Ensemble-dependent condensate statistics and correlations in an ideal Bose gas
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)]≈ 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.
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BibTeX
@misc{augustynowicz2026ensembledependent,
title = {{Ensemble-dependent condensate statistics and correlations in an ideal Bose gas}},
author = {Szymon Augustynowicz and Jan Okoński and Maciej B. Kruk and Ilja Zebergs and Jan Joachim Arlt and Kazimierz Rzążewski and Krzysztof Pawłowski},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.36118},
eprint = {2610.36118},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.36118},
}
RIS
TY - UNPB
TI - Ensemble-dependent condensate statistics and correlations in an ideal Bose gas
AU - Szymon Augustynowicz
AU - Jan Okoński
AU - Maciej B. Kruk
AU - Ilja Zebergs
AU - Jan Joachim Arlt
AU - Kazimierz Rzążewski
AU - Krzysztof Pawłowski
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2610.36118
UR - https://arxiv.org/abs/2610.36118
AB - 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)]≈ 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.
ER -