Bose-Einstein condensation in generalised d dimensions

TL;DR

This paper investigates Bose-Einstein condensation in systems with arbitrary dimensions, revealing how the condensation temperature varies with dimensionality, especially noting a sharp drop above three dimensions.

Contribution

It extends the analysis of Bose-Einstein condensation to generalized dimensions, providing insights into how dimensionality affects condensation temperature and state density.

Findings

Condensation occurs in dimensions d ≥ 3.

Condensation temperature drops sharply above three dimensions.

Temperature decreases monotonically as dimensionality increases.

Abstract

The density of bosonic states are calculated for spinless free massive bosons in generalised d dimensions. The number of bosons are calculated in the lowest energy state. The Bose Einstein condensation was found in generalised dimensions (on and above d = 3) and the condensation temperature was observed to drop abruptly above three dimensions and decreases monotonically as the dimensionalities of the system increases. The rate of fall of the condensation temperature decreases as the dimensionality increases. This article is aimed to the University graduate students.