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Classical singularities and Semi-Poisson statistics in quantum chaos and disordered systems

A. M. Garcia-Garcia
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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.

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A. M. Garcia-Garcia. 2005-08-26. Classical singularities and Semi-Poisson statistics in quantum chaos and disordered systems. https://doi.org/10.1103/physreve.72.066210

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