Abstract
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.
Funder
Deutsche Forschungsgemeinschaft
Subject
General Physics and Astronomy
Reference109 articles.
1. Ergodic properties of eigenfunctions (in Russian);Shnirelman;Usp. Math. Nauk,1974
2. Ergodicité et fonctions propres du laplacien (in French);Colin de Verdière;Commun. Math. Phys.,1985
3. Uniform distribution of eigenfunctions on compact hyperbolic surfaces;Zelditch;Duke Math. J.,1987
4. Ergodicity of eigenfunctions for ergodic billiards;Zelditch;Commun. Math. Phys.,1996
5. Rate of quantum ergodicity in Euclidean billiards;Bäcker;Phys. Rev. E,1998