  We introduce an elementary quantum system consisting of a set of spins on a
graph and a particle hopping between its nodes. The quantum state is build
sequentially, applying a unitary transformation that couples neighboring spins
and, at a node, the local spin with the particle. We observe the relaxation of
the system towards a stationary paramagnetic or ferromagnetic state, and
demonstrate that it is related to eigenvectors thermalization and random matrix
statistics. The relation between these macroscopic properties and interaction
generated entanglement is discussed.
