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We study a general class of translation invariant quantum Markov evolutionsfor a particle on $\bbZ^d$. The evolution consists of free flow, interrupted byscattering events. We assume spatial locality of the scattering events andexponentially fast relaxation of the momentum distribution. It is shown thatthe particle position diffuses in the long time limit. This generalizesstandard results about central limit theorems for classical (non-quantum)Markov processes.

Diffusive behavior from a quantum master equation