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.
Cite
@article{arxiv.0707.3964,
title = {Universality in quantum chaos and the one parameter scaling theory},
author = {Antonio M. Garcia-Garcia and Jiao Wang},
journal= {arXiv preprint arXiv:0707.3964},
year = {2009}
}
Comments
4 pages, 2 figures, acknowledgment added, typos corrected