Uniform approximation for diffractive contributions to the trace formula in billiard systems
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چکیده
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. PACS numbers: 03.40.Kf Waves and wave propagation: general mathematical aspects. 03.65.Sq Semiclassical theories and applications. 05.45.+b Theory and models of chaotic systems. IPNO/TH 96-22 ULM-TP/96-3 submitted to Physical Review E ∗ Unité de Recherche des Universités Paris XI et Paris VI associée au CNRS
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تاریخ انتشار 1996