Related papers: Escape Rates and Physically Relevant Measures for …
We investigate the scaling of the escape rate from piecewise-linear dynamical systems displaying intermittency due to the presence of an indifferent fixed-point. Strong intermittent behaviour in the dynamics can result in the system…
Dynamical billiards consist of a particle on a two-dimensional table, bouncing elastically off a boundary curve. The state of the system is given by two numbers: one describing the location along the curve where the bounce occurs, and…
We present experimental results on the eigenfrequency statistics of a superconducting, chaotic microwave billiard containing a rotatable obstacle. Deviations of the spectral fluctuations from predictions based on Gaussian orthogonal…
The changeover from normal to super diffusion in time dependent billiards is explained analytically. The unlimited energy growth for an ensemble of bouncing particles in time dependent billiards is obtained by means of a two dimensional…
Systems of pinned billiard balls serve as simplified models of collisions, where all particles remain fixed in their positions while their (pseudo-)velocities evolve in accordance with the laws of conservation of energy and momentum. For…
The present work consists of a numerical study of the dynamics of irrational polygonal billiards. Our contribution reinforces the hypothesis that these systems could be Strongly Mixing, although never demonstrably chaotic, and discuss the…
We consider the open stadium billiard, consisting of two semicircles joined by parallel straight sides with one hole situated somewhere on one of the sides. Due to the hyperbolic nature of the stadium billiard, the initial decay of…
The random billiard walk is a stochastic process $(L_t)_{t\geq 0}$ in which a laser moves through the Coxeter arrangement of an affine Weyl group in $\mathbb{R}^d$, reflecting at each hyperplane with probability $p\in (0, 1)$ and…
We present experimental studies of the geometry-specific quantum scattering in microwave billiards of a given shape. We perform full quantum mechanical scattering calculations and find an excellent agreement with the experimental results.…
Consider a periodic tiling of a plane by equal triangles obtained from the equilateral tiling by a linear transformation. We study a following tiling billiard: a ball follows straight segments and bounces of the boundaries of the tiles into…
We prove some partial results on the periodicity of billiard systems on graphs. The results specialize to the case of $n$ billiards with equal mass on the unit interval or circle traveling at the same speed.
We remove a small disc from the flat two-dimensional torus and consider a point-like particle that starts moving from the center of the disc with linear trajectory. We provide asymptotic estimates for the moments of the first exit time,…
We consider a random walk in a stationary ergodic environment in $\mathbb Z$, with unbounded jumps. In addition to uniform ellipticity and a bound on the tails of the possible jumps, we assume a condition of strong transience to the right…
In an ordinary billiard system trajectories of a Hamiltonian system are elastically reflected after a collision with a hypersurface (scatterer). If the scatterer is a submanifold of codimension more than one, we say that the billiard is…
Semiconductor billiards are often considered as ideal systems for studying dynamical chaos in the quantum mechanical limit. In the traditional picture, once the electron's mean free path, as determined by the mobility, becomes larger than…
We consider the breathing circle billiard, in which a point particle moves freely inside a disk. The radius varies periodically in time, with elastic reflections at the moving boundary. In this system the angular momentum is preserved, and…
We study billiard in the plane endowed with symmetric \$\mathbb{Z}^2\$-periodic obstacles of a right-angled polygonal shape. One of our main interests is the dependence of the diffusion rate of the billiard on the shape of the obstacle. We…
In billiard systems with a flux line semiclassical approximations for the density of states contain contributions from periodic orbits as well as from diffractive orbits that are scattered on the flux line. We derive a semiclassical…
In this short note, we propose a new and short approach to polynomial escape rates, which can be applied to various open systems with intermittency. The tool of our approach is the maximal large deviations developed in \cite{mldp}.
We investigate the escape dynamics of the doubling map with a time-periodic hole. We use Ulam's method to calculate the escape rate as a function of the control parameters. We consider two cases, oscillating or breathing holes, where the…