Chaotic resonance modes in dielectric cavities: Product of conditionally invariant measure and universal fluctuations

TL;DR

This paper proposes that chaotic resonance modes in dielectric cavities are formed by a product of a classical measure and universal fluctuations, with multifractality explaining mode scarring.

Contribution

It introduces a conjecture linking classical dynamics and universal fluctuations to chaotic resonance modes, supported by analysis of dielectric cavities with chaotic ray dynamics.

Findings

Chaotic resonance modes are a product of classical measure and universal fluctuations.

Multifractal structure depends on mode lifetime and explains mode averaging.

Supported by analysis of dielectric cavities with chaotic ray dynamics.

Abstract

We conjecture that chaotic resonance modes in scattering systems are a product of a conditionally invariant measure from classical dynamics and universal exponentially distributed fluctuations. The multifractal structure of the first factor depends strongly on the lifetime of the mode and describes the average of modes with similar lifetime. The conjecture is supported for a dielectric cavity with chaotic ray dynamics at small wavelengths, in particular for experimentally relevant modes with longest lifetime. We explain scarring of the vast majority of modes along segments of rays based on multifractality and universal fluctuations, which is conceptually different from periodic-orbit scarring.