Resonance states of the three-disk scattering system

TL;DR

This paper investigates the resonance states in the three-disk scattering system, confirming a conjecture about their factorization, analyzing their statistical properties, and introducing a new numerical method to explore the semiclassical limit.

Contribution

It confirms a conjecture about the factorization of resonance states, introduces a new numerical method, and verifies the fractal Weyl law in the three-disk system.

Findings

Resonance states are composed of two factors: universal intensity fluctuations and a classical density.

Ray-segment scars dominate resonance states at small wavelengths.

The new numerical method extends the semiclassical analysis range.

Abstract

For the paradigmatic three-disk scattering system, we confirm a recent conjecture for open chaotic systems, which claims that resonance states are composed of two factors. In particular, we demonstrate that one factor is given by universal exponentially distributed intensity fluctuations. The other factor, supposed to be a classical density depending on the lifetime of the resonance state, is found to be very well described by a classical construction. Furthermore, ray-segment scars, recently observed in dielectric cavities, dominate every resonance state at small wavelengths also in the three-disk scattering system. We introduce a new numerical method for computing resonances, which allows for going much further into the semiclassical limit. As a consequence we are able to confirm the fractal Weyl law over a correspondingly large range.