Distorted plane waves in chaotic scattering

Scattering of plane elastic waves by three-dimensional diffraction gratings

Quantum Resonances in Chaotic Scattering

This letter summarizes numerical results from [1] which show that in quantum systems with chaotic classical dynamics, the number of scattering resonances near an energy E scales like h̄− D(KE)+1 2 . Here, KE denotes the subset of the classical energy surface {H = E} which stays bounded for all time under the flow of H and D (KE) denotes its fractal dimension. Since the number of bound states in ...

Plane waves in three dimensions

We saw that a whitening filter in three dimensions is a small volume with shape defined by subroutine createhelix(). It might seem natural that the number of points on the xand y-axes be related to the number of plane waves present. Instead, I assert that if the volume contains plane waves, we don’t want a volume filter to whiten it; we can use a pair of planar filters to do so and the order of...

Chaotic scattering on graphs

Quantized, compact graphs are excellent paradigms for quantum chaos in bounded systems. Connecting them with leads to infinity, we show that they display all the features which characterize quantum chaotic scattering. We derive exact expressions for the scattering matrix, and an exact trace formula for the density of resonances, in terms of classical orbits, analogous to the semiclassical theor...

Dissipative chaotic scattering.

We show that weak dissipation, typical in realistic situations, can have a metamorphic consequence on nonhyperbolic chaotic scattering in the sense that the physically important particle-decay law is altered, no matter how small the amount of dissipation. As a result, the previous conclusion about the unity of the fractal dimension of the set of singularities in scattering functions, a major cl...