Weyl formulas for annular ray-splitting billiards

Details Weyl formulas for annular ray-splitting billiards Weyl formulas for annular ray-splitting billiards

2003-05-20

arxiv.org/abs/nlin/0305034v1

Phys. Rev. E68, 046204 (2003)

Nonlinear Sciences

Chaotic Dynamics

Scientific paper

10.1103/PhysRevE.68.046204

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.

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