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This paper presents rigorous mathematical analysis of large-deviation estimates for particle distributions in a non-interacting Bose gas within the canonical ensemble. The study reveals distinct exponential decay rates for left- and right-tail probabilities as the system size approaches infinity, offering fundamental insights into the statistical mechanics of quantum gases. While mathematically dense, these results advance the theoretical understanding of Bose-Einstein condensation without introducing new hardware or algorithmic applications.
Large Deviations for the Bose--Einstein Condensate of the Ideal Gas in the Canonical Ensemble
arXiv:2608.26378v1 Announce Type: cross Abstract: We consider a non-interacting Bose gas governed by a general one-particle Hamiltonian in the canonical ensemble. Our main results are large-deviation estimates for the number of particles in the Bose--Einstein condensate. We show that the left- and right-tail probabilities decay at different exponential rates as the number of particles tends to infinity.
Abstract:We consider a non-interacting Bose gas governed by a general one-particle Hamiltonian in the canonical ensemble. Our main results are large-deviation estimates for the number of particles in the Bose--Einstein condensate. We show that the left- and right-tail probabilities decay at different exponential rates as the number of particles tends to infinity.
Mathematical Physics (math-ph); Quantum Gases (cond-mat.quant-gas); Probability (math.PR); Quantum Physics (quant-ph)
arXiv:2608.26378 [math-ph]
(or arXiv:2608.26378v1 [math-ph] for this version)
https://doi.org/10.48550/arXiv.2608.26378 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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