Test of semiclassical amplitudes for quantum ray-splitting systems

We compute semiclassically and numerically the weights of ray-splitting orbits in the density of states of a rectangular and an annular ray-splitting billiard. The agreement between the semiclassical and the numerical results is very good, confirming the necessity of including reflection and transmission coefficients of non-Newtonian ray-splitting orbits in semiclassical expressions for the density of states of ray-splitting systems.