Condensate fluctuations of a trapped, ideal Bose gas

For a non-self-interacting Bose gas with a fixed, large number of particles confined to a trap, as the ground-state occupation becomes macroscopic, the condensate number fluctuations remain microscopic. However, this is the only significant aspect in which the grand canonical description differs from canonical or microcanonical in the thermodynamic limit. General arguments and estimates including some of the vanishingly small quantities are compared to explicit, fixed-number calculations for ${10}^{2}$--${10}^{6}$ particles. \textcopyright{} 1996 The American Physical Society.

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