Repeated quantum interactions Quantum Langevin equation and the low density limit
Dhahri, Ameur (2008), Repeated quantum interactions Quantum Langevin equation and the low density limit. https://basepub.dauphine.fr/handle/123456789/17398
TypeDocument de travail / Working paper
Series titlecahier de recherche CEREMADE- Paris-Dauphine
MetadataShow full item record
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)We consider a repeated quantum interaction model describing a small system HhS in interaction with each one of the identical copies of the chain N/N∗ /Cn+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 connection between the time scale h and the classical low density limit. We introduce a chemical potential μ related to the time h as follows: h2 = eβμ . 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.
Subjects / KeywordsPoisson processes; low density limit; quantum stochastique differentiel equation (or quantum Langevin equation); Repeated quantum interactions
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