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Resonance Eigenfunction Hypothesis for Chaotic Systems.

Konstantin Clauß1, Martin J Körber1, Arnd Bäcker1,2

  • 1Technische Universität Dresden, Institut für Theoretische Physik and Center for Dynamics, 01062 Dresden, Germany.

Physical Review Letters
|September 1, 2018
PubMed
Summary
This summary is machine-generated.

A new hypothesis explains resonance eigenfunction distribution in chaotic systems. Fast-decaying eigenfunctions localize in phase space regions farthest from the chaotic saddle, a finding demonstrated numerically.

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Area of Science:

  • Physics
  • Quantum Chaos
  • Statistical Mechanics

Background:

  • Chaotic systems exhibit complex dynamics.
  • Resonance eigenfunctions are crucial for understanding system behavior.
  • Escape through an opening introduces unique challenges in chaotic systems.

Purpose of the Study:

  • To propose a hypothesis for the average phase-space distribution of resonance eigenfunctions in chaotic systems with escape.
  • To explain the classical localization of fast-decaying resonance eigenfunctions.
  • To investigate the dependence on decay rate and the semiclassical limit.

Main Methods:

  • Formulating a hypothesis based on classical measures.
  • Describing eigenfunctions using conditionally invariant measures.
  • Numerical demonstration using the standard map.

Main Results:

  • Eigenfunctions with decay rate γ are described by a classical measure that is conditionally invariant and uniformly distributed.
  • Localization of fast-decaying resonance eigenfunctions occurs in phase-space regions farthest from the chaotic saddle.
  • The hypothesis is numerically validated for the standard map.

Conclusions:

  • The proposed hypothesis provides a framework for understanding resonance eigenfunction distributions in chaotic systems.
  • The findings offer insights into the localization phenomena of eigenfunctions.
  • The study highlights the interplay between classical and quantum descriptions in chaotic dynamics.