Repeated Interaction Quantum Systems: Van Hove Limits and Asymptotic States |
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Authors: | Rodrigo Vargas |
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Institution: | (1) Institut Fourier, Université de Grenoble I, 100 rue des Maths, BP 74, 38402 St Martin d’Hères, France |
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Abstract: | We establish the existence of two weak coupling regime effective dynamics for an open quantum system of repeated interactions
(vanishing strength and individual interaction duration, respectively). This generalizes known results (Attal and Joye in
J. Stat. Phys. 126:1241–1283, 2007) in that the von Neumann algebras describing the system and the chain element may not be of finite type. Then (but now assuming
that the small system is of finite type), we prove that both effective dynamics capture the long-term behavior of the system:
existence of a unique asymptotic state for them implies the same property for the respective exact dynamics—provided that
the perturbation parameter is sufficiently small. The zero-th order term in a power series expansion in the perturbation parameter
of such an asymptotic state is given by the asymptotic state of the effective dynamics. We conclude by working out the case
in which the small system and the chain element are spins.
Dedicated to Mariana Huerta.
This work was partially funded by Nucleus Millennium Information and Randomness P04-069-F. |
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Keywords: | Repeated interaction quantum systems Van Hove limit Asymptotic state Perturbation theory |
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