Scars and other weak localization effects in classically chaotic systems

There is much latitude between the known requirements of Schnirelman's theo rem regarding the ergodicity of individual high-energy eigenstates of class ically chaotic systems, and the extremes of random matrix theory. Some eige nstate statistics and long-time transport behavior bear nonrandom imprints of the underlying classical dynamics while simultaneously obeying Schnirelm an's theorem. Here we review the issues and give evidence for the Sinai bil liard having non Random Matrix Theory behavior, even as h --> 0.