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The weak coupling limit as a quantum functional central limit. (English) Zbl 0703.60096
Summary: We show that, in the weak coupling limit, the laser model process converges weakly in the sense of the matrix elements to a quantum diffusion whose equation is explicitly obtained. We prove convergence, in the same sense, of the Heisenberg evolution of an observable of the system to the solution of a quantum Langevin equation. As a corollary of this result, via the quantum Feynman-Kac technique, one can recover previous results on the quantum master equation for reduced evolutions of open systems. When applied to some particular model (e.g. the free Boson gas) our results allow to interpret the Lamb shift as an Itô correction term and to express the pumping rates in terms of quantities related to the original Hamiltonian model.

MSC:
60K35 Interacting random processes; statistical mechanics type models; percolation theory
81S25 Quantum stochastic calculus
60F99 Limit theorems in probability theory
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