Resonance Eigenfunction Hypothesis for Chaotic Systems

Konstantin Clauß, Martin J. Körber, Arnd Bäcker, and Roland Ketzmerick
Phys. Rev. Lett. 121, 074101 – Published 13 August 2018

Abstract

A hypothesis about the average phase-space distribution of resonance eigenfunctions in chaotic systems with escape through an opening is proposed. Eigenfunctions with decay rate γ are described by a classical measure that (i) is conditionally invariant with classical decay rate γ and (ii) is uniformly distributed on sets with the same temporal distance to the quantum resolved chaotic saddle. This explains the localization of fast-decaying resonance eigenfunctions classically. It is found to occur in the phase-space region having the largest distance to the chaotic saddle. We discuss the dependence on the decay rate γ and the semiclassical limit. The hypothesis is numerically demonstrated for the standard map.

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  • Received 8 March 2018

DOI:https://doi.org/10.1103/PhysRevLett.121.074101

© 2018 American Physical Society

Physics Subject Headings (PhySH)

Nonlinear Dynamics

Authors & Affiliations

Konstantin Clauß1, Martin J. Körber1, Arnd Bäcker1,2, and Roland Ketzmerick1,2

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

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Issue

Vol. 121, Iss. 7 — 17 August 2018

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