Progress in the mathematical theory of quantum disordered systems

We review recent progress in the mathematical theory of quantum disordered systems: the Anderson transition (joint work with Domin-gos Marchetti), the (quantum and classical) Edwards-anderson spin-glass model and return to equilibrium for a class of spin glass models, which includes the EA model initially in a very large transverse magnetic field. In recent years there has been a significant progress in the mathematical theory of (quantum) disordered systems. Our purpose here is to present the main ideas (without proofs), with a clear discussion of their conceptual and physical relevance, as well as a brief comparison with the recent, analogou