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