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The large deviation principle and some models of an interacting boson gas. (English) Zbl 0679.76124
Summary: This is a study of the equilibrium thermodynamics of the Huang-Yang- Luttinger model of a boson gas [K. Huang, C. N. Yang and J. M. Luttinger, Phys. Rev. 105, 776-784 (1957)] with a hard-sphere repulsion using large deviation methods; we contrast its properties with those of the mean field model. We prove the existence of the grand canonical pressure in the thermodynamic limit and derive two alternative expressions for the pressure as a function of the chemical potential. We prove the existence of condensate for values of the chemical potential above a critical value and verify a prediction of Thouless that there is a jump in the density of condensate at the critical value. We show also that, at fixed mean density, the density of condensate is an increasing function of the strength of the repulsive interaction. In an appendix, we give proofs of the large deviation results used in the body of the paper.

76Y05 Quantum hydrodynamics and relativistic hydrodynamics
82B10 Quantum equilibrium statistical mechanics (general)
Full Text: DOI
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