Conditions for the appearance of wave chaos in quantum singular systems with a pointlike scatterer.

In this paper, we discuss quantum properties of singular systems with a single pointlike scatterer that are almost integrable (pseudointegrable). Special emphasis is placed on the investigation of the appearance of so-called wave chaos. Based on a general argument, we deduce the necessary condition for the appearance of wave chaos in singular systems with a pointlike scatterer. Numerical results of a rectangular billiard with a single pointlike scatterer show that the signature of wave chaos is observed in various energy regions according to the value of the coupling constant of the scatterer, as expected from the general argument.