相关论文: Diffractive orbits in an open microwave billiard

We investigate the statistical properties of wavefunctions in an open chaotic cavity. When the number of channels in the openings of the billiard is increased by varying the frequency, wavefunctions cross over from real to complex. The…

The semiclassical description of billiard spectra is extended to include the diffractive contributions from orbits which are nearly tangent to a concave part of the boundary. The leading correction for an unstable isolated orbit is of the…

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…

The frequency dependence of the interlayer conductivity of a layered Fermi liquid in a magnetic field which is tilted away from the normal to the layers is considered. For both quasi-one- and quasi-two-dimensional systems resonances occur…

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,…

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…

Isospectral domains are non-isometric regions of space for which the spectra of the Laplace-Beltrami operator coincide. In the two-dimensional Euclidean space, instances of such domains have been given. It has been proved for these examples…

We study the statistical properties of wavefunctions in a chaotic billiard that is opened up to the outside world. Upon increasing the openings, the billiard wavefunctions cross over from real to complex. Each wavefunction is characterized…

We introduce and investigate billiard systems with an adjusted ray dynamics that accounts for modifications of the conventional reflection of rays due to universal wave effects. We show that even small modifications of the specular…

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…

We review some properties of periodic orbit families in polygonal billiards and discuss in particular a sum rule that they obey. In addition, we provide algorithms to determine periodic orbit families and present numerical results that shed…

We study the resonances of the quantum kicked rotor subjected to an excitation that follows a deterministic time-dependent prescription. For the primary resonances we find an analytical relation between the long-time behavior of the…

Experiments with superconducting microwave cavities have been performed in our laboratory for more than two decades. The purpose of the present article is to recapitulate some of the highlights achieved. We briefly review (i) results…

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…

Evidence for dynamical tunneling is observed in studies of the transmission, and wave functions, of a soft-walled microwave cavity resonator. In contrast to previous work, we identify the conditions for dynamical tunneling by monitoring the…

Diffractive systems are quantum-mechanical models with point-like singularities where usual semiclassical approximation breaks down. An overview of recent investigations of such systems is presented. The following examples are considered in…

Sufficiently differentiable oval billiards always have invariant rotational curves, but there are only two types of ovals with an invariant horizontal circle in its phase-space: the constant width ovals and some very special symmetric…

We study diffraction corrections to the semiclassical spectral density of dispersing (Sinai) billiards. They modify the contributions of periodic orbits (PO's), with at least one segment which is almost tangent to the concave part of the…

This article presents experimental results on properties of waves propagating in an unbounded and a bounded photonic crystal consisting of metallic cylinders which are arranged in a triangular lattice. First, we present transmission…

We report on experimental studies that were performed with a microwave Dirac billiard (DB), that is, a flat resonator containing metallic cylinders arranged on a triangular grid, whose shape has a threefold rotational C3 symmetry. Its band…