Classical intermittency and quantum Anderson transition

TL;DR

This paper explores the quantum spectral properties of 1D systems with classical intermittency, revealing similarities to Anderson transition phenomena and suggesting relevance for non-KAM Hamiltonians with complex phase space structures.

Contribution

It introduces a semiclassical approach linking classical intermittency to quantum spectral correlations, highlighting potential relevance for non-KAM Hamiltonians and higher-dimensional systems.

Findings

Spectral correlations resemble those of disordered systems at the Anderson transition.

Intermittency in classical systems influences quantum spectral properties.

Potential extension of results to higher dimensions and long-range hopping models.

Abstract

We investigate the quantum properties of 1D quantum systems whose classical counterpart presents intermittency. The spectral correlations are expressed in terms of the eigenvalues of an anomalous diffusion operator by using recent semiclassical techniques. For certain values of the parameters 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 (non-KAM) Hamiltonians with a classical phase space filled by cantori. Finally we discuss the extension of our results to higher dimensions and their relation to Anderson models with long range hopping.