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We consider a multi-dimensional billiard system in an (n+1)-dimensional Euclidean space, the direct product of the "horizontal" hyperplane and the "vertical" line. The hypersurface that determines the system is assumed to be smooth and…

We consider a billiard model of a self-bound, interacting three-body system in two spatial dimensions. Numerical studies show that the classical dynamics is chaotic. The corresponding quantum system displays spectral fluctuations that…

Students in introductory physics courses struggle to understand virtual image formation by a plane mirror and the proper construction of ray diagrams. This difficulty, if not sufficiently addressed, results in further problems throughout…

Generic one-parameter billiards are studied both classically and quantally. The classical dynamics for the billiards makes a transition from regular to fully chaotic motion through intermediary soft chaotic system. The energy spectra of the…

The purpose of this article is to construct a toolbox, in Dynamical Systems, to support the idea that ``whenever we can prove a limit theorem in the classical sense for a dynamical system, we can prove a suitable almost-sure version based…

We present numerical simulations of magnetic billiards inside a convex domain in the plane.

This study introduces a method for simulating quantum systems using electrical networks. Our approach leverages a generalized similarity transformation, which connects different Hamiltonians, enabling well-defined paths for quantum system…

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…

Semiclassical approximations often involve the use of stationary phase approximations. This method can be applied when $\hbar$ is small in comparison to relevant actions or action differences in the corresponding classical system. In many…

In standard (mathematical) billiards a point particle moves uniformly in a billiard table with elastic reflections off the boundary. We show that in transition from mathematical billiards to physical billiards, where a finite size hard…

In this paper we are interested in the motion of a ball inside a billiard table bounded by a particular smooth curve. This table belongs to a family of billiards which can all be drawn by a common process: the so-called gardener's string…

We survey applications of the theory of hyperbolic (and to a lesser extent non hyperbolic) billiards to some fundamental problems of statistical physics and their mathematically rigorous derivations in the framework of classical Hamiltonian…

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…

A circular Andreev billiard in a uniform magnetic field is studied. It is demonstrated that the classical dynamics is pseudointegrable in the same sense as for rational polygonal billiards. The relation to a specific polygon, the asymmetric…

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,…

A quantum wave function with localization on classical periodic orbits in a mesoscopic elliptic billiard has been achieved by appropriately superposing nearly degenerate eigenstates expressed as products of Mathieu functions. We analyze and…

The classical and quantum behavior of a particle inside a square box under the influence of the gravitational field is studied. Detailed calculations on periodic orbits, probability densities as well as expectation values and uncertainties…

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…

Rational polygonal billiards are one of the key models among the larger class of pseudo-integrable billiards. Their billiard flow may be lifted to the geodesic flow on a translation surface. Whereas such classical billiards have been much…

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…