1/N-Expansion and the Dilute Bose Gas Beyond Mean-field Theory

TL;DR

This paper applies the 1/N-expansion method to analyze the dilute Bose gas at various temperatures, deriving expressions beyond mean-field theory and confirming known critical densities for Bose condensation.

Contribution

It extends the analysis of the dilute Bose gas beyond mean-field approximation using the 1/N-expansion at finite temperature.

Findings

Derived free energy and number density expressions to next-to-leading order in 1/N.

Reproduced the known critical density for Bose condensation.

Validated the 1/N-expansion approach outside the critical region at weak coupling.

Abstract

We consider the nonrelativistic interacting Bose gas at zero and finite temperature. Using the 1/N-expansion, we derive expressions for the free energy density and the number density to next-to-leading order in 1/N. Outside the critical region and at weak coupling, our calculations reduce to the well-known mean-field results for the dilute Bose gas. We also rederive the nonperturbative critical density for Bose condensation which was first calculated by Baym, Blaizot, Holzmann, Lal\"oe, and Vautherin.