2007/02/28 by Maguelonne Chevallier, Werner Krauth · 1 citation
Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Quantum Mechanics and Non-Hermitian Physics #Quantum, superfluid, helium dynamics #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.76.051109
published as Physical Review E 76, 051109 (2007) · 6 pages, extensive rewriting, new section on maximum-length cycles
arxiv created 2007/06/28 · openalex publication_date 2007/11/09 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We 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 L3 the sum of the cycle probabilities of length k>>L2 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 pik in the thermodynamic limit. We also determine the function pik 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.