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A perturbed mean field model of an interacting boson gas and the large deviation principle |
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| Authors: | M van den Berg T C Dorlas J T Lewis J V Pulé |
| Institution: | (1) Department of Mathematics, Heriot-Watt University, Riccarton, EH144AS Edinburgh, Scotland;(2) School of Theoretical Physics, Dublin Institute for Advanced Studies, 10 Burlington Road, Dubin 4, Ireland;(3) Department of Mathematical Physics, University College, Belfield, Dublin 4, Ireland |
| Abstract: | 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 Huang-Yang-Luttinger model). The proof uses a large deviation result for the occupation measure of the free boson gas which is of independent interest. |
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