Left-Right Husimi Representation of Chaotic Resonance States: Invariance and Factorization

TL;DR

This paper introduces a left-right Husimi representation for chaotic resonance states, demonstrating its quantum invariance and factorization into classical and quantum components, supported by numerical evidence.

Contribution

It establishes the quantum invariance and factorization properties of the left-right Husimi representation in chaotic scattering systems, a novel insight in quantum chaos analysis.

Findings

Invariance under classical dynamics in the semiclassical limit

Factorization into classical multifractal structure and quantum fluctuations

Numerical confirmation across multiple systems

Abstract

For chaotic scattering systems we investigate the left-right Husimi representation, which combines left and right resonance states. We demonstrate that the left-right Husimi representation is invariant in the semiclassical limit under the corresponding closed classical dynamics, which we call quantum invariance. Furthermore, we show that it factorizes into a classical multifractal structure times universal quantum fluctuations. Numerical results for a dielectric cavity, the three-disk scattering system, and quantum maps confirm both the quantum invariance and the factorization.