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arXiv:chao-dyn/9505011 · Physical Review Letters

Diffractive Orbits in Quantum Billiards

Nicolas Pavloff, C. Schmit

Published Jul 3, 1995• 52 citations
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Abstract

We study diffractive effects in two-dimensional polygonal billiards. We derive an analytical trace formula accounting for the role of the nonclassical diffractive orbits in the quantum spectrum. As an illustration, the method is applied to a triangular billiard.
DOI
10.1103/physrevlett.75.61

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Diffractive Orbits in Quantum Billiards

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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 for single-diffractive orbits 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.
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