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arXiv:2610.36118

Ensemble-dependent condensate statistics and correlations in an ideal Bose gas

Szymon Augustynowicz, Jan Okoński, Maciej Bartłomiej Kruk, Ilja Zebergs, Jan Joachim Arlt, Kazimierz Rza̧żewski, Krzysztof Pawłowski

Published Oct 26, 2026• 0 citations
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Abstract

The choice of statistical ensemble has a measurable impact on the statistical description of Bose-Einstein condensates beyond the well-known grand canonical anomaly. We develop a segmented-contour approach for the ideal Bose gas, which refines the saddle-point approximation by including non-Gaussian corrections in the canonical and microcanonical ensembles. The method applies to a broad class of noninteracting spectra, and provides efficient access to condensate fluctuations, higher moments, and correlation functions. For a three-dimensional harmonic trap with fixed anisotropy, we find that the ratio of the maxima of the microcanonical and canonical condensate-number variances approaches the theoretically predicted asymptotic value $1-3ζ(3)^2/[4ζ(2)ζ(4)]\approx 0.391$ only extremely slowly with increasing particle number. We also show that ensemble effects are visible in the second-order correlation function $g^{(2)}(x)$ near the condensation crossover. After ballistic release from a three-dimensional harmonic trap, the time evolution of $g^{(2)}(x)$ preserves the differences between statistical ensembles.

DOI
10.48550/arxiv.2610.36118

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We consider Bose-Einstein condensation of noninteracting homogeneous three-dimensional gas in canonical ensemble when both particle number NNN and total momentum P\mathbf{P}P of all particles are fixed. Using the saddle-point method, we derive the large-NNN analytical approximations for partition function, free energy, and statistical distributions of occupation numbers of different single-particle energy levels. At temperatures below the critical point of phase transition, we predict, in some ranges of P\mathbf{P}P, fragmentation of the condensate, when more than one single-particle level is macroscopically occupied. The occupation number distributions have approximately Gaussian shapes for the levels hosting the condensate, and exponential shapes for other, noncondensate levels. Our analysis demonstrates breaking of Galilean invariance of moving finite-temperature many-particle system in the presence of Bose-Einstein condensation and extends the theory of moving and rotating quantum systems to the finite-temperature large-NNN limit.