Bose-Einstein Condensation of Confined and Non-interacting Bose Particles by the Integral Representation of Bose Functions

TL;DR

This paper investigates Bose-Einstein condensation of non-interacting bosons in a 3D harmonic trap using integral representations of Bose functions, clarifying the relation between particle number and transition temperature, and comparing thermodynamic properties.

Contribution

It introduces an integral representation approach to analyze Bose-Einstein condensation, providing new insights and confirming results with series representations.

Findings

Relation between particle number and transition temperature clarified

Next-order thermodynamic terms derived

Properties closely match series representation results

Abstract

With the integral representation of Bose functions, the Bose-Einstein condensation of non-interacting bosons in a three-dimensional harmonic trap was studied. The relation between the particle number and its phase transition temperature was clarified. Some next-order terms in the thermodynamic expansions were obtained. We plotted the chemical potential, the mean energy, and the specific heat and found most of these properties obtained by using the integral representation were almost identical with those of the series representation of Bose functions.