منابع مشابه
Dynamical 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 کاملAn Introduction to Dynamical Billiards
Some billiard tables in R2 contain crucial references to dynamical systems but can be analyzed with Euclidean geometry. In this expository paper, we will analyze billiard trajectories in circles, circular rings, and ellipses as well as relate their charactersitics to ergodic theory and dynamical systems.
متن کاملWave Dynamical Chaos in Superconducting Microwave Billiards
During the last few years we have studied the chaotic behavior of special Euclidian geometries, so-called billiards, from the quantum or in more general sense “wave dynamical” point of view [1–3]. Due to the equivalence between the stationary Schrödinger equation and the classical Helmholtz equation in the two-dimensional case (plain billiards), it is possible to simulate “quantum chaos” with t...
متن کاملQuantum and wave dynamical chaos in superconducting microwave billiards.
Experiments with superconducting microwave cavities have been performed in our laboratory for more than two decades. The purpose of the present article is to recapitulate some of the highlights achieved. We briefly review (i) results obtained with flat, cylindrical microwave resonators, so-called microwave billiards, concerning the universal fluctuation properties of the eigenvalues of classica...
متن کاملTrack Billiards
We study a class of planar billiards having the remarkable property that their phase space consists up to a set of zero measure of two invariant sets formed by orbits moving in opposite directions. The tables of these billiards are tubular neighborhoods of differentiable Jordan curves that are unions of finitely many segments and arcs of circles. We prove that under proper conditions on the seg...
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ژورنال
عنوان ژورنال: Scholarpedia
سال: 2007
ISSN: 1941-6016
DOI: 10.4249/scholarpedia.1813