Chevallier Krauth 2007
From Werner KRAUTH
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| M. Chevallier, W. Krauth ''Off-diagonal long-range order, cycle probabilities, and condensate fraction in the ideal Bose gas'' Physical Review E '''76''' 051109 (2007) | M. Chevallier, W. Krauth ''Off-diagonal long-range order, cycle probabilities, and condensate fraction in the ideal Bose gas'' Physical Review E '''76''' 051109 (2007) | ||
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| + | '''Abstract:''' | ||
| + | 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 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 \pi_k in the thermodynamic limit. We also determine the function \pi_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. | ||
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| + | [http://arxiv.org/abs/cond-mat/0702269v2 Electronic version (arXiv)] | ||
Current revision
M. Chevallier, W. Krauth Off-diagonal long-range order, cycle probabilities, and condensate fraction in the ideal Bose gas Physical Review E 76 051109 (2007)
Abstract: 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 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 \pi_k in the thermodynamic limit. We also determine the function \pi_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.
