Critical Temperature of Bose-Einstein Condensation of Hard Sphere Gases

TL;DR

This paper uses Monte Carlo simulations to determine how repulsive interactions affect the critical temperature of Bose-Einstein condensation in hard-sphere gases, revealing a density-dependent increase at low densities and behavior similar to liquid helium at high densities.

Contribution

It provides the first detailed numerical analysis of the critical temperature shift due to interactions in 3D hard-sphere Bose gases using path-integral Monte Carlo methods.

Findings

Critical temperature increases with density at low densities following a power law with exponent 1/3.

At high densities, the critical temperature is lower than the non-interacting case, matching liquid helium behavior.

A microscopic explanation for the observed temperature shifts is provided.

Abstract

We determine the critical temperature of a 3-d homogeneous system of hard-sphere Bosons by path-integral Monte Carlo simulations and finite-size scaling. At low densities, we find that the critical temperature is increased by the repulsive interactions, in the form of a power law in density with exponent 1/3: $\Delta T_C/T_0\sim (na^3)^{1/3}$. At high densities the result for liquid helium, namely a lower critical temperature than in the non-interacting case, is recovered. We give a microscopic explanation for the observed behavior.