A simple but very general model of an SU(2) spin coupled to a large external system is presented. The possible interactions are described by a new class of gaussian SU(2)xU(N) random matrix ensemble. The model is solved in the large N limit, for any value of the spin j and generic interactions. Besides its mathematical interest as a non-trivial random matrix model, the model illustrates various phenomena: decoherence dynamics, the emergence of the classical phase space for the spin, Markovian and non-Markovian quantum diffusion in phase space.

IPhT Saclay