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Hierarchical Fractal Weyl Laws for Chaotic Resonance States in Open Mixed Systems

In open chaotic systems the number of long-lived resonance states obeys a fractal Weyl law, which depends on the fractal dimension of the chaotic saddle. We study the generic case of a mixed phase space with regular and chaotic dynamics. We find a hierarchy of fractal Weyl laws, one for each region of the hierarchical decomposition of the chaotic phase-space component. This is based on our observation of hierarchical resonance states localizing on these regions. Numerically this is verified for the standard map and a hierarchical model system.

preprint2013arXivOpen access
Martin J. KörberMatthias MichlerArnd BäckerRoland Ketzmerick
nlin.CDquant-ph
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Martin J. KörberMatthias MichlerArnd BäckerRoland Ketzmerick

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