Fluctuation indices for atomic systems with Bose-Einstein condensate

TL;DR

This paper introduces fluctuation indices to assess the thermodynamic stability of Bose-Einstein condensate systems, revealing stability conditions for various configurations and highlighting the absence of anomalous fluctuations in stable systems.

Contribution

It develops the concept of fluctuation indices for analyzing stability in Bose-Einstein condensates, providing new stability criteria for different trapping geometries and interactions.

Findings

Ideal uniform Bose gas is unstable thermodynamically.

Trapped gases are stable if the confining dimension exceeds two.

Interacting three-dimensional Bose condensates are stable.

Abstract

The notion of fluctuation indices, characterizing thermodynamic stability of statistical systems, is advanced. These indices are especially useful for investigating the stability of nonuniform and trapped atomic assemblies. The fluctuation indices are calculated for several systems with Bose-Einstein condensate. It is shown that: the ideal uniform Bose-condensed gas is thermodynamically unstable; trapped ideal gases are stable for the confining dimension larger than two; trapped gases, under the confining dimension two, are weakly unstable; harmonically trapped gas is stable only for the spatial dimension three; one-dimensional harmonically trapped gas is unstable; two-dimensional gas in a harmonic trap represents a marginal case, being weakly unstable; interacting nonuniform three-dimensional Bose-condensed gas is stable. There are no thermodynamically anomalous particle fluctuations in stable Bose-condensed systems.