Transition temperature and thermodynamic properties of homogeneous weakly interacting Bose gas in self-consistent Popov approximation

TL;DR

This paper investigates the shift in transition temperature and thermodynamic properties of a weakly interacting Bose gas using the Popov approximation, aligning well with Monte Carlo simulations and experimental data.

Contribution

It derives a universal formula for the transition temperature shift in a weakly interacting Bose gas using the Popov approximation, validated by simulations and experiments.

Findings

The transition temperature shift is proportional to the s-wave scattering length.

Results agree with Monte Carlo simulation data.

Thermodynamic properties match experimental observations.

Abstract

This study utilizes the Cornwall-Jackiw-Tomboulis effective action approach combined with variational perturbation theory to investigate the relative shift in the transition temperature of a homogeneous, repulsive, weakly interacting Bose gas compared to that of an ideal Bose gas. By applying both the one-loop and self-consistent Popov approximations, the universal form of the relative shift in the transition temperature is derived, demonstrating its proportionality to the s-wave scattering length. The results exhibit excellent agreement with those obtained from precise Monte Carlo simulations. Furthermore, the zero-point energy and various thermodynamic properties are examined in both the condensed and normal phases. A comparison with experimental data reveals an excellent agreement, further validating the findings.