Random matrix ensembles for models of spins decoherence

I present a class of random matrix ensembles relevant for the study of the dynamics of quantum decoherence for quantum spins. These ensembles generalize the standard GUE and GOE ensemble. For a single large spin, they lead to exact solutions for the dynamics of decoherence and for quantum diffusion, including non-markovian regimes. Generalizations to closed systems of quantum spins lead to interesting problems, involving free probabilities.