English

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.

Keywords

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

R2 v1 2026-07-22T09:55:26.372Z