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arXiv · 1803.02631

Resonance eigenfunction hypothesis for chaotic systems

Konstantin Clauß·Martin J. Körber·Arnd Bäcker·Roland Ketzmerick
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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 $\gamma$ are described by a classical measure that $(i)$ is conditionally invariant with classical decay rate $\gamma$ 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 $\gamma$ and the semiclassical limit. The hypothesis is numerically demonstrated for the standard map.

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Konstantin Clauß, Martin J. Körber, Arnd Bäcker, Roland Ketzmerick. 2018-03-07. Resonance eigenfunction hypothesis for chaotic systems. https://doi.org/10.1103/physrevlett.121.074101

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