Resonance states at Casati wave numbers for the 3-disk billiard

Abstract

Resonance states of the 3-disk scattering system are presented for the first Casati wave number $k \approx 912$ and the second Casati wave number $k \approx 91242$. They show multifractal structure in phase space, similar to the pioneering work by Casati et al. [Physica D 131, 311 (1999)] for an open chaotic quantum map. In position space we observe scarring along segments of rays, related to multifractality and universal fluctuations, as recently found for dielectric cavities. To the best of our knowledge this resonance state at the second Casati wave number has a much larger wave number than published resonance states for the 3-disk scattering system or any other open or closed chaotic billiard.