Nonperiodic echoes from mushroom billiard hats

Abstract

Mushroom billiards have the remarkable property to show one or more clear cut integrable islands in one or several chaotic seas, without any fractal boundaries. The islands correspond to orbits confined to the hats of the mushrooms, which they share with the chaotic orbits. It is thus interesting to ask how long a chaotic orbit will remain in the hat before returning to the stem. This question is equivalent to the inquiry about delay times for scattering from the hat of the mushroom into an opening where the stem should be. For fixed angular momentum we find that no more than three different delay times are possible. This induces striking nonperiodic structures in the delay times that may be of importance for mesoscopic devices and should be accessible to microwave experiments.

arXiv commentSubmitted to Phys. Rev. E without the appendix

References in corpus (11)

• Semiclassical Foundation of Universality in Quantum Chaos
• Stickiness in Hamiltonian systems: from sharply divided to hierarchical phase space
• Quantum transport through ballistic cavities: soft vs. hard quantum chaos
• Stickiness in mushroom billiards
• Complete S-matrix in a microwave cavity at room temperature
• First experimental evidence for quantum echoes in scattering systems
• One-Particle and Few-Particle Billiards
• Self-pulsing effect in chaotic scattering
• Generic occurrence of rings in rotating systems
• Quantum and classical echoes in scattering systems described by simple Smale horseshoes
• Canonically Transformed Detectors Applied to the Classical Inverse Scattering Problem

Cited by in corpus (9)

• Leaking Chaotic Systems
• Spectral fluctuations of billiards with mixed dynamics: from time series to superstatistics
• Playing relativistic billiards beyond graphene
• Prevalence of marginally unstable periodic orbits in chaotic billiards
• Open Mushrooms: Stickiness revisited
• Escape time statistics for mushroom billiards
• Nonperiodic echoes from quantum mushroom billiard hats
• Few Islands Approximation of Hamiltonian System with divided Phase Space
• About Imperfect Mushroom Billiards