Classical intermittency and the quantum Anderson transition.
We investigate the properties of quantum systems whose classical counterpart presents intermittency. It is shown, by using recent semiclassical techniques, that the quantum spectral correlations of such systems are expressed in terms of the eigenvalues of an anomalous diffusion operator. For certain values of the parameters leading to ballistic diffusion and 1/f noise the spectral properties of our model show similarities with those of a disordered system at the Anderson transition. In Hamiltonian systems, intermittency is closely related to the presence of cantori in the classical phase space. We suggest, based on this relation, that our findings may be relevant for the description of the spectral correlations of Hamiltonians with a classical phase space homogeneously filled by cantori. Finally we discuss the extension of our results to higher dimensions and their relation to Anderson models with long-range hopping.
García-García
Antonio M
AM
Laboratoire de Physique Théorique et Modèles Statistiques, Bâtiment 100, Université de Paris-Sud, 91405 Orsay Cedex, France.