Abstract
We study equilibrium states of a quantum Bose gas using Kubo-Martin-Schwinger boundary conditions, for a special class of time evolutions, namely the quasi-free evolutions. Under suitable restrictions, in particular positivity of the elementary excitation spectrum, we are able to describe the states fulfilling the Kubo-Martin-Schwinger conditions. In contrast to the Fermi case the solution is, in general, not unique; this is related to a possible Bose condensation.
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This work is a part of a «Thèse de Doctorat d'Etat» presented to the «Faculté des Sciences de Marseille», under the number A.O. 3680.
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Rocca, F., Sirugue, M. & Testard, D. On a class of equilibrium states under the Kubo-Martin-Schwinger condition. Commun.Math. Phys. 19, 119–141 (1970). https://doi.org/10.1007/BF01646630
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DOI: https://doi.org/10.1007/BF01646630