Classical Region of a Trapped Bose Gas

TL;DR

This paper characterizes the classical region of a harmonically trapped Bose gas across various parameters, using Hartree-Fock theory to account for interactions and comparing with classical field calculations.

Contribution

It introduces a Hartree-Fock based method to analyze the classical region of an interacting Bose gas, extending understanding beyond idealized models.

Findings

Interactions significantly alter the classical region.

Hartree-Fock approach qualitatively matches classical field results.

Classical region depends on temperature, particle number, and interaction strength.

Abstract

The classical region of a Bose gas consists of all single-particle modes that have a high average occupation and are well-described by a classical field. Highly-occupied modes only occur in massive Bose gases at ultra-cold temperatures, in contrast to the photon case where there are highly-occupied modes at all temperatures. For the Bose gas the number of these modes is dependent on the temperature, the total number of particles and their interaction strength. In this paper we characterize the classical region of a harmonically trapped Bose gas over a wide parameter regime. We use a Hartree-Fock approach to account for the effects of interactions, which we observe to significantly change the classical region as compared to the idealized case. We compare our results to full classical field calculations and show that the Hartree-Fock approach provides a qualitatively accurate description of classical region for the interacting gas.