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 supersharp 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.

• Received 13 January 2012

DOI:https://doi.org/10.1103/PhysRevE.85.036202