On Bose-Einstein Condensation in any Dimension

TL;DR

This paper explores Bose-Einstein condensation across all dimensions, revealing that large ground state populations occur under degeneracy conditions, with unique behaviors in one and two dimensions, and discusses implications for astrophysics and temperature-dependent mass scenarios.

Contribution

It provides a microscopic analysis of Bose-Einstein condensation in arbitrary dimensions, including finite systems and astrophysical implications, extending understanding beyond traditional three-dimensional cases.

Findings

Condensation occurs at any dimension D under degeneracy.

In 1D, the condensation is diffuse.

In 2D, it manifests as a quasi-condensate.

Abstract

Arbitrarily large ground state population is a general property of any ideal bose gas when conditions of degeneracy are satisfied; it occurs at any dimension D. For $D = 1$, the condensation is diffuse, at $D = 2$ it is a sort of quasi-condensate. The discussion is made by following a microscopic approach and for finite systems. Some astrophysical consequences are discussed, as well as the temperature-dependent mass case.