Bose-Einstein condensation in arbitrarily shaped cavities

TL;DR

This paper analyzes how the shape and size of a cavity influence Bose-Einstein condensation of an ideal Bose gas, focusing on thermodynamical properties and critical temperature using spectral and integral methods.

Contribution

It introduces two equivalent methods to evaluate the thermodynamics of Bose gases in arbitrarily shaped cavities, emphasizing the impact of cavity geometry on condensation.

Findings

Finite cavity size affects critical temperature.

Spectral analysis provides accurate density of states.

Asymptotic formulas derived for simple cavity shapes.

Abstract

We discuss the phenomenon of Bose-Einstein condensation of an ideal non-relativistic Bose gas in an arbitrarily shaped cavity. The influence of the finite extension of the cavity on all thermodynamical quantities, especially on the critical temperature of the system, is considered. We use two main methods which are shown to be equivalent. The first deals with the partition function as a sum over energy levels and uses a Mellin-Barnes integral representation to extract an asymptotic formula. The second method converts the sum over the energy levels to an integral with a suitable density of states factor obtained from spectral analysis. The application to some simple cavities is discussed.