Statistical measures for eigenfunctions of nonseparable quantum billiard systems

We study two statistical measures for eigenfunctions of several classically pseudointegrable and chaotic billiard systems: The directional energy distribution and the nodal line curvature distribution. A sharp distinction between the classically pseudointegrable and the chaotic systems is possible with both of these measures. They can also be used to distinguish between regular and irregular eigenfunctions of the billiard systems. Using the same data set additionally the amplitude distribution is calculated for single regular and irregular states and accumulated over several hundred states. The well-known Gaussian prediction holds well for irregular wave functions of the pseudointegrable system, too.