Investigation of Bose condensation in ideal Bose gas trapped under generic power law potential in $d$ dimension

TL;DR

This paper analyzes how Bose condensation characteristics change for an ideal Bose gas under a generic power law potential in arbitrary dimensions, revealing a hidden hierarchy of phase transitions.

Contribution

It presents new theorems about specific heat and uncovers a hidden hierarchy of Bose condensation transitions in trapped systems.

Findings

Hierarchy of condensation transitions identified

Theorems on specific heat at constant volume derived

Hidden phase transition hierarchy revealed

Abstract

The changes in characteristics of Bose condensation of ideal Bose gas due to an external generic power law potential $U=\sum_{i=1} ^d c_i |\frac{x_i}{a_i}|^{n_i}$ are studied carefully. Detailed calculation of Kim $et$ $al.$ (S. H. Kim, C. K. Kim and K. Nahm, J Phys. Condens. Matter 11 10269 (1999).) yielded the hierarchy of condensation transitions with changing fractional dimensionality. In this manuscript, some theorems regarding specific heat at constant volume $C_V$ are presented. Careful examination of these theorems reveal the existence of hidden hierarchy of the condensation transition in trapped systems as well.