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The low density limit for an N-level system interacting with a free Bose or Fermi gas. (English) Zbl 0614.46069
It is proved that the reduced dynamics of an N-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.
Reviewer: H.Araki

46N99 Miscellaneous applications of functional analysis
82B10 Quantum equilibrium statistical mechanics (general)
47A40 Scattering theory of linear operators
Full Text: DOI
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