Modified semiclassical approximation for trapped Bose gases

TL;DR

This paper introduces a generalized semiclassical approximation that extends its applicability to low-dimensional trapped Bose gases, accurately describing Bose-Einstein condensation and thermodynamic properties where standard methods fail.

Contribution

A modified semiclassical approach is proposed, enabling analysis of Bose gases in low-dimensional traps and providing results consistent with quantum calculations.

Findings

Agreement with quantum calculations for harmonic traps.

Effective thermodynamic limit defined for any confining dimension.

Analysis of thermodynamic properties in low-dimensional traps.

Abstract

A generalization of the semiclassical approximation is suggested allowing for an essential extension of its region of applicability. In particular, it becomes possible to describe Bose-Einstein condensation of a trapped gas in low-dimensional traps and in traps of low confining dimensions, for which the standard semiclassical approximation is not applicable. The results of the modified approach are shown to coincide with purely quantum-mechanical calculations for harmonic traps, including the one-dimensional harmonic trap. The advantage of the semiclassical approximation is in its simplicity and generality. Power-law potentials of arbitrary powers are considered. Effective thermodynamic limit is defined for any confining dimension. The behaviour of the specific heat, isothermal compressibility, and density fluctuations is analyzed, with an emphasis on low confining dimensions, where the usual semiclassical method fails. The peculiarities of the thermodynamic characteristics in the effective thermodynamic limit are discussed.