Local random vector model for semiclassical fractal structure of chaotic resonance states
arXiv:2112.12626 · doi:10.1088/1751-8121/ac62b9
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 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.
References in corpus (43)
- Statistics of resonance poles, phase shifts and time delays in quantum chaotic scattering for systems with broken time reversal invariance
- Topologically protected defect states in open photonic systems with non-hermitian charge-conjugation and parity-time symmetry
- Leaking Chaotic Systems
- Truncations of random unitary matrices
- Quasi-Scarred Resonances in a Spiral-Shaped Microcavity
- Fractal Weyl laws for chaotic open systems
- Quantum-to-classical crossover of quasi-bound states in open quantum systems
- Quantum Mechanics and Semiclassics of Hyperbolic n-Disk Scattering Systems
- Semiclassical structure of chaotic resonance eigenfunctions
- On the rate of quantum ergodicity in Euclidean billiards
- Fractal Weyl law for chaotic microcavities: Fresnel's laws imply multifractal scattering
- Numerical Study of Quantum Resonances in Chaotic Scattering
- Spectra of Random Contractions and Scattering Theory for Discrete-Time Systems
- Frobenius-Perron Resonances for Maps with a Mixed Phase Space
- Ulam method and fractal Weyl law for Perron--Frobenius operators
- From scattering theory to complex wave dynamics in non-hermitian PT-symmetric resonators
- Decoherence scenarios from micro- to macroscopic superpositions
- Amplitude distribution of eigenfunctions in mixed systems
- Quantization of generic chaotic 3D billiard with smooth boundary II: structure of high-lying eigenstates
- Resonances of the Frobenius-Perron Operator for a Hamiltonian Map with a Mixed Phase Space
- Quantum chaotic resonances from short periodic orbits
- Weyl's law and quantum ergodicity for maps with divided phase space
- Fractal Weyl laws for quantum decay in generic dynamical systems
- Classical versus Quantum Time Evolution of Densities at Limited Phase-Space Resolution
- Fractal Weyl law behavior in an open, chaotic Hamiltonian system
- Quantum statistics of overlapping modes in open resonators
- Fractal Weyl law for three-dimensional chaotic hard-sphere scattering systems
- Spatial structure of lasing modes in wave-chaotic semiconductor microcavities
- Hierarchical Fractal Weyl Laws for Chaotic Resonance States in Open Mixed Systems
- Resonance distribution in open quantum chaotic systems
- Resonance eigenfunction hypothesis for chaotic systems
- On the resonance eigenstates of an open quantum baker map
- Short periodic orbit approach to resonances and the fractal Weyl law
- Chaotic Systems with Absorption
- Formation and interaction of resonance chains in the open 3-disk system
- Quantum billiards and constrained random wave correlations
- Structure of resonance eigenfunctions for chaotic systems with partial escape
- Quantum signatures of classical multifractal measures
- Localization of Chaotic Resonance States due to a Partial Transport Barrier
- Short periodic orbits theory for partially open quantum maps
- Universal intensity statistics of multifractal resonance states
- Chaotic Explosions
- Asymptotic mean density of sub-unitary ensemble