Condensate Fluctuations in Trapped Bose Gases: Canonical vs. Microcanonical Ensemble*
نویسندگان
چکیده
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 oneand 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. PACS numbers: 05.30.Jp, 03.75.Fi, 32.80.Pj Typeset using REVTEX ∗Dedicated to Professor Dr. Siegfried Großmann on the occasion of his 68-th birthday
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