Condensation of N interacting bosons: Hybrid approach to condensate fluctuations

TL;DR

This paper introduces a hybrid theoretical method to accurately compute fluctuations and distribution functions in Bose-Einstein condensates of interacting bosons, applicable across temperature ranges.

Contribution

A novel approach combining master equation and quasiparticle techniques for precise analysis of BEC fluctuations in both ideal and interacting cases.

Findings

Accurately models condensate fluctuations at all temperatures.

Demonstrates smooth transition of condensate particle number through critical temperature.

Validates method with comparison to ideal gas results.

Abstract

We present a new method of calculating the distribution function and fluctuations for a Bose-Einstein condensate (BEC) of N interacting atoms. The present formulation combines our previous master equation and canonical ensemble quasiparticle techniques. It is applicable both for ideal and interacting Bogoliubov BEC and yields remarkable accuracy at all temperatures. For the interacting gas of 200 bosons in a box we plot the temperature dependence of the first four central moments of the condensate particle number and compare the results with the ideal gas. For the interacting mesoscopic BEC, as with the ideal gas, we find a smooth transition for the condensate particle number as we pass through the critical temperature.