Multiple multipole method for resonances in a chaotic resonator

We use the multipole expansion method for computing the resonances in a classically chaotic two-dimensional region that has the shape of a bow-tie. We assume the Helmholtz equation with impedance boundary condition. The quantum ergodicity of classically chaotic systems has been studied extensively, both theoretically and experimentally, in mathematics and in physics. Resonances are usually computed by boundary element or finite element methods (www.ireap.umd.edu/MURI-2001/Review_8June02/02_Anlage.pdf). We derive a quasi-analytic method for the matrix equation and use Newton´s method for computing the resonances. Our results have been tested against a numerical solution using the boundary element method based on layer potential which is solved via Nyström discretization method.