The Bose gas beyond mean field

TL;DR

This paper analytically investigates a homogeneous Bose gas with repulsive interactions beyond mean-field approximation, revealing how these forces modify thermodynamic properties and momentum distribution in the low-density regime.

Contribution

It derives the form of thermodynamic functions for small interaction scales, providing the first analytical correction to mean-field theory for such Bose gases.

Findings

Repulsive forces increase pressure at fixed density.

They decrease density at fixed chemical potential.

They flatten the Bose momentum distribution.

Abstract

We study a homogeneous Bose gas with purely repulsive forces. Using the Kac scaling of the binary potential we derive analytically the form of the thermodynamic functions of the gas for small but finite values of the scaling parameter in the low density regime. In this way we determine dominant corrections to the mean-field theory. It turns out that repulsive forces increase the pressure at fixed density and decrease the density at given chemical potential (the temperature is kept constant). They also flatten the Bose momentum distribution. However, the present analysis cannot be extended to the region where the mean-field theory predicts the appearence of condensate.