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Systèmes dynamiques quantiques ouverts

Abstract : Some open quantum systems are studied with the recent dynamical systems theory. Volterra equation drives the dynamics of a system interacting with a reservoir. Davies had proven markovian results in the weak limit. Davies generator and Van Hove operator are strictly defined and computed for classical models. A completely positive semigroup acting on the observables of the system is given by its generator-Davies generator. We give conditions to obtain the complete positivity which are satisfied by the standard models. A direct method solves the master equation for a system of harmonic oscillators. We establish relaxation to a steady state which turns out to be an equilibrium state. Feshbach formula links up the resolvent of the liouvillean and Davies generator of the system. Under specific assumptions on the bosonic field, we build a stationary Gaussian process. The dynamics of the density matrices of the system can turned out Markovian if an invariant measure exists.
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Contributor : Dominique Fellah <>
Submitted on : Tuesday, July 16, 2013 - 12:15:01 PM
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  • HAL Id : tel-00845012, version 1



Dominique Fellah. Systèmes dynamiques quantiques ouverts. Physique mathématique [math-ph]. Université du Sud Toulon Var, 2004. Français. ⟨tel-00845012⟩



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