Resonance Eigenfunction Hypothesis for Chaotic Systems

Physical Review Letters
Konstantin ClaußRoland Ketzmerick

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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Citations

Oct 24, 2019·Physical Review. E·Agustín M BilenOlivier Giraud
Dec 25, 2019·Physical Review. E·Konstantin ClaußRoland Ketzmerick
May 20, 2021·Physical Review. E·Konstantin ClaußRoland Ketzmerick
Jun 18, 2021·Physical Review. E·Domenico LippolisHajime Yoshino

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