Quantum Statistical Mechanics of General Mean Field Systems

Raggio, G. A. and Werner, R. F. (1988) Quantum Statistical Mechanics of General Mean Field Systems. (Preprint)

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We consider mean field modules for n identical systems interacting with each other, and with another additional system. Each Hamiltonian H_n is taken to be symmetric with respect to permutations of the identical systems, and for large n and arbitrary k, (n+k)^(-1)H_(n+k) is approximately equal to n^(-1)H_n, taken as an operator of the larger system, and resymmetrised. The validity of the Gibbs Variational Principle is established; firstly, at the level of the states of the infinite system, then secondly at the level of the states of the single system. A generalized gap-equation is obtained at this second level. In some cases, the variational problem reduces further; this leads to a non-commutative version of the larger deviation results of Cramer-Varadhan for R^d-valued random variables.

Item Type: Article
Divisions: School of Theoretical Physics > Preprints
Date Deposited: 10 Jul 2018 14:57
Last Modified: 21 Dec 2022 14:36
URI: https://dair.dias.ie/id/eprint/902

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