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Condensate Fluctuations in Trapped Bose Gases: Canonical vs. Microcanonical Ensemble

Martin Holthaus·Eva Kalinowski·Klaus Kirsten
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Abstract

We study the fluctuation of the number of particles in ideal Bose-Einstein condensates, both within the canonical and the microcanonical ensemble. Employing the Mellin-Barnes transformation, we derive simple expressions that link the canonical number of condensate particles, its fluctuation, and the difference between canonical and microcanonical fluctuations to the poles of a Zeta function that is determined by the excited single-particle levels of the trapping potential. For the particular examples of one- and three-dimensional harmonic traps we explore the microcanonical statistics in detail, with the help of the saddle-point method. Emphasizing the close connection between the partition theory of integer numbers and the statistical mechanics of ideal Bosons in one-dimensional harmonic traps, and utilizing thermodynamical arguments, we also derive an accurate formula for the fluctuation of the number of summands that occur when a large integer is partitioned.

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Martin Holthaus, Eva Kalinowski, Klaus Kirsten. 1998-04-16. Condensate Fluctuations in Trapped Bose Gases: Canonical vs. Microcanonical Ensemble. https://doi.org/10.1006/aphy.1998.5852

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