Local random vector model for semiclassical fractal structure of chaotic resonance states

TL;DR

This paper develops a local random vector model to describe the fractal structure of resonance states in chaotic scattering systems, bridging semiclassical analysis with multifractal measures and demonstrating its effectiveness through numerical simulations.

Contribution

It introduces a local randomization approach on phase space for the baker map with escape, enabling a semiclassical description of resonance states across decay rates.

Findings

Classical measures accurately describe resonance states in the randomized baker map.

Decreasing randomization scale aligns results with the deterministic baker map.

Multifractal structures persist down to the Planck scale in deterministic systems.

Abstract

The semiclassical structure of resonance states of classically chaotic scattering systems with partial escape is investigated. We introduce a local randomization on phase space for the baker map with escape, which separates the smallest multifractal scale from the scale of the Planck cell. This allows for deriving a semiclassical description of resonance states based on a local random vector model and conditional invariance. We numerically demonstrate that the resulting classical measures perfectly describe resonance states of all decay rates $\gamma$ for the randomized baker map. By decreasing the scale of randomization these results are compared to the deterministic baker map with partial escape. This gives the best available description of its resonance states. Quantitative differences indicate that a semiclassical description for deterministic chaotic systems must take into account that the multifractal structures persist down to the Planck scale.