Related Experiment Video
Updated: Aug 29, 2026

Impacts of Free-falling Spheres on a Deep Liquid Pool with Altered Fluid and Impactor Surface Conditions
Published on: February 17, 2019
Weyl formulas for annular ray-splitting billiards
Yves Décanini1, Antoine Folacci
1SPE, UMR CNRS 6134, Equipe Physique Semi-Classique (et) de la Matière Condensée, Faculté des Sciences, Université de Corse, Boîte Postale 52, 20250 Corte, France. decanini@univ-corse.fr
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 [Berry and Howls, Proc. R. Soc. London, Ser. A 447, 527 (1994)]. 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.
Related Concept Videos
The de Broglie Wavelength
Bessel Function of Order Zero
Singularity Functions for Bending Moment
Bewley Lattice Diagram
Divergence and Curl of Magnetic Field
Singularity Functions for Shear

