Consequences of flooding on spectral statistics

Torsten Rudolf, Normann Mertig, Steffen Löck, and Arnd Bäcker
Phys. Rev. E 85, 036213 – Published 22 March 2012

Abstract

We study spectral statistics in systems with a mixed phase space, in which regions of regular and chaotic motion coexist. Increasing their density of states, we observe a transition of the level-spacing distribution P(s) from Berry-Robnik to Wigner statistics, although the underlying classical phase-space structure and the effective Planck constant heff remain unchanged. This transition is induced by flooding, i.e., the disappearance of regular states due to increasing regular-to-chaotic couplings. We account for this effect by a flooding-improved Berry-Robnik distribution, in which an effectively reduced size of the regular island enters. To additionally describe power-law level repulsion at small spacings, we extend this prediction by explicitly considering the tunneling couplings between regular and chaotic states. This results in a flooding- and tunneling-improved Berry-Robnik distribution which is in excellent agreement with numerical data.

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  • Received 20 January 2012

DOI:https://doi.org/10.1103/PhysRevE.85.036213

©2012 American Physical Society

Authors & Affiliations

Torsten Rudolf1,2, Normann Mertig1,2, Steffen Löck1, and Arnd Bäcker1,2

  • 1Institut für Theoretische Physik, Technische Universität Dresden, 01062 Dresden, Germany
  • 2Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Straße 38, 01187 Dresden, Germany

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Issue

Vol. 85, Iss. 3 — March 2012

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