Master equation vs. partition function: canonical statistics of ideal Bose-Einstein condensates

Within the canonical ensemble, a partially condensed ideal Bose gas with ar bitrary single-particle energies is equivalent to a system of uncoupled har monic oscillators. We exploit this equivalence for deriving a formula which expresses all cumulants of the canonical distribution governing the number of condensate particles in terms of the poles of a generalized Zeta functi on provided by the single-particle spectrum. This formula lends itself to s ystematic asymptotic expansions which capture the non-Gaussian character of the condensate fluctuations with utmost precision even for relatively smal l, finite systems, as confirmed by comparison with exact numerical calculat ions. We use these results for assessing the accuracy of a recently develop ed master equation approach to the canonical condensate statistics; this ap proach turns out to be quite accurate even when the master equation is solv ed within a simple quasithermal approximation. As a further application of the cumulant formula we show that, and explain why, all cumulants of a homo geneous Bose-Einstein condensate "in a box" higher than the first retain a dependence on the boundary conditions in the thermodynamic limit. (C) 2001 Elsevier Science B.V. All rights reserved.