English
Related papers

Related papers: Physical Versus Mathematical Billiards: From Regul…

200 papers

We study nonlinear dynamics of the kicked particle whose motion is confined by square billiard. The kick source is considered as localized at the center of square with central symmetric spatial distribution. It is found that ensemble…

Chaotic Dynamics · Physics 2015-05-28 D. U. Matrasulov , U. R. Salomov , G. M. Milibaeva , N. E. Iskandarov

While many dynamical systems of mechanical origin, in particular billiards, are strongly chaotic -- enjoy exponential mixing, the rates of mixing in many other models are slow (algebraic, or polynomial). The dynamics in the latter are…

Mathematical Physics · Physics 2009-11-10 Nikolai Chernov , Hong-Kun Zhang

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…

Dynamical Systems · Mathematics 2026-02-18 Patrick Bishop , Summer Chenoweth , Emmanuel Fleurantin , Evelyn Sander , Jason Mireles James

Spatial diffusion of particles in periodic potential models has provided a good framework for studying the role of chaos in global properties of classical systems. Here a bidimensional "soft" billiard, classically modeled from an optical…

Statistical Mechanics · Physics 2022-05-16 Matheus J. Lazarotto , Iberê L. Caldas , Yves Elskens

The seminal physical model for investigating formulations of nonlinear dynamics is the billiard. Gravitational billiards provide an experimentally accessible arena for their investigation. We present a mathematical model that captures the…

Chaotic Dynamics · Physics 2015-03-19 Alexandre E. Hartl , Bruce N. Miller , Andre P. Mazzoleni

We report a dynamical phase transition from integrability to non-integrability in a simple oval-like billiard with boundary $R(\theta)=1+\epsilon\cos(p\theta)$. For $\epsilon=0$, the phase space is {\it foliated} by invariant curves…

We examine the spectral properties of three-dimensional quantum billiards with a single pointlike scatterer inside. It is found that the spectrum shows chaotic (random-matrix-like) characteristics when the inverse of the formal strength…

chao-dyn · Physics 2009-10-30 T. Shigehara , Taksu Cheon

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…

Chaotic Dynamics · Physics 2015-07-27 Cameron K. Langer , Bruce N. Miller

We report on the numerical simulation of the double-slit experiment, where the initial wave-packet is bounded inside a billiard domain with perfectly reflecting walls. If the shape of the billiard is such that the classical ray dynamics is…

Chaotic Dynamics · Physics 2009-11-10 Giulio Casati , Tomaz Prosen

We examine the quantum motion of two particles interacting through a contact force which are confined in a rectangular domain in two and three dimensions. When there is a difference in the mass scale of two particles, adiabatic separation…

High Energy Physics - Theory · Physics 2008-11-26 Taksu Cheon , T. Shigehara

We introduce a class of convex, higher-dimensional billiard models which generalise stadium billiards. These models correspond to the free motion of a point-particle in a region bounded by cylinders cut by planes. They are motivated by…

Chaotic Dynamics · Physics 2013-02-07 Thomas Gilbert , David P. Sanders

We consider a strictly convex billiard table with $C^2$ boundary, with the dynamics subjected to random perturbations. Each time the billiard ball hits the boundary its reflection angle has a random perturbation. The perturbation…

Dynamical Systems · Mathematics 2018-06-15 Roberto Markarian , Leonardo T. Rolla , Vladas Sidoravicius , Fabio A. Tal , Maria E. Vares

We study the thermal rectification phenomenon in ``billiard'' systems with interacting particles. This interaction induces a local dynamical response of the billiard to an external thermodynamic gradient. To explain this dynamical effect we…

Statistical Mechanics · Physics 2008-07-15 Jean-Pierre Eckmann , Carlos Mejia-Monasterio

In this article we study the one-dimensional dynamics of elastic collisions of particles with positive and negative mass. We show that such systems are equivalent to billiards induced by an inner product of possibly indefinite signature, we…

Mathematical Physics · Physics 2019-03-27 Alfonso Artigue

The billiard problem of statistical physics is considered in a new geometric approach with a symmetric phase space. The structure and topological features of typical billiard phase portrait are defined. The connection between geometric,…

Chaotic Dynamics · Physics 2007-05-23 Sergey V. Naydenov , Vladimir V. Yanovsky

In the present work we explore the concept of solitary wave billiards. I.e., instead of a point particle, we examine a solitary wave in an enclosed region and explore its collision with the boundaries and the resulting trajectories in cases…

Pattern Formation and Solitons · Physics 2023-04-12 J. Cuevas-Maraver , P. G. Kevrekidis , H. Zhang

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…

Mathematical Physics · Physics 2025-12-02 Krzysztof Burdzy , Jeremy G. Hoskins , Stefan Steinerberger

Polygonal billiards exhibit a rich and complex dynamical behavior. In recent years polygonal billiards have attracted great attention due to their application in the understanding of anomalous transport, but also at the fundamental level,…

Chaotic Dynamics · Physics 2024-05-14 Jordan Orchard , Federico Frascoli , Lamberto Rondoni , Carlos Mejía-Monasterio

We adapt ideas from geometrical optics and classical billiard dynamics to consider particle trajectories with constant velocity on a cone with specular reflections off an elliptical boundary formed by the intersection with a tilted plane,…

Chaotic Dynamics · Physics 2025-08-06 Lara Braverman , David R. Nelson

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…

Dynamical Systems · Mathematics 2025-08-12 Stefano Baranzini