Resonance states in chaotic scattering

Date: Thursday 20th March 2025

Abstract

Eigenfunctions in closed quantum systems with a chaotic classical limit are equidistributed following the quantum ergodicity theorem. In contrast, in open scattering systems one finds that resonance states have a multifractal structure. How is this structure generated from the underlying classical dynamics?

We answer this by generalizing Ulam’s matrix approximation of the Perron-Frobenius operator. It gives rise to a conditionally invariant measure describing resonance states in the semiclassical limit. Numerical examples are a dielectric cavity and the three-disk scattering system.