Transition Temperature of a Uniform Imperfect Bose Gas

TL;DR

This paper calculates the transition temperature of a uniform dilute Bose gas with repulsive interactions, finding it higher than the ideal case, but contradicting previous analytical and numerical results.

Contribution

It introduces a new calculation of the transition temperature using virial expansion, revealing a discrepancy with existing results and providing an alternative perspective.

Findings

Transition temperature is increased by a fractional amount proportional to (na^3)^{1/6}.

The result disagrees with all existing analytical and numerical findings.

The calculated magnitude matches Toyoda's result but with opposite sign.

Abstract

We calculate the transition temperature of a uniform dilute Bose gas with repulsive interactions, using a known virial expansion of the equation of state. We find that the transition temperature is higher than that of an ideal gas, with a fractional increase K_0(na^3)^{1/6}, where n is the density and a is the S-wave scattering length, and K_0 is a constant given in the paper. This disagrees with all existing results, analytical or numerical. It agrees exactly in magnitude with a result due to Toyoda, but has the opposite sign.