M. Holthaus et al., Master equation vs. partition function: canonical statistics of ideal Bose-Einstein condensates, PHYSICA A, 300(3-4), 2001, pp. 433-467
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
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