The large deviation principle and some models of an interacting boson gas

M. van den Berg, J. T. Lewis, J. V. Pulé

Research output: Contribution to journalArticle

Abstract

This is a study of the equilibrium thermodynamics of the Huang-Yang-Luttinger model of a boson gas 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. © 1988 Springer-Verlag.

Original languageEnglish
Pages (from-to)61-85
Number of pages25
JournalCommunications in Mathematical Physics
Volume118
Issue number1
DOIs
Publication statusPublished - Mar 1988

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Large Deviation Principle
Condensate
Bosons
Chemical Potential
Large Deviations
Critical value
Thermodynamic Equilibrium
Mean-field Model
Increasing Functions
Thermodynamic Limit
Hard Spheres
Jump
Model
Verify
Prediction
Alternatives
Interaction
Gas

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van den Berg, M. ; Lewis, J. T. ; Pulé, J. V. / The large deviation principle and some models of an interacting boson gas. In: Communications in Mathematical Physics. 1988 ; Vol. 118, No. 1. pp. 61-85.
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The large deviation principle and some models of an interacting boson gas. / van den Berg, M.; Lewis, J. T.; Pulé, J. V.

In: Communications in Mathematical Physics, Vol. 118, No. 1, 03.1988, p. 61-85.

Research output: Contribution to journalArticle

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