zeta-function regularization and the interacting Bose gas at low temperature

TL;DR

This paper applies zeta-function regularization to analyze the thermodynamic properties of the interacting Bose gas at low temperatures, providing general results for energy and pressure without interaction restrictions.

Contribution

It introduces a general zeta-function approach to study the Bose gas and extends it to binary mixtures with analytical solutions for equal-mass species.

Findings

Ground state energy and pressure calculated at zero and finite temperature.

Method applicable to general interaction forms.

Analytical results for binary mixtures with equal masses.

Abstract

zeta-function methods are used to study the properties of the non-relativistic interacting Bose gas at finite temperature and density. Results for the ground state energy and pressure are obtained at both zero and finite temperature. The method used does not restrict the form of the interaction, which can be completely general. A similar procedure is then applied to evaluate the ground state energy of a binary mixture consisting of different bosons. Analytical results are obtained in the case where the two species have the same mass.