Super-sharp resonances in chaotic wave scattering

Abstract

Wave scattering in chaotic systems can be characterized by its spectrum of resonances, $z_n=E_n-i\frac{{\Gamma }_n}{2}$, where $E_n$ is related to the energy and ${\Gamma }_n$ is the decay rate or width of the resonance. If the corresponding ray dynamics is chaotic, a gap is believed to develop in the large-energy limit: almost all ${\Gamma }_n$ become larger than some $\gamma$. However, rare cases with $\Gamma <\gamma$ may be present and actually dominate scattering events. We consider the statistical properties of these super-sharp resonances. We find that their number does not follow the fractal Weyl law conjectured for the bulk of the spectrum. We also test, for a simple model, the universal predictions of random matrix theory for density of states inside the gap and the hereby derived probability distribution of gap size.

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• Resonances in open quantum maps
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• Resonance eigenfunction hypothesis for chaotic systems
• Multimode Lasing in Wave-Chaotic Semiconductor Microlasers
• Multifractality of open quantum systems
• Chaotic resonance modes in dielectric cavities: Product of conditionally invariant measure and universal fluctuations
• Improved fractal Weyl bounds for hyperbolic manifolds
• Semiclassical theory of chaotic quantum resonances
• Resonance spectra for quantum maps of kicked scattering systems by complex scaling
• Left-Right Husimi Representation of Chaotic Resonance States: Invariance and Factorization