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A perturbed mean field model of an interacting Boson gas and the large deviation principle. (English) Zbl 0693.60088
Summary: This is a study of the equilibrium thermodynamics of a mean-field model of an interacting boson gas perturbed by a term quadratic in the occupation numbers of the free-gas energy-levels. We prove the existence of the pressure in the thermodynamic limit. We obtain also a variational formula for the pressure; this enables us to compare the effect of a smooth quadratic perturbation with that of a singular one [the K. Huang, C. N. Yang and J. M. Luttinger model, Phys. Rev. 105, 776-784 (1957)]. The proof uses a large deviation result for the occupation measure of the free boson gas which is of independent interest.

MSC:
60K35 Interacting random processes; statistical mechanics type models; percolation theory
82B05 Classical equilibrium statistical mechanics (general)
60F10 Large deviations
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