Abstract:

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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