Universality in quantum chaos and the one parameter scaling theory

TL;DR

This paper extends the one parameter scaling theory to quantum chaos, providing a refined classification of universality classes that includes Anderson localization effects and predicts a new class related to the metal-insulator transition.

Contribution

It introduces a novel application of the OPT to quantum chaos, refining universality class distinctions and predicting a new class associated with the metal-insulator transition.

Findings

Proposes a refined universality classification including Anderson localization.

Predicts a new universality class related to the metal-insulator transition.

Provides examples of quantum chaos systems exhibiting these classes.

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.