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Mathematical problems of irreversible statistical mechanics for quantum systems. I: Analytic continuation of the collision and destruction operators by spectral deformation method

par Courbage, Maurice
Référence Journal of mathematical physics, 23, 4, page (646-651)
Publication Publié, 1981

Article révisé par les pairs

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Résumé :

We study some mathematical problems posed in nonequilibrium statistical mechanics and subdynamics theory developed by Prigogine and coworkers. We study in the superspace of the Hilbert-Schmidt operators the solution of the Liouville-von Neumann equation. The application in this frame of the spectral deformation methods yields expression of analytic continuations of a class of matrix elements of the resolvent of the Liouville-von Neumann operator, and this allows the analytic continuation of the collision and destruction operators. However, it is impossible to obtain simultaneously analytic continuation of the creation operator in this frame. The above results will be used in the second part of the article in order to study the pseudo-Markovian equation. © 1982 American Institute of Physics.