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dc.contributor.authorDhahri, Ameur
dc.subjectRepeated quantum interactionsen
dc.subjectquantum stochastique differentiel equation (or quantum Langevin equation)en
dc.subjectlow density limiten
dc.subjectPoisson processesen
dc.titleLow Density Limit and the Quantum Langevin equation for the Heat Bathen
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenWe consider a repeated quantum interaction model describing a small system $\Hh_S$ in interaction with each one of the identical copies of the chain $\bigotimes_{\N^*}\C^{n+1}$, modeling a heat bath, one after another during the same short time intervals $[0,h]$. We suppose that the repeated quantum interaction Hamiltonian is split in two parts: a free part and an interaction part with time scale of order $h$. After giving the GNS representation, we establish the relation between the time scale $h$ and the classical low density limit. We introduce a chemical potential $\mu$ related to the time $h$ as follows: $h^2=e^{\beta\mu}$. We further prove that the solution of the associated discrete evolution equation converges strongly, when $h$ tends to 0, to the unitary solution of a quantum Langevin equation directed by Poisson processes.en
dc.relation.isversionofjnlnameOpen Systems & Information Dynamics
dc.relation.isversionofjnlpublisherWorld Scientific
dc.subject.ddclabelProbabilités et mathématiques appliquéesen

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