Nonlinear Sciences – Chaotic Dynamics
Scientific paper
2012-01-16
Phys. Rev. E 85, 036202 (2012)
Nonlinear Sciences
Chaotic Dynamics
Scientific paper
10.1103/PhysRevE.85.036202
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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