Related papers: Billiards and toy gravitons
The two-body problem is extensively studied in open systems and asymptotically flat spacetimes. However, there are many systems where radiation is trapped: they range from radiating charges in cavities to low-energy excitations of massive…
The aim of the paper is to unify the efforts in the study of integrable billiards within quadrics in flat and curved spaces and to explore further the interplay of symplectic and contact integrability. As a starting point in this direction,…
Recent experiments have shown that many species of microorganisms leave a solid surface at a fixed angle determined by steric interactions and near-field hydrodynamics. This angle is completely independent of the incoming angle. For several…
Quantum dynamica of a massless Dirac particle in time-dependent 1D box and circular billiard with time-dependent radius is studied. An exact analytical wave functions and eigenvalues are obtained for the case of linear time-dependence of…
We study stochastic billiards in infinite planar domains with curvilinear boundaries: that is, piecewise deterministic motion with randomness introduced via random reflections at the domain boundary. Physical motivation for the process…
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…
A billiard is a dynamical system in which a particle alternates between motion in a straight line and specular reflection from a boundary. For billiards in non-convex areas bounded by segments of confocal quadrics are studied. The topology…
Neutrino billiards serve as a model system for the study of aspects of relativistic quantum chaos. These are relativistic quantum billiards consisting of a spin-1/2 particle which is confined to a planar domain by imposing boundary…
We consider a mechanical system consisting of an infinite rod (a straight line) and a ball (a massless point) on the plane. The rod rotates uniformly around one of its points. The ball is reflected elastically when colliding with the rod…
The pseudo-Euclidean Toda-like system of cosmological origin is considered. When certain restrictions on the parameters of the model are imposed, the dynamics of the model near the ``singularity'' is reduced to a billiard on the…
We discuss various experiments on the time decay of velocity autocorrelation functions in billiards. We perform new experiments and find results which are compatible with an exponential mixing hypothesis, first put forward by [FM]: they do…
Dynamical billiards, or the behavior of a particle traveling in a planar region $D$ undergoing elastic collisions with the boundary, has been extensively studied and is used to model many physical phenomena such as a Boltzmann gas. Of…
We present a game inspired by research on the possible number of billiard ball collisions in the whole Euclidean space. One player tries to place $n$ static "balls" with zero radius (i.e., points) in a way that will minimize the total…
In this paper, we define a variant of billiards in which the ball bounces around a square grid erasing walls as it goes. We prove that there exist periodic tunnels with arbitrarily large period from any possible starting point, that there…
Random-matrix theory is used to show that the proximity to a superconductor opens a gap in the excitation spectrum of an electron gas confined to a billiard with a chaotic classical dynamics. In contrast, a gapless spectrum is obtained for…
We explore the dynamical evolution of an ensemble of non-interacting particles propagating freely in an elliptical billiard with harmonically driven boundaries. The existence of Fermi acceleration is shown thereby refuting the established…
We call internal-wave billiard the dynamical system of a point particle that moves freely inside a planar domain (the table) and is reflected by its boundary according to this rule: reflections are standard Fresnel reflections but with the…
In an ordinary billiard 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…
We study stochastic billiards on general tables: a particle moves according to its constant velocity inside some domain ${\mathcal D} \subset {\mathbb R}^d$ until it hits the boundary and bounces randomly inside according to some reflection…
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…