Wave chaos in quantum systems with point interaction

The authors study perturbations H of the quantized version H0 of integrable Hamiltonian systems by point interactions. They relate the eigenvalues of H to the zeros of a certain meromorphic function ξ. Assuming the eigenvalues of H0 are Poisson distributed, they get detailed information on the joint distribution of the zeros of ξ and give bounds on the probability density for the spacings of eigenvalues of H. Their results confirm the wave chaos phenomenon, as different from the quantum chaos phenomenon predicted by random matrix theory