Classical singularities and semi-Poisson statistics in disordered systems.
We investigate a one-dimensional disordered Hamiltonian with a nonanalytical dispersion relation whose level statistics is exactly described by semi-Poisson statistics. It is shown that this result is robust, namely, it does not depend on the microscopic details of the Hamiltonian but only on the type of nonanalytical potential. We also argue that a deterministic kicked rotator with a steplike potential has the same spectral properties. Semi-Poisson statistics, typical of pseudointegrable billiards, have been frequently claimed to describe critical statistics, namely, the level statistics of a disordered system at the Anderson transition. However, we provide convincing evidence they are indeed different: each of them has its origin in a different type of classical singularity.
Physics Department, Princeton University, Princeton, New Jersey 08544, USA.
Antonio M
AM
García-García