Related papers: Triaxial Ellipsoidal Quantum Billiards
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…
Billiards in ellipses have a confocal ellipse or hyperbola as caustic. The goal of this paper is to prove that for each billiard of one type there exists an isometric counterpart of the other type. Isometry means here that the lengths of…
We present a comprehensive review of the nodal domains and lines of quantum billiards, emphasizing a quantitative comparison of theoretical findings to experiments. The nodal statistics are shown to distinguish not only between regular and…
We discuss the localization of wavefunctions along planes containing the shortest periodic orbits in a three-dimensional billiard system with axial symmetry. This model mimicks the self-consistent mean field of a heavy nucleus at…
We investigate the properties of eigenstates and local density of states (LDOS) for a periodic 2D rippled billiard, focusing on their quantum-classical correspondence in energy representation. To construct the classical counterparts of LDOS…
A relationship between two old mathematical subjects is observed: the theory of hypergeometric functions and the separability in classical mechanics. Separable potential perturbations of the integrable billiard systems and the Jacobi…
We give a beautiful explicit example of a convex plane curve such that the outer billiard has a given finite number of invariant curves. Moreover, the dynamics on these curves is a standard shift. This example can be considered as an outer…
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…
In the thermodynamics of nanoscopic systems the relation between classical and quantum mechanical description is of particular importance. To scrutinize this correspondence we have picked out two 2-dim billiard systems. Both systems are…
We study the motion of classical particles confined in a two-dimensional "nuclear" billiard whose walls undergo periodic shape oscillations according to a fixed multipolarity. The presence of a coupling term in the single particle…
We examine the quantum mechanical eigensolutions of the two-dimensional infinite well or quantum billiard system consisting of a circular boundary with an infinite barrier or baffle along a radius. Because of the change in boundary…
An elementary application of Algorithmic Complexity Theory to the polygonal approximations of curved billiards-integrable and chaotic-unveils the equivalence of this problem to the procedure of quantization of classical systems: the scaling…
We present polynomial Poisson algebras for the 8 classical potentials in two-dimensional Euclidian space that separate in cartesian coordinates and allow a third order integral of motion. Some of the classical superintegrale potentials do…
A rotating system, such as a star, liquid drop, or atomic nucleus, may rotate as an oblate spheroid about its symmetry axis or, if the angular velocity is greater than a critical value, as a triaxial ellipsoid about a principal axis. The…
N point particles move within a billiard table made of two circular cavities connected by a straight channel. The usual billiard dynamics is modified so that it remains deterministic, phase space volumes preserving and time reversal…
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…
Barrier billiards are simple examples of pseudo-integrable models which form an appealing but poorly investigated subclass of dynamical systems. The paper examines the semiclassical limit of the exact quantum transfer operator for barrier…
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…
Recent investigations of fractal conductance fluctuations (FCF) in electron billiards reveal crucial discrepancies between experimental behavior and the semiclassical Landauer-Buttiker (SLB) theory that predicted their existence. In…
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…