Uniform approximation for diffractive contributions to the trace formula in billiard systems

Martin Sieber 1, 2, Nicolas Pavloff 1, Charles Schmit 1

Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 55 (1997) 2279-2299

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.

  • 1. Division de Physique Théorique, IPN,
    Université Paris XI - Paris Sud
  • 2. Abteilung Theoretische Physik,
    Universität Ulm