Quantum Chaos for point scatterers on flat tori

The Laplacian with a delta potential on a flat torus is a popular model to study the transition between integrability and chaos in quantum systems. Whereas the dynamics of the associated classical system is pseudo-integrable, the quantum system is believed to exhibit features of quantised chaotic systems. I will discuss joint work with Zeév Rudnick and Pär Kurlberg on the statistical properties of the wave functions of this system.