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

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.

19 pages, 10 figures

References in corpus (18)

• Husimi functions at dielectric interfaces: Inside-outside duality for optical systems and beyond
• Quantum-to-classical crossover of quasi-bound states in open quantum systems
• Semiclassical structure of chaotic resonance eigenfunctions
• Fractal Weyl law for chaotic microcavities: Fresnel's laws imply multifractal scattering
• Fractal Weyl law for quantum fractal eigenstates
• Weyl asymptotics: From closed to open systems
• Resonance distribution in open quantum chaotic systems
• A model for chaotic dielectric microresonators
• On the resonance eigenstates of an open quantum baker map
• Universal intensity statistics of multifractal resonance states
• Classical transients and the support of open quantum maps
• Semiclassical Husimi distributions for non-Hermitian quantum systems
• Transient features of quantum open maps
• Chaotic Explosions
• Resonance states of the three-disk scattering system
• Spectral gap for obstacle scattering in dimension 2
• Semiclassical Limit of Resonance States in Chaotic Scattering
• Decay Rates of Optical Modes Unveil the Island Structures in Mixed Phase Space