Diffusion Approximation of Stochastic Master Equations with Jumps

Details Diffusion Approximation of Stochastic Master Equations with Jumps Diffusion Approximation of Stochastic Master Equations with Jumps

2009-07-23

arxiv.org/abs/0907.3996v2

Physics

Mathematical Physics

15 pages

Scientific paper

In the presence of quantum measurements with direct photon detection the evolution of open quantum systems is usually described by stochastic master equations with jumps. Heuristically, from these equations one can obtain diffusion models as approximation. A necessary condition for a general diffusion approximation for jump master equations is presented. This approximation is rigorously proved by using techniques for Markov process which are based upon the convergence of Markov generators and martingale problems. This result is illustrated by rigorously obtaining the diffusion approximation for homodyne and heterodyne detection.

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