On the theory of Bose-condensate fluctuations in finite size systems

TL;DR

This paper derives asymptotic formulas for Bose-condensate fluctuations in finite systems, valid across all temperatures including the critical point, and confirms their accuracy against exact calculations.

Contribution

It provides a comprehensive asymptotic expansion for the grand partition function of an ideal Bose gas in the canonical ensemble, valid for any particle number and temperature.

Findings

Asymptotic formulas agree quantitatively with exact fluctuations

Formulas are valid across the entire temperature range, including the critical point

Enhances understanding of finite-size effects in Bose-Einstein condensation

Abstract

An asymptotic expansions for the grand partition function of ideal Bose gas in the canonical ensemble with arbitrary number of particles is obtained. It is shown that the expressions found are valid in the whole temperature region, the critical temperature included. A comparison between the asymptotic formulas for Bose-condensate fluctuations and the exact ones is carried out and their quantitative agreement is established.