Weyl formulas for annular ray-splitting billiards
Chaotic Dynamics
2007-05-23 v1 Condensed Matter
Classical Physics
Abstract
We consider the distribution of eigenvalues for the wave equation in annular (electromagnetic or acoustic) ray-splitting billiards. These systems are interesting in that the derivation of the associated smoothed spectral counting function can be considered as a canonical problem. This is achieved by extending a formalism developed by Berry and Howls for ordinary (without ray-splitting) billiards. Our results are confirmed by numerical computations and permit us to infer a set of rules useful in order to obtain Weyl formulas for more general ray-splitting billiards.
Cite
@article{arxiv.nlin/0305034,
title = {Weyl formulas for annular ray-splitting billiards},
author = {Yves Décanini and Antoine Folacci},
journal= {arXiv preprint arXiv:nlin/0305034},
year = {2007}
}