The transition temperature of the dilute interacting Bose gas

TL;DR

This paper investigates how the critical temperature of a dilute Bose gas increases linearly with the s-wave scattering length, using a self-consistent approach to account for infrared divergences and comparing results with numerical simulations.

Contribution

It introduces a non-perturbative method to estimate the shift in critical temperature due to interactions in a dilute Bose gas.

Findings

Critical temperature increases linearly with scattering length.

Infrared divergences prevent perturbative calculation of the shift.

Self-consistent quasiparticle spectrum aligns with numerical results.

Abstract

We show that the critical temperature of a uniform dilute Bose gas must increase linearly with the s-wave scattering length describing the repulsion between the particles. Because of infrared divergences, the magnitude of the shift cannot be obtained from perturbation theory, even in the weak coupling regime; rather, it is proportional to the size of the critical region in momentum space. By means of a self-consistent calculation of the quasiparticle spectrum at low momenta at the transition, we find an estimate of the effect in reasonable agreement with numerical simulations.