Systematic Semiclassical Expansion for Harmonically Trapped Ideal Bose Gases

TL;DR

This paper develops a generalized semiclassical method for harmonically trapped ideal Bose gases, enabling analytical calculations of thermodynamic properties for small particle numbers and low-dimensional traps, where previous methods failed.

Contribution

It introduces a systematic extension of the semiclassical approximation, broadening its applicability to small systems and low-dimensional traps.

Findings

Analytical expressions for critical temperature derived

Temperature dependence of heat capacity calculated

Condensate fraction behavior characterized

Abstract

Using a field-theoretic approach, we systematically generalize the usual semiclassical approximation for a harmonically trapped ideal Bose gas in such a way that its range of applicability is essentially extended. With this we can analytically calculate thermodynamic properties even for small particle numbers. In particular, it now becomes possible to determine the critical temperature as well as the temperature dependence of both heat capacity and condensate fraction in low-dimensional traps, where the standard semiclassical approximation is not even applicable.