1999/07/12 by Ulrich Gerland
Computer Science · Physics and Astronomy · #Nonlinear Dynamics and Pattern Formation #Quantum chaos and dynamical systems #Theoretical and Computational Physics #chao-dyn #cond-mat.dis-nn #nlin.CD
paper · pdf · doi:10.1103/physrevlett.83.1139
8 pages, 2 figures, accepted for publication in Phys. Rev. Lett
arxiv created 1999/07/12 · openalex publication_date 1999/08/09 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider a Sinai billiard where the usual hard disk scatterer is replaced by a repulsive potential with V(r)\ensuremath∼\ensuremathλr^\ensuremath-\ensuremathα close to the origin. Using periodic orbit theory and numerical evidence we show that its spectral statistics tends to Poisson statistics for large energies when \ensuremathα<2 and to Wigner-Dyson statistics when \ensuremathα>2, while for \ensuremathα\phantom\rule0ex0ex=\phantom\rule0ex0ex2 it is independent of energy, but depends on \ensuremathλ. We apply the approach of Altshuler and Levitov [Phys. Rep. 288, 487 (1997)] to show that the transition in the spectral statistics is accompanied by a dynamical localization-delocalization transition. This behavior is reminiscent of a metal-insulator transition in disordered electronic systems.