Spectral statistics and dynamical localization: Sharp transition in a generalized sinai billiard

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

We consider a Sinai billiard where the usual hard disk scatterer is replaced by a repulsive potential with V(r)∼λr−α 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 α < 2 and to Wigner-Dyson statistics when α > 2, while for α = 2 it is independent of energy, but depends on λ. 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.

Original languageEnglish
Pages (from-to)1139-1142
Number of pages4
JournalPhysical Review Letters
Volume83
Issue number6
DOIs
StatePublished - 1 Jan 1999
Externally publishedYes

Fingerprint

Dive into the research topics of 'Spectral statistics and dynamical localization: Sharp transition in a generalized sinai billiard'. Together they form a unique fingerprint.

Cite this