Transition Temperature of Dilute, Weakly Repulsive Bose Gas

TL;DR

This paper investigates how the Bose-Einstein condensation temperature in a dilute, weakly interacting Bose gas depends on the scattering length, revealing that $T_c$ increases with $a$ and exploring different regularization methods.

Contribution

It introduces two approaches to regularize infrared divergence and compute the shift in $T_c$ due to weak interactions in a Bose gas.

Findings

$T_c$ increases with scattering length $a$

One method yields a $a\sqrt{| ext{ln}a|}$-like shift in $T_c$

Numerical calculations of the shift are performed

Abstract

Within a quasiparticle framework, we reconsider the issue of computing the Bose-Einstein condensation temperature ($T_c$) in a weakly non-ideal Bose gas. The main result of this and previous investigations is that $T_c$ increases with the scattering length $a$, with the leading dependence being either linear or log-linear in $a$. The calculation of $T_c$ reduces to that of computing the excitation spectrum near the transition. We report two approaches to regularizing the infrared divergence at the transition point. One leads to a $a\sqrt{|\ln{a}|}$-like shift in $T_c$, and the other allows numerical calculations for the shift.