IEEE Antennas and Propagation Society Symposium, Vol. 4, pp. 4440 - 4443, June 20-25, 2004

A Closed form Solution of the Helmholtz Equation for a Class of Chaotic Resonators

F. Seydou, O. Ramahi
University of Maryland
College Park, MD 20742


We study numerically the solution of the Helmholtz equation in a classically chaotic two-dimensional region in the shape of a bow-tie. The quantum ergodicity of classically chaotic systems has been studied extensively, both theoretically and experimentally, in mathematics and in physics. Despite this long tradition, we are able to present a new rigorous result using only elementary calculus. In particular, a closed form solution is derived by using multipole expansions. Our results have been validated by an integral equation method based on layer potential which is solved via the Nystro/spl uml/m discretization method.

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