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The low density limit for anN-level system interacting with a free bose or fermi gas

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Abstract

It is proved that the reduced dynamics of anN-level system coupled to a free quantum gas converges to a quantum dynamical semigroup in the low density limit. The proof uses a perturbation series of the quantum BBGKY-hierarchy, and the analysis of this series is based on scattering theory. The limiting semigroup contains the full scattering cross section, but it does not depend on the statistics of the reservoir. The dynamics of the semigroup is discussed.

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  1. Fachbereich Physik, Universität München, D-8000, München, Federal Republic of Germany

    R. Dümcke

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  1. R. Dümcke
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Communicated by J. L. Lebowitz

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Dümcke, R. The low density limit for anN-level system interacting with a free bose or fermi gas. Commun.Math. Phys. 97, 331–359 (1985). https://doi.org/10.1007/BF01213401

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  • DOI: https://doi.org/10.1007/BF01213401

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