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

TL;DR

This paper investigates resonance states at very high wave numbers in the 3-disk billiard system, revealing multifractal phase space structures, ray scar patterns, and universal fluctuations, extending the known wave number range significantly.

Contribution

It presents the first analysis of resonance states at the second Casati wave number, demonstrating multifractality and scarring at unprecedentedly high wave numbers in the 3-disk billiard.

Findings

Resonance states exhibit multifractal structure in phase space.

Ray segments show scarring related to multifractality.

First observation of such high wave number resonance states in this system.

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.