Related papers: Diffractive orbits in quantum billiards

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 classical inner and outer billiards can be formulated in variational terms, with length and area as the respective generating functions. The other two combinations, ``inner with area'' and ``outer with length,'' are more recently…

We study a class of planar billiards having the remarkable property that their phase space consists up to a set of zero measure of two invariant sets formed by orbits moving in opposite directions. The tables of these billiards are tubular…

Polygonal billiards are an example of pseudo-chaotic dynamics, a combination of integrable evolution and sudden jumps due to conical singular points that arise from the corners of the polygons. Such pseudo-chaotic behaviour, often…

Astute variations in the geometry of mathematical billiard tables have been and continue to be a source of understanding their wide range of dynamical behaviors, from regular to chaotic. Viewing standard specular billiards in the broader…

We study the notion of Fagnano orbits for dual polygonal billiards. We used them to characterize regular polygons and we study the iteration of the developing map.

Using semi-classical formalism and asymptotic proliferation law of periodic orbits, we obtain an analytical expressions for the two-level cluster function, spectral form factor, level spacing distribution and the number variance for…

We investigate the semiclassical energy spectrum of quantum elliptic billiard. The nearest neighbor spacing distribution, level number variance and spectral rigidity support the notion that the elliptic billiard is a generic integrable…

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,…

We present an extensive numerical study of spectral statistics and eigenfunctions of quantized triangular billiards. We compute two million consecutive eigenvalues for six representative cases of triangular billiards, three with generic…

We study the dielectric annular billiard as a quantum chaotic model of a micro-optical resonator. It differs from conventional billiards with hard-wall boundary conditions in that it is partially open and composed of two dielectric media…

A correspondence between the orbits of a system of 2 complex, homogeneous, polynomial ordinary differential equations with real coefficients and those of a polygonal billiard is displayed. This correspondence is general, in the sense that…

The quantum dynamics of a chaotic billiard with moving boundary is considered in this work. We found a shape parameter Hamiltonian expansion which enables us to obtain the spectrum of the deformed billiard for deformations so large as the…

In this paper we define and study the billiard problem on bounded regions on surfaces of constant curvature. We show that this problem defines a 2-dimensional conservative and reversible dynamical system, defined by a Twist diffeomorphism,…

We study matrix element fluctuations of the two-body screened Coulomb interaction and of the one-body surface charge potential in ballistic quantum dots, comparing behavior in actual chaotic billiards with analytic results previously…

Billiards tables - a minimal model for particles moving in a confined region - are known to present classical (and quantum) different features according to their shape, ranging from strongly chaotic to integrable dynamics. Here we consider…

The diffraction trace formula ({\em Phys. Rev. Lett.} {\bf 73}, 2304 (1994)) and spectral determinant are tested on the open three disk scattering system. The system contains a generic and exponentially growing number of diffraction…

We give the asymptotic growth of the number of primitive periodic trajectories of a two dimensional dispersive billiard, when we prescribe their number of bounces on one of the obstacles.

The semiclassical theory for billiards with mixed boundary conditions is developed and explicit expressions for the smooth and the oscillatory parts of the spectral density are derived. The parametric dependence of the spectrum on the…

We investigate statistical properties of several classes of periodic billiard models which are diffusive. An introductory chapter gives motivation, and then a review of statistical properties of dynamical systems is given in chapter 2. In…