Comparative studies of many-body corrections to an interacting Bose condensate

TL;DR

This paper compares various many-body theoretical approaches to fluctuation corrections in a weakly interacting Bose condensate, assessing their impact on transition temperature, phase transition order, and key identities.

Contribution

It introduces a comprehensive comparison of fluctuation effects using generalized RPA and T-matrix approximations, addressing a longstanding problem in cold atom physics.

Findings

Density and particle-particle fluctuation effects differ significantly.

Some approximations satisfy the Nepomnyashchii-Nepomnyashchii identity.

Transition temperature predictions vary across methods.

Abstract

We compare many-body theories describing fluctuation corrections to the mean-field theory in a weakly interacting Bose-condensed gas. Using a generalized random-phase approximation, we include both density fluctuations and fluctuations in the particle-particle scattering channel in a consistent manner. We also separately examine effects of the fluctuations within the framework of the random-phase approximation. Effects of fluctuations in the particle-particle scattering channel are also separately examined by using the many-body T-matrix approximation. We assess these approximations with respect to the transition temperature, the order of phase transition, as well as the so-called Nepomnyashchii-Nepomnyashchii identity, which states the vanishing off-diagonal self-energy in the low-energy and low-momentum limit. Since the construction of a consistent theory for interacting bosons which satisfies various required conditions is a long standing problem in cold atom physics, our results would be useful for this important challenge.