相关论文: Billiards with polynomial mixing rates
Chaotic multiscale dynamical systems are common in many areas of science, one of the examples being the interaction of the low-frequency dynamics in the atmosphere with the fast turbulent weather dynamics. One of the key questions about…
We propose geometric tools that are suitable for studying the behavior of a billiard trajectory in a homogeneous force field. Two examples are considered: a vertical plane with an open top and with a parabolic or right angle boundary at the…
We study eigenstates of chaotic billiards in the momentum representation and propose the radially integrated momentum distribution as useful measure to detect localization effects. For the momentum distribution, the radially integrated…
We investigate the question of the rate of mixing for observables of a Z d-extension of a probability preserving dynamical system with good spectral properties. We state general mixing results, including expansions of every order. The main…
In this paper we have tested several general numerical methods in solving the quantum billiards, such as the boundary integral method (BIM) and the plane wave decomposition method (PWDM). We performed extensive numerical investigations of…
Classical billiards constitute an important class of dynamical systems. They have not only been in used in mathematical disciplines such as ergodic theory, but their properties demonstrate fundamental physical phenomena that can be observed…
We study the stability of periodic trajectories of planar inverse magnetic billiards, a dynamical system whose trajectories are straight lines inside a connected planar domain $\Omega$ and circular arcs outside $\Omega$. Explicit examples…
In this work, we construct linearly stable periodic orbits in $3$-dimensional domains with boundaries containing focusing components (small pieces of a sphere) where we place these components arbitrarily far apart. It demonstrates that we…
Have you ever played or watched a game of pool? If so, you have already seen a billiard system in action. In mathematics and physics, a billiard system describes a ball that moves in straight lines and bounces off walls. Despite these…
The purpose of this paper is to study the dynamics of a square billiard with a non-standard reflection law such that the angle of reflection of the particle is a linear contraction of the angle of incidence. We present numerical and…
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 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…
Efficient mixing of fluids is essential in many practical applications to achieve homogeneity. For microscopic systems, however, both diffusion and turbulence are ineffective methods to achieve chaotic mixing due to the low Reynolds number,…
This paper investigates the dynamics of optical billiards, a generalization of classic billiards, where light rays travel within a refractive medium and reflect elastically at the boundary. Inspired by studies of acoustic modes in rapidly…
We introduce and study several random combinatorial billiard trajectories. Such a system, which depends on a fixed parameter $p\in(0,1)$, models a beam of light that travels in a Euclidean space, occasionally randomly reflecting off of a…
The connected configuration space of a so called cylindric billiard system is a flat torus minus finitely many spherical cylinders. The dynamical system describes the uniform motion of a point particle in this configuration space with…
We develop a framework for dealing with smooth approximations to billiards with corners in the two-dimensional setting. Let a polygonal trajectory in a billiard start and end up at the same billiard's corner point. We prove that smooth…
Balanced knockout tournaments are ubiquitous in sports competitions and are also used in decision-making and elections. The traditional computational question, that asks to compute a draw (optimal draw) that maximizes the winning…
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 study polygonal billiards with one-sided vertical mirror scattered on a square billiard table. We associate trajectories of these kinds of billiards with double rotations and study orbit behavior and questions of complexity.