Abstract
This paper is the final one in a series in which we investigate some models of an interacting Bose gas using Varadhan's large deviation version of Laplacian asymptotics; in it we study the equilibrium thermodynamics of the full diagonal model of a Bose gas. We obtain a formula expressing the pressure, in the thermodynamic limit, as the supremum of a functional over the space of positive bounded measures. We analyse this formula for a large class of interaction kernels and show that there is a critical temperature below which there is Bose-Einstein condensation.
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Lee, T.D., Yang, C.N.: The many-body problem in quantum mechanics and quantum statistical mechanics. Phys. Rev.105, 1119–1120 (1957)
Huang, K., Yang, C.N., Luttinger, J.M.: Imperfect Bose gas with hard-sphere interactions. Phys. Rev.105, 776–784 (1957)
Thouless, D.J.: The quantum mechanics of many-body systems. New York: Academic Press 1961
Yang, C.N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. J. Math. Phys.10, 1115–1122 (1969)
Dorlas, T.C., Lewis, J.T., Pulé, J.V.: The Yang-Yang thermodynamic formalism and large deviations. Commun. Math. Phys.124, 365–402 (1984).
Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schrödinger model. To appear in Commun. Math. Phys. (1993)
Davies, E.B.: The thermodynamic limit for an imperfect boson gas. Commun. Math. Phys.28, 69–86 (1972)
van den Berg, M., Lewis, J. T., de Smedt, Ph.: Condensation in the imperfect boson gas. J. Stat. Phys.37, 697–707 (1984)
Lewis, J.T., Pulé, J.V., Zagrebnov, V.A.: The large deviation principle for the Kac distribution. Helv. Phys. Acta.61, 1063–1078 (1988)
van den Berg, M., Dorlas, T.C., Lewis, J.T., Pulé, J.V.: A perturbed meanfield model of an interacting boson gas and the large deviation principle. Commun. Math. Phys.127, 41–69 (1990)
van den Berg, M., Lewis, J.T., Pulé, J.V.: The large deviation principle and some models of an interacting boson gas. Commun. Math. Phys.118, 61–85 (1988)
van den Berg, M., Dorlas, T. C., Lewis, J.T., Pulé, J.V.: The pressure in the Huang-Yang-Luttinger model of an interacting boson gas. Commun. Math. Phys.128, 231–245 (1990)
Dorlas, T.C., Lewis, J.T., Pulé, J.V.: Condensation in some perturbed meanfield models of a Bose gas. Helv. Phys. Acta64, 1200–1224 (1991)
Varadhan, S.R.S.: Asymptotic probabilities and differential equations. Commun. Pure Appl. Math.19, 261–286 (1966)
Girardeau, M.: Relationship between systems of inpenetrable bosons and fermions in one dimension. J. Math. Phys.1, 516–523 (1960)
van den Berg, M., Lewis, J.T., Pulé, J.V.: A general theory of Bose-Einstein condensation. Helv. Phys. Acta.59, 1271–1288 (1986)
Bourbaki, N., Éléments de mathématiques, chap IX: Intégration. Paris: Hermann 1969
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Communicated by J. Föhlich
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Dorlas, T.C., Lewis, J.T. & Pulé, J.V. The full diagonal model of a Bose gas. Commun.Math. Phys. 156, 37–65 (1993). https://doi.org/10.1007/BF02096732
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DOI: https://doi.org/10.1007/BF02096732