopic approach and explain, within our new formalism, the physical origin of these effects. Furthermore, we discuss the potential formulation of a consistent finite-temperature mean-field theory, which we claim necessiates an analysis beyond the conventional treatment.