Abstract
Using the Kubo-Martin-Schwinger boundary condition for equilibrium states of quantum statistical mechanics of fermion gas, we prove that forT≠;0 a one-particle evolution (corresponding essentially to bilinear hamiltonians) generally defines a unique equilibrium state, which is quasi-free. Conversely any quasi-free state is the equilibrium state for a single one-particle evolution if it has no Fock part in its product decomposition. Limiting cases whereT → 0 andT → ∞ are studied. In the case whereT → 0 one shows that the state generally converges to a Fock state linked to the evolution.
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This work is a part of a “Thèse de Doctorat d'Etat” presented to the “Faculté des Sciences de Marseille”, April 23, 1969, under the number A.O. 3073.
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Rocca, F., Sirugue, M. & Testard, D. On a class of equilibrium states under the Kubo-Martin-Schwinger boundary condition. Commun.Math. Phys. 13, 317–334 (1969). https://doi.org/10.1007/BF01645416
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DOI: https://doi.org/10.1007/BF01645416