Long-time semiclassical dynamics of chaos: The stadium billiard

In a recent Letter [Phys. Rev. Lett. 67, 664 (1991)] we found semiclassical propagation to be remarkably accurate in the chaotic stadium billiard long after classical fine structure had developed on a scale much smaller than ħ. We give a complete account of that work and derive an approximate time scale for the validity of the semiclassical approximation as a function of ħ.