Formation and interaction of resonance chains in the open 3-disk system
arXiv:1311.5128 · doi:10.1088/1367-2630/16/3/033029
Abstract
In ballistic open quantum systems one often observes that the resonances in the complex-energy plane form a clear chain structure. Taking the open 3-disk system as a paradigmatic model system, we investigate how this chain structure is reflected in the resonance states and how it is connected to the underlying classical dynamics. Using an efficient scattering approach we observe that resonance states along one chain are clearly correlated while resonance states of different chains show an anticorrelation. Studying the phase space representations of the resonance states we find that their localization in phase space oscillate between different regions of the classical trapped set as one moves along the chains and that these oscillations are connected to a modulation of the resonance spacing. A single resonance chain is thus no WKB quantization of a single periodic orbits, but the structure of several oscillating chains arises from the interaction of several periodic orbits. We illuminate the physical mechanism behind these findings by combining the semiclassical cycle expansion with a quantum graph model.
25 pages, 15 figures
References in corpus (19)
- Fractal Weyl laws for chaotic open systems
- 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
- Quantum-to-classical correspondence in open chaotic systems
- Directional emission of stadium-shaped micro-lasers
- Weyl asymptotics: From closed to open systems
- General linewidth formula for steady-state multimode lasing in arbitrary cavities
- Excess quantum noise due to mode nonorthogonality in dielectric microresonators
- Shot noise and transport in small quantum cavities with large openings
- Statistics of eigenfunctions in open chaotic systems: a perturbative approach
- Fractal Weyl law for three-dimensional chaotic hard-sphere scattering systems
- Lifetime statistics in chaotic dielectric microresonators
- A model for chaotic dielectric microresonators
- On the resonance eigenstates of an open quantum baker map
- Distribution of resonances in the quantum open baker map
- Avoided level crossing statistics in open chaotic billiards
- Fractal Weyl law for Linux Kernel Architecture
- Probing eigenfunction nonorthogonality by parametric shifts of resonance widths
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- Resonance eigenfunction hypothesis for chaotic systems
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- Chaotic resonance modes in dielectric cavities: Product of conditionally invariant measure and universal fluctuations
- Semiclassical Formulae For Wigner Distributions
- Improved fractal Weyl bounds for hyperbolic manifolds
- Resonance chains and geometric limits on Schottky surfaces
- Local random vector model for semiclassical fractal structure of chaotic resonance states
- Resonance chains in open systems, generalized zeta functions and clustering of the length spectrum
- Resonance states of the three-disk scattering system
- Semiclassical Limit of Resonance States in Chaotic Scattering
- Left-Right Husimi Representation of Chaotic Resonance States: Invariance and Factorization