Diffractive corrections in the trace formula for polygonal billiards

@article{Bogomolny2000DiffractiveCI,
title={Diffractive corrections in the trace formula for polygonal billiards},
author={Bogomolny and Pavloff and Schmit},
journal={Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics},
year={2000},
volume={61 4 Pt A},
pages={3689-711}
}

We derive contributions to the trace formula for the spectral density accounting for the role of diffractive orbits in two-dimensional polygonal billiards. In polygons, diffraction typically occurs at the boundary of a family of trajectories. In this case the first diffractive correction to the contribution of the family to the periodic orbit expansion is of order of that of an isolated orbit, and gives the first sqrt[Planck's over 2pi] correction to the leading semiclassical term. Keller's… CONTINUE READING