Thermodynamics of ideal Bose gas under generic power law potential in $d$-dimension

TL;DR

This paper systematically analyzes the thermodynamic behavior of an ideal Bose gas in arbitrary dimensions under a generic power law potential, deriving conditions for Bose-Einstein condensation and heat capacity discontinuities.

Contribution

It provides a unified framework for understanding Bose-Einstein condensation in various potentials and dimensions, extending previous results to more general conditions.

Findings

Conditions for Bose-Einstein condensation in generic potentials

Discontinuity of heat capacity at critical temperature

Dependence of thermodynamic quantities on potential, particles, and dimension

Abstract

Thermodynamic properties of ideal Bose gas trapped in an external generic power law potential are investigated systematically from the grand thermodynamic potential in $d$ dimensional space. The most general conditions for Bose-Einstein condensate and the discontinuous conditions of heat capacity at the critical temperature in presence of generic power law potential are presented in this manuscript. The dependence of the physical quantities on external potential, particle characteristics and space dimensionality are discussed. The more general results obtained in this paper presents an unified illustration of Bose-Einstein condensation of ideal Bose systems as they reduces to the expressions and conclusions available in the literature with appropiate choice of power law exponent.