Smoothed density of states for problems with ray splitting

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Abstract
Ray splitting is the phenomenon whereby a ray incident on a boundary splits into more than one ray traveling away from the boundary. Motivated by the recent application of ideas of quantum chaos to cases with ray splitting, we present an analysis of the smoothed density of states for two-dimensional billiardlike systems with ray splitting. Using a simple heuristic technique, we obtain a contribution (analogous to the usual perimeter contribution) that is proportional to the length of the ray splitting boundary. The result is expressed in a general form, allowing application to a variety of physical situations. A comparison is also made of the analytical result with numerical data from a particular example. © 1996 The American Physical Society.