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Condensate fluctuations in the dilute Bose gas

Alexander Yu. Cherny
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Abstract

The fluctuations of a number of particles in the Bose-Einstein condensate are studied in the grand canonical ensemble with an effective single-mode Hamiltonian, which is derived from an assumption that the mode corresponding to the Bose-Einstein condensate does not asymptotically correlate with other modes. The fluctuations are evaluated in the dilute limit with a proposed simple method, which is beyond the mean-field approximation. The accuracy of the latter is estimated; it is shown that the mean-field scheme does not work for the single-mode Hamiltonian, while for the Hartree Hamiltonian it allows us to estimate the condensate fluctuations up to a numerical factor. As a hypothesis, a formula is proposed that relates the fluctuations in the canonical ensemble with that of the grand canonical one.

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Alexander Yu. Cherny. 2005-04-12. Condensate fluctuations in the dilute Bose gas. https://doi.org/10.1103/physreva.71.043605

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