The explicit expression of the fugacity for weakly interacting Bose and Fermi gases

TL;DR

This paper derives explicit formulas for the fugacity of weakly interacting Bose and Fermi gases in various dimensions, using advanced mathematical methods, and discusses phase transitions in Bose gases.

Contribution

It provides the first explicit expressions for fugacity in weakly interacting quantum gases using the Riemann-Hilbert boundary problem approach.

Findings

Explicit fugacity formulas for 2D and 3D gases

Analysis of Bose-Einstein condensation in hard-sphere Bose gases

Application of Riemann-Hilbert problem to quantum gases

Abstract

In this paper, we calculate the explicit expression for the fugacity for two- and three-dimensional weakly interacting Bose and Fermi gases from their equations of state in isochoric and isobaric processes, respectively, based on the mathematical result of the boundary problem of analytic functions --- the homogeneous Riemann-Hilbert problem. We also discuss the Bose-Einstein condensation phase transition of three-dimensional hard-sphere Bose gases.