Repeated quantum interactions Quantum Langevin equation and the low density limit

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dc.creatorDhahri, Ameur
dc.date2008-03-20
dc.date2009-02-23
dc.date.accessioned2026-07-07T12:44:32Z
dc.date.available2026-07-07T12:44:32Z
dc.descriptionWe 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 $μ$ related to the time $h$ as follows: $h^2=e^{βμ}$. 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.
dc.description18 pages
dc.identifierhttps://arxiv.org/abs/0803.3059
dc.identifierhttp://arxiv.org/abs/0803.3059
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/220802
dc.subjectProbability
dc.subjectMathematical Physics
dc.titleRepeated quantum interactions Quantum Langevin equation and the low density limit
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