Exact quantization of the scattering from a classically chaotic repellor

Abstract

The S matrix for the scattering of a point particle from three hard discs fixed on a plane is calculated exactly using Green’s theorem. The S matrix is obtained explicitly from S=I−iCM⁻¹D, where the matrix M describes the multiple scattering between the three discs and the matrices C and D describe the free propagation from the edges of the three discs to large distances. The scattering resonances are located in the complex wave number plane as the zeros of the determinant of the matrix M, and their symmetry representations are determined. The results of this calculation are compared with the results obtained from the semiclassical approximation described in the preceding paper.