Universality in quantum chaos and the one parameter scaling theory

Abstract

We adapt the one parameter scaling theory (OPT) to the context of quantum chaos. As a result we propose a more precise characterization of the universality classes associated to Wigner-Dyson and Poisson statistics which takes into account Anderson localization effects. Based also on the OPT we predict a new universality class in quantum chaos related to the metal-insulator transition and provide several examples. In low dimensions it is characterized by classical superdiffusion or a fractal spectrum, in higher dimensions it can also have a purely quantum origin as in the case of disordered systems. Our findings open the possibility of studying the metal insulator transition experimentally in a much broader type of systems.