Boundary Effects on Bose-Einstein Condensation in Ultra-Static Space-Times

TL;DR

This paper investigates how boundary conditions influence Bose-Einstein condensation in an ultra-static space-time, focusing on high-temperature behavior and the effects of boundaries on thermodynamic properties for both charged and neutral bosons.

Contribution

It provides a detailed analysis of boundary effects on Bose-Einstein condensation using heat kernel expansion and Mellin transform methods in relativistic gases.

Findings

Boundary conditions significantly affect the depletion coefficient.

High temperature expansion reveals boundary influence on thermodynamic relations.

Differences observed between Dirichlet and Neumann boundary conditions.

Abstract

The boundary effects on the Bose-Einstein condensation of a Bose gas with a nonvanishing chemical potential on an ultra-static space-time are studied. High temperature regime, which is the relevant regime for the relativistic gas, is studied through the heat kernel expansion for both Dirichlet and Neumann boundary conditions. The high temperature expansion in the presence of a chemical potential is generated via the Mellin transform methods as applied to the harmonic sums representing the free energy and the depletion coefficient. The effects of boundary conditions on the relation between depletion coefficient and temperature are analyzed. The analysis is done for both charged and neutral bosons.