Transition temperature of the homogeneous imperfect Bose gas

TL;DR

This paper investigates how interactions affect the transition temperature of a homogeneous dilute Bose gas using advanced field-theoretic methods, revealing a universal linear correction related to scattering length.

Contribution

It introduces a novel analysis of the transition temperature shift using Cornwall-Jackiw-Tomboulis formalism within the improved Hartree-Fock approximation, highlighting a universal linear correction.

Findings

The transition temperature shift is linear in the scattering length.

The slope matches previous numerical results.

Non-universal terms also contribute to the shift.

Abstract

Beyond standard approaches in existing literature, we explore the relative shift in the transition temperature of a homogeneous dilute Bose gas using the Cornwall-Jackiw-Tomboulis effective action formalism within the improved Hartree-Fock approximation. The first correction to the enhancement of the transition temperature, as compared to that of the ideal Bose gas, is expressed in a universal form: it is linear with respect to the scattering length. The slope of this linear relationship shows excellent agreement with the exact numerical calculations presented in previous studies. Additionally, we identify non-universal terms contributing to the shift.