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Low Density Limit and the Quantum Langevin equation for the Heat Bath

Dhahri, Ameur (2009), Low Density Limit and the Quantum Langevin equation for the Heat Bath, Open Systems & Information Dynamics, 16, 4. http://dx.doi.org/10.1142/S1230161209000268

Type
Article accepté pour publication ou publié
External document link
http://hal.archives-ouvertes.fr/hal-00265934/en/
Date
2009
Journal name
Open Systems & Information Dynamics
Volume
16
Number
4
Publisher
World Scientific
Publication identifier
http://dx.doi.org/10.1142/S1230161209000268
Metadata
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Author(s)
Dhahri, Ameur
Abstract (EN)
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.
Subjects / Keywords
Repeated quantum interactions; quantum stochastique differentiel equation (or quantum Langevin equation); low density limit; Poisson processes

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