Semiclassical Limit of Resonance States in Chaotic Scattering
arXiv:2408.17088 · doi:10.1103/PhysRevLett.134.020404
Abstract
Resonance states in quantum chaotic scattering systems have a multifractal structure that depends on their decay rate. We show how classical dynamics describes this structure for all decay rates in the semiclassical limit. This result for chaotic scattering systems corresponds to the well-established quantum ergodicity for closed chaotic systems. Specifically, we generalize Ulam's matrix approximation of the Perron-Frobenius operator, giving rise to conditionally invariant measures of various decay rates. There are many matrix approximations leading to the same decay rate and we conjecture a criterion for selecting the one relevant for resonance states. Numerically, we demonstrate that resonance states in the semiclassical limit converge to the selected measure. Example systems are a dielectric cavity, the three-disk scattering system, and open quantum maps.
7 pages, 4 figures, The supplemental material provides further information and Python code for determining the proposed measures
References in corpus (14)
- Combining directional light output and ultralow loss in deformed microdisks
- Chaos-assisted directional light emission from microcavity lasers
- Quantum-to-classical crossover of quasi-bound states in open quantum systems
- Semiclassical structure of chaotic resonance eigenfunctions
- Fractal Weyl law for quantum fractal eigenstates
- Directional emission of stadium-shaped micro-lasers
- Resonances in open quantum maps
- Ulam method for the Chirikov standard map
- Universal intensity statistics of multifractal resonance states
- Impact of cavity geometry on microlaser dynamics
- Semiclassical Husimi distributions for non-Hermitian quantum systems
- Chaotic Explosions
- Local random vector model for semiclassical fractal structure of chaotic resonance states
- Resonance states of the three-disk scattering system