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تسجيل مستخدم جديدRepeated quantum interactions Quantum Langevin equation and the low density limit
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Ameur Dhahri
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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: $h^2=e^{betamu}$. 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.
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