Bose-Einstein Condensation on Product Manifolds

TL;DR

This paper studies Bose-Einstein condensation on product manifolds combining 3D Euclidean space with compact manifolds, calculating thermodynamic properties using spectral zeta-function methods under experimental confinement conditions.

Contribution

It introduces a spectral zeta-function approach to explicitly compute thermodynamic quantities for Bose gases on product manifolds with boundary and confinement.

Findings

Explicit formulas for critical temperature and specific heat.

Application of spectral zeta-functions to condensed matter systems.

Analysis of Bose-Einstein condensation in complex geometries.

Abstract

We investigate the phenomenon of Bose-Einstein condensation on manifolds constructed as a product of a three-dimensional Euclidian space and a general smooth, compact $d$-dimensional manifold possibly with boundary. By using spectral $\zeta$-function methods, we are able to explicitly provide thermodynamical quantities like the critical temperature and the specific heat when the gas of bosons is confined, in the three-dimensional manifold, by the experimentally relevant anisotropic harmonic oscillator potential.