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Microcanonical fluctuations of the condensate in weakly interacting Bose gases

Zbigniew Idziaszek
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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.

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Zbigniew Idziaszek. 2005-01-25. Microcanonical fluctuations of the condensate in weakly interacting Bose gases. https://doi.org/10.1103/physreva.71.053604

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