相关论文: Chaotic time-dependent billiards

Chaos, namely exponential sensitivity to initial conditions, is generally considered a nuisance, inasmuch as it prevents long-term predictions in physical systems. Here, we present an easily accessible approach to undo deterministic chaos…

We study, analytically and numerically, the classical and quantum properties of a nearly spherical 3D billiard. In particular we show the appearence of quantum non ergodic behaviour and of the deviations from Random Matrix Theory…

In this paper we show that, under certain generic conditions, billiards on ovals have only a finite number of periodic orbits, for each period, all non-degenerate and at least one of them is hyperbolic. Moreover, the invariant curves of two…

Light propagation on a two-dimensional curved surface embedded in a three-dimensional space has attracted increasing attention as an analog model of four-dimensional curved spacetime in laboratory. Despite recent developments in modern…

Quantum ergodicity of classically chaotic systems has been studied extensively both theoretically and experimentally, in mathematics, and in physics. Despite this long tradition we are able to present a new rigorous result using only…

We show that the complexity of the billiard in a typical polygon grows cubically and the number of saddle connections grows quadratically along certain subsequences. It is known that the set of points whose first n-bounces hits the same…

Imperfections of Bunimovich mushroom Billiards are analyzed. Any experiment will be affected by such imperfections, and it will be necessary to estimate their influence. In particular some of the corners will be rounded and small deviations…

We consider an elliptic billiard whose shape slowly changes. During slow evolution of the billiard certain resonance conditions can be fulfilled. We study the phenomena of capture into a resonance and scattering on resonances which lead to…

We present a dynamical analysis of a classical billiard chain -- a channel with parallel semi-circular walls, which can serve as a model for a bended optical fiber. An interesting feature of this model is the fact that the phase space…

Some scaling properties for classical light ray dynamics inside a periodically corrugated waveguide are studied by use of a simplified two-dimensional nonlinear area-preserving map. It is shown that the phase space is mixed. The chaotic sea…

The elliptical stadium is a curve constructed by joining two half-ellipses, with half axes a>1 and b=1, by two straight segments of equal length 2h. In this work we find bounds on h, for a close to 1, to assure the positiveness of a…

Numerical calculations studying bound eigenstates in chaotic regions of phase space, including those of the stadium billiard, are summarized. These calculations demonstrate that the scars of periodic orbit model is seriously flawed. An…

We study the interplay of dissipation and harmonic driving in the elliptical billiard. These two competing processes balance each other, which leads to a destruction of Fermi acceleration and thus to a saturation of the ensemble averaged…

We investigate a class of mechanical billiards, where a particle moves in a planar region under the influence of an n-centre potential and reflects elastically on a straight wall. Motivated by Boltzmann's original billiard model we explore…

Billiard systems offer a simple setting to study regular and chaotic dynamics. Gravitational billiards are generalizations of these classical billiards which are amenable to both analytical and experimental investigations. Most previous…

In a series of pump and probe experiments, we study the lifetime statistics of a quantum chaotic resonator when the number of open channels is greater than one. Our design embeds a stadium billiard into a two dimensional photonic crystal…

We discuss the propagation of kinetic energy through billiard balls fixed in place along a one-dimensional segment. The number of billiard balls is assumed to be large but finite and we assume kinetic energy propagates following the usual…

We investigate the classical scattering dynamics of the driven elliptical billiard. Two fundamental scattering mechanisms are identified and employed to understand the rich behavior of the escape rate. A long-time algebraic decay which can…

We propose a flower shape billiard in order to study the irregular parameter dependence of chaotic normal diffusion. Our model is an open system consisting of periodically distributed obstacles of flower shape, and it is strongly chaotic…

We study finite two dimensional spin lattices with definite geometry (spin billiards) demonstrating the display of collective integrable or chaotic dynamics depending on their shape. We show that such systems can be quantum simulated by…