Off-diagonal long-range order, cycle probabilities, and condensate fraction in the ideal Bose gas

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dc.creatorChevallier, Maguelonne
dc.creatorKrauth, Werner
dc.date2007-02-11
dc.date2007-06-28
dc.date.accessioned2026-07-07T09:21:01Z
dc.date.available2026-07-07T09:21:01Z
dc.descriptionWe discuss the relationship between the cycle probabilities in the path-integral representation of the ideal Bose gas, off-diagonal long-range order, and Bose--Einstein condensation. Starting from the Landsberg recursion relation for the canonic partition function, we use elementary considerations to show that in a box of size L^3 the sum of the cycle probabilities of length k >> L^2 equals the off-diagonal long-range order parameter in the thermodynamic limit. For arbitrary systems of ideal bosons, the integer derivative of the cycle probabilities is related to the probability of condensing k bosons. We use this relation to derive the precise form of the π_k in the thermodynamic limit. We also determine the function π_k for arbitrary systems. Furthermore we use the cycle probabilities to compute the probability distribution of the maximum-length cycles both at T=0, where the ideal Bose gas reduces to the study of random permutations, and at finite temperature. We close with comments on the cycle probabilities in interacting Bose gases.
dc.description6 pages, extensive rewriting, new section on maximum-length cycles
dc.identifierhttps://arxiv.org/abs/cond-mat/0702269
dc.identifierhttp://arxiv.org/abs/cond-mat/0702269
dc.identifierPhysical Review E 76, 051109 (2007)
dc.identifierdoi:10.1103/PhysRevE.76.051109
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/154878
dc.subjectStatistical Mechanics
dc.titleOff-diagonal long-range order, cycle probabilities, and condensate fraction in the ideal Bose gas
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