Related papers: Elliptic billiard - a non-trivial integrable syste…
The eigenvalues of the Hyperspherical billiard are calculated in the semiclassical approximation. The eigenvalues where this approximation fails are identified and found to be related to caustics that approach the wall of the billiard. The…
We study quantum-mechanical tunneling between symmetry-related pairs of regular phase space regions that are separated by a chaotic layer. We consider the annular billiard, and use scattering theory to relate the splitting of…
We apply a molecular dynamics scheme to analyze classically chaotic properties of a two-dimensional circular billiard system containing two Coulomb-interacting electrons. As such, the system resembles a prototype model for a semiconductor…
We consider billiards obtained by removing from the plane finitely many strictly convex analytic obstacles satisfying the non-eclipse condition. The restriction of the dynamics to the set of non-escaping orbits is conjugated to a subshift,…
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…
We show that wave functions in planar rational polygonal billiards (all angles rationally related to Pi) can be expanded in a basis of quasi-stationary and spatially regular states. Unlike the energy eigenstates, these states are directly…
In a recent letter [Phys. Rev. Lett. {\bf 100}, 164101 (2008)] and within the context of quantized chaotic billiards, random plane wave and semiclassical theoretical approaches were applied to an example of a relatively new class of…
A variety of mesoscopic systems can be represented as a billiard with a random coupling to the exterior at the boundary. Examples include quantum dots with multiple leads, quantum corrals with different kinds of atoms forming the boundary,…
We studied the statistical properties of a quantum system in the pseudo-integrable regime through the gap ratios between consecutive energy levels of the scattering spectra. A two-dimensional quantum billiard containing a point-like…
We investigate the existence of elliptic islands for a special family of periodic orbits of a two-parameter family of maps corresponding to the billiard problem on the elliptical stadium. The hyperbolic or elliptical character of these…
The barrier billiard is the simplest example of pseudo-integrable models with interesting and intricate classical and quantum properties. Using the Wiener-Hopf method it is demonstrated that quantum mechanics of a rectangular billiard with…
We consider billiard ball motion in a convex domain of the Euclidean plane bounded by a piece-wise smooth curve influenced by the constant magnetic field. We show that if there exists a polynomial in velocities integral of the magnetic…
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…
The role of electronic interactions in the level structure of semiconductor quantum dots is analyzed in terms of the correspondence to the integrability of a classical system that models these structures. We find that an otherwise simple…
Particle motion in a smoothly oscillating non-integrable billiard is known to result in unbounded energy growth. Though the asymptotic energy growth rate of an ensemble of particles in an oscillating chaotic billiard is known to be…
We study dissipative polygonal outer billiards, i.e. outer billiards about convex polygons with a contractive reflection law. We prove that dissipative outer billiards about any triangle and the square are asymptotically periodic, i.e. they…
The billiard systems within quadrics, playing the role of discrete analogues of geodesics on ellipsoids, are incorporated into the theory of integrable quad-graphs. An initial observation is that the Six-pointed star theorem, as the…
Billiard systems, broadly speaking, may be regarded as models of mechanical systems in which rigid parts interact through elastic impulsive (collision) forces. When it is desired or necessary to account for linear/angular momentum exchange…
We introduce symplectic billiards for pairs of possibly non-convex polygons. After establishing basic properties, we give several criteria on pairs of polygons for the symplectic billiard map to be fully periodic, i.e. $\textit{every}$…
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…