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

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 wave model and conditional invariance. We numerically demonstrate that the resulting classical measures perfectly describe resonance states of all decay rates γ for the randomized baker map. Comparison to the baker map without randomization shows very good agreement of the multifractal structures. Quantitative differences indicate that a semiclassical description for systems without randomization must take into account that the multifractal structures persist down to the Planck scale.