### 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 language | English |
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Pages (from-to) | 61-85 |

Number of pages | 25 |

Journal | Communications in Mathematical Physics |

Volume | 118 |

Issue number | 1 |

DOIs | |

Publication status | Published - Mar 1988 |

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*Communications in Mathematical Physics*,

*118*(1), 61-85. https://doi.org/10.1007/BF01218477

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*Communications in Mathematical Physics*, vol. 118, no. 1, pp. 61-85. https://doi.org/10.1007/BF01218477

**The large deviation principle and some models of an interacting boson gas.** / van den Berg, M.; Lewis, J. T.; Pulé, J. V.

Research output: Contribution to journal › Article

TY - JOUR

T1 - The large deviation principle and some models of an interacting boson gas

AU - van den Berg, M.

AU - Lewis, J. T.

AU - Pulé, J. V.

PY - 1988/3

Y1 - 1988/3

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0002617758&partnerID=8YFLogxK

U2 - 10.1007/BF01218477

DO - 10.1007/BF01218477

M3 - Article

VL - 118

SP - 61

EP - 85

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 1

ER -