Some topics in quantum disordered systems

We discuss some recent results connected with the properties of temperature states of quantum disordered systems. This analysis falls within the natural framework of operator algebras. Among the results quoted here, we recall some ergodic and spectral properties of KMS states, the possibility of defining the chemical potential independently of the disorder, and finally the question of the Gibbsianess for KMS states. This analysis can be considered as a step towards fully understanding the very complicated structure of the set of temperature states of quantum spin glasses, and its connection with the breakdown of the symmetry for replicas.