Condensate density and superfluid mass density of a dilute Bose gas near the condensation transition

TL;DR

This paper analyzes the critical behavior of condensate and superfluid densities in a dilute Bose gas near the transition temperature, revealing the breakdown of mean field theory and deriving the critical exponent for the condensate fraction.

Contribution

It provides a detailed scaling analysis near the transition, showing the breakdown of mean field theory and calculating the critical exponent using a self-consistent two-loop approach.

Findings

Condensate and superfluid densities share similar scaling functions below $T_c$.

Mean field theory breaks down close to the critical temperature.

Critical exponent for the condensate fraction is approximately 0.66.

Abstract

We derive, through analysis of the structure of diagrammatic perturbation theory, the scaling behavior of the condensate and superfluid mass density of a dilute Bose gas just below the condensation transition. Sufficiently below the critical temperature, $T_c$, the system is governed by the mean field (Bogoliubov) description of the particle excitations. Close to $T_c$, however, mean field breaks down and the system undergoes a second order phase transition, rather than the first order transition predicted in Bogoliubov theory. Both condensation and superfluidity occur at the same critical temperature, $T_c$ and have similar scaling functions below $T_c$, but different finite size scaling at $T_c$ to leading order in the system size. Through a simple self-consistent two loop calculation we derive the critical exponent for the condensate fraction, $2\beta\simeq 0.66$.