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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.
We consider a non-interacting bipartite quantum system $mathcal H_S^Aotimesmathcal H_S^B$ undergoing repeated quantum interactions with an environment modeled by a chain of independant quantum systems interacting one after the other with the bipartit
A quantum system interacting with a dilute gas experiences irreversible dynamics. The corresponding master equation can be derived within two different approaches: The fully quantum description in the low-density limit and the semiclassical collision
We consider the general physical situation of a quantum system $H_0$ interacting with a chain of exterior systems $bigotimes_N H$, one after the other, during a small interval of time $h$ and following some Hamiltonian $H$ on $H_0 otimes H$. We discu
We prove that the distribution of eigenvectors of generalized Wigner matrices is universal both in the bulk and at the edge. This includes a probabilistic version of local quantum unique ergodicity and asymptotic normality of the eigenvector entries.
In this article, we study the density function of the numerical solution of the splitting averaged vector field (AVF) scheme for the stochastic Langevin equation. To deal with the non-globally monotone coefficient in the considered equation, we first