Semiclassical wave functions for open quantum billiards

摘要

We present a semiclassical approximation to the scattering wave function u0002(r,k) for an open quantum billiard,nwhich is based on the reconstruction of the Feynman path integral. We demonstrate its remarkable numericalnaccuracy for the open rectangular billiard and show that the convergence of the semiclassical wave function to thenfull quantum state is controlled by the mean path length or equivalently the dwell time for a given scattering state.nIn the numerical implementation a cutoff length in the maximum path length or, equivalently, a maximum dwellntime τmax included implies a finite energy resolution u0004E ∼ τn−1nmax. Possible applications include leaky billiardsnand systems with decoherence present.