Maxwell's Demon at work: Two types of Bose condensate fluctuations in power-law traps

TL;DR

This paper investigates Bose condensate fluctuations in power-law traps using Maxwell's Demon ensemble, revealing two fluctuation behaviors depending on heat capacity discontinuity at the transition.

Contribution

It introduces a unified integral approach to analyze condensate fluctuations in different trap types, distinguishing fluctuation behaviors based on heat capacity properties.

Findings

Fluctuations vanish linearly with temperature when heat capacity is continuous.

Fluctuations vanish algebraically with temperature when heat capacity is discontinuous.

The method applies to both canonical and microcanonical ensembles.

Abstract

After discussing the key idea underlying the Maxwell's Demon ensemble, we employ this idea for calculating fluctuations of ideal Bose gas condensates in traps with power-law single-particle energy spectra. Two essentially different cases have to be distinguished. If the heat capacity remains continuous at the condensation point in the large-N-limit, the fluctuations of the number of condensate particles vanish linearly with temperature, independent of the trap characteristics. If the heat capacity becomes discontinuous, the fluctuations vanish algebraically with temperature, with an exponent determined by the trap. Our results are based on an integral representation that yields the solution to both the canonical and the microcanonical fluctuation problem in a singularly transparent manner.