Semiclassical structure of chaotic resonance eigenfunctions

Abstract

We study the resonance (or Gamow) eigenstates of open chaotic systems in the semiclassical limit, distinguishing between left and right eigenstates of the non-unitary quantum propagator, and also between short-lived and long-lived states. The long-lived left (right) eigenstates are shown to concentrate as $\hslash \to 0$ on the forward (backward) trapped set of the classical dynamics. The limit of a sequence of eigenstates $\{\psi (\hslash ){\}}_{\hslash \to 0}$ is found to exhibit a remarkably rich structure in phase space that depends on the corresponding limiting decay rate. These results are illustrated for the open baker map, for which the probability density in position space is observed to have self-similarity properties.

4 pages, 4 figures; some minor corrections, some changes in presentation

References in corpus (6)

• Fractal Weyl laws for chaotic open systems
• Quantum-to-classical crossover of quasi-bound states in open quantum systems
• Quantum-to-classical correspondence in open chaotic systems
• Dynamical model for the quantum-to-classical crossover of shot noise
• Noiseless scattering states in a chaotic cavity
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Cited by in corpus (11)

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• Directional emission of stadium-shaped micro-lasers
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• Scarring in open quantum systems
• Multifractality and intermediate statistics in quantum maps
• 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
• Some open questions in "wave chaos"
• Quantum Localization in Open Chaotic Systems