Uniform approximation for diffractive contributions to the trace formula in billiard systems
chao-dyn
2009-10-28 v1 Chaotic Dynamics
Abstract
We derive contributions to the trace formula for the spectral density accounting for the role of diffractive orbits in two-dimensional billiard systems with corners. This is achieved by using the exact Sommerfeld solution for the Green function of a wedge. We obtain a uniformly valid formula which interpolates between formerly separate approaches (the geometrical theory of diffraction and Gutzwiller's trace formula). It yields excellent numerical agreement with exact quantum results, also in cases where other methods fail.
Cite
@article{arxiv.chao-dyn/9610006,
title = {Uniform approximation for diffractive contributions to the trace formula in billiard systems},
author = {Martin Sieber and Nicolas Pavloff and Charles Schmit},
journal= {arXiv preprint arXiv:chao-dyn/9610006},
year = {2009}
}
Comments
LaTeX, 41 pages including 12 PostScript figures, submitted to Phys. Rev. E