2005/07/31 by Antonio M. Garcı́a-Garcı́a, A. M. Garcia-Garcia
Mathematics · Physics and Astronomy · #Classical mechanics #Cold Atom Physics and Bose-Einstein Condensates #Gravitational singularity #Hamiltonian (control theory) #Hamiltonian system #Mathematical analysis #Mathematics #Physics #Poisson distribution #Quantum chaos and dynamical systems #Quantum mechanics #Quantum, superfluid, helium dynamics #Singularity #Statistical physics #Statistics #cond-mat.dis-nn #cond-mat.mes-hall #hep-th #nlin.CD
paper · pdf · doi:10.1103/physreve.72.066210
published as Phys.Rev. E72 (2005) 066210 · typos corrected, 4 pages, 3 figures
arxiv created 2005/08/26 · openalex publication_date 2005/12/20 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.