dc.contributor.author Dhahri, Ameur dc.date.accessioned 2010-03-09T14:09:28Z dc.date.available 2010-03-09T14:09:28Z dc.date.issued 2009 dc.identifier.uri https://basepub.dauphine.fr/handle/123456789/3670 dc.language.iso en en dc.subject Repeated quantum interactions en dc.subject quantum stochastique differentiel equation (or quantum Langevin equation) en dc.subject low density limit en dc.subject Poisson processes en dc.subject.ddc 519 en dc.title Low Density Limit and the Quantum Langevin equation for the Heat Bath en dc.type Article accepté pour publication ou publié dc.description.abstracten We 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.isversionofjnlname Open Systems & Information Dynamics dc.relation.isversionofjnlvol 16 dc.relation.isversionofjnlissue 4 dc.relation.isversionofjnldate 2009 dc.relation.isversionofdoi http://dx.doi.org/10.1142/S1230161209000268 dc.identifier.urlsite http://hal.archives-ouvertes.fr/hal-00265934/en/ en dc.description.sponsorshipprivate oui en dc.relation.isversionofjnlpublisher World Scientific dc.subject.ddclabel Probabilités et mathématiques appliquées en
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