منابع مشابه
Stickiness in mushroom billiards.
We investigate the dynamical properties of chaotic trajectories in mushroom billiards. These billiards present a well-defined simple border between a single regular region and a single chaotic component. We find that the stickiness of chaotic trajectories near the border of the regular region occurs through an infinite number of marginally unstable periodic orbits. These orbits have zero measur...
متن کاملQuantum mushroom billiards.
We report the first large-scale statistical study of very high-lying eigenmodes (quantum states) of the mushroom billiard proposed by L. A. Bunimovich [Chaos 11, 802 (2001)]. The phase space of this mixed system is unusual in that it has a single regular region and a single chaotic region, and no KAM hierarchy. We verify Percival's conjecture to high accuracy (1.7%). We propose a model for dyna...
متن کاملDynamical tunneling in mushroom billiards.
We study the fundamental question of dynamical tunneling in generic two-dimensional Hamiltonian systems by considering regular-to-chaotic tunneling rates. Experimentally, we use microwave spectra to investigate a mushroom billiard with adjustable foot height. Numerically, we obtain tunneling rates from high precision eigenvalues using the improved method of particular solutions. Analytically, a...
متن کاملMushroom Billiards, Volume 53, Number 3
334 NOTICES OF THE AMS VOLUME 53, NUMBER 3 T wo 20th century discoveries transformed scientists’ understanding of nonlinear phenomena [16]. One was KolmogorovArnold-Moser (KAM) theory, which demonstrated the stability of regular dynamics for small perturbations of Hamiltonian systems [4, 5, 11, 15]. The other was the theory of stochasticity of dynamical systems (loosely called “chaos theory”), ...
متن کاملMarginally unstable periodic orbits in semiclassical mushroom billiards.
Optical mushroom-shaped billiards offer a unique opportunity to isolate and study semiclassical modes concentrated on nondispersive, marginally unstable periodic orbits. Here we show that the openness of the cavity to external electromagnetic fields leads to unanticipated consequences for the far-field radiation pattern, including directional emission. This is mediated by interactions of margin...
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ژورنال
عنوان ژورنال: Chaos: An Interdisciplinary Journal of Nonlinear Science
سال: 2005
ISSN: 1054-1500,1089-7682
DOI: 10.1063/1.1979211