Weyl formulas for annular ray-splitting billiards

Antoine Folacci; Yves D\'ecanini

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Weyl formulas for annular ray-splitting billiards

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arxiv nlin/0305034 v1 pith:52GDPVIZ submitted 2003-05-20 nlin.CD cond-matphysics.class-ph

Weyl formulas for annular ray-splitting billiards

Yves D\'ecanini , Antoine Folacci This is my paper

classification nlin.CD cond-matphysics.class-ph

keywords billiardsray-splittingannularformulasweylachievedacousticassociated

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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.

Weyl formulas for annular ray-splitting billiards

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