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, diffusion models can be obtained from these equations as approximation. A condition for a general diffusion approximation for jump master equations is presented. This approximation is rigorously proved by using ...

We derive the hydrodynamic limit of a kinetic equation where interactions in velocity are modelled by linear operator (Fokker-Planck or Linear Boltzmann) and force Vlasov term is stochastic process with high amplitude short-range correlation. In scales regime we consider, scalar second-order partial differential equation. Compared to deterministic case, also observe phenomenon enhanced diffusion.