Physicists have been interested in the connections between Quantum Mechanics and Classical Mechanics for long. The basic idea is that classical integrability (periodicity of orbits) and quantum integrability (Poisson distribution of eigenvalues) should be somewhat related one to each other. Some numerical experiments support this, however, it is well-known that is not true nor precise. Those experiments hinted that corners and obstacles could be nice sources of examples that break this connection because (quantum) wave are much more sensitive to them that classical trajectories. In the limit, point-obstacles should be the perfect model to consider: a zero measure set of orbits are perturbed but quantum waves still feel the perturbation. In this talk we will explain how these systems are defined, give some ideas on how to capture high-energy phenomena of these quantum waves and compute the diffraction this point-obstacle produces on the d-spheres.

The aim of this talk will be to describe the asymptotic properties of the eigenfunctions of magnetic Laplacians on the flat torus of dimension 2. I will explain that, under a geometric control condition on the magnetic field, the eigenfunctions satisfy equidistribution properties as the eigenvalue tends to infinity. This is a joint work with Léo Morin (Copenhagen).