Ideal Quantum Gases in D-dimensional Space and Power-law Potentials

TL;DR

This paper derives properties like density of states and critical temperatures for ideal quantum gases in D-dimensional space with power-law potentials, revealing conditions for Bose-Einstein condensation.

Contribution

It provides a general semiclassical framework for analyzing quantum gases in arbitrary power-law traps across multiple dimensions.

Findings

Density of states and profiles derived for D-dimensional power-law potentials.

Critical temperatures for Bose-Einstein condensation established.

Condensation occurs if and only if D/2 + D/n > 1.

Abstract

We investigate ideal quantum gases in D-dimensional space and confined in a generic external potential by using the semiclassical approximation. In particular, we derive density of states, density profiles and critical temperatures for Fermions and Bosons trapped in isotropic power-law potentials. Form such results, one can easily obtain those of quantum gases in a rigid box and in a harmonic trap. Finally, we show that the Bose-Einstein condensation can set up in a confining power-law potential if and only if ${D/2}+{D/n}>1$, where $D$ is the space dimension and $n$ is the power-law exponent.