Relaxation of a Simple Quantum Random Matrix Model

Abstract: We will derive here the relaxation behavior of a simple quantum random matrix model. The aim is to derive the effective equations which rise when a random matrix interaction is taken in the weak coupling limit. The physical situation this model represents is that a quantum particle restricted to move on two sites, where every site has N possible energy states. The hopping from one site to another is then modeled by a random matrix. The techniques used here can be applied to many variations of the model.