Classical singularities and Semi-Poisson statistics in quantum chaos and disordered systems
Abstract
We investigate a 1D disordered Hamiltonian with a non analytical step-like dispersion relation whose level statistics is exactly described by Semi-Poisson statistics(SP). It is shown that this result is robust, namely, does not depend neither on the microscopic details of the potential nor on a magnetic flux but only on the type of non-analyticity. We also argue that a deterministic kicked rotator with a non-analytical step-like potential has the same spectral properties. Semi-Poisson statistics (SP), typical of pseudo-integrable billiards, has been frequently claimed to describe critical statistics, namely, the level statistics of a disordered system at the Anderson transition (AT). However we provide convincing evidence they are indeed different: each of them has its origin in a different type of classical singularities.
Cite
@article{arxiv.cond-mat/0507272,
title = {Classical singularities and Semi-Poisson statistics in quantum chaos and disordered systems},
author = {A. M. Garcia-Garcia},
journal= {arXiv preprint arXiv:cond-mat/0507272},
year = {2009}
}
Comments
typos corrected, 4 pages, 3 figures