Avoided crossings: Curvature distribution and behavior of eigenfunctions of pseudointegrable and chaotic billiards

We perform numerical studies on the curvature distribution of classically pseudointegrable and chaotic quantum billiards. This curvature distribution is Gaussian orthogonal ensemble-like for both systems and corresponds to linear level repulsion. The billiards show nonuniversal behavior at low curvatures. As an aside, avoided crossings of three levels are investigated for both systems. Strong interaction between the levels Ei and Ei+2 is shown. Eigenvalues and eigenfunctions are calculated very precisely by a grid method with an asymmetric sparse matrix.