Microcanonical fluctuations of the condensate in weakly interacting Bose gases

TL;DR

This paper investigates the fluctuations of Bose condensate atoms in weakly interacting gases, showing ensemble equivalence in the thermodynamic limit and contrasting behavior with ideal gases.

Contribution

It provides a particle-number-conserving analysis of condensate fluctuations in both homogeneous and trapped weakly interacting Bose gases, highlighting ensemble equivalences and differences.

Findings

Microcanonical and canonical fluctuations are equivalent in the thermodynamic limit for interacting gases.

Predictions of traditional and particle-number-conserving theories agree at low temperatures.

Contrasts with ideal gases where fluctuations differ in the thermodynamic limit.

Abstract

We study fluctuations of the number of Bose condensed atoms in weakly interacting homogeneous and trapped gases. For a homogeneous system we apply the particle-number-conserving formulation of the Bogoliubov theory and calculate the condensate fluctuations within the canonical and the microcanonical ensembles. We demonstrate that, at least in the low-temperature regime, predictions of the particle-number-conserving and traditional, nonconserving theory are identical, and lead to the anomalous scaling of fluctuations. Furthermore, the microcanonical fluctuations differ from the canonical ones by a quantity which scales normally in the number of particles, thus predictions of both ensembles are equivalent in the thermodynamic limit. We observe a similar behavior for a weakly interacting gas in a harmonic trap. This is in contrast to the trapped, ideal gas, where microcanonical and canonical fluctuations are different in the thermodynamic limit.