Fabricio Macia (Madrid)

Dispersion and observability for completely integrable Schrödinger flows

Abstract: I will present some results on weak dispersion and unique continuation (observability) for linear Schrödinger equations that are obtained as the quantization of a completely integrable Hamiltonian system. The model case corresponds to the linear Schrödinger equation (with a potential) on the flat torus. Our results are obtained through a detailed analysis of semiclassical measures corresponding to sequences of solutions, which is performed using a two-microlocal approach. This is a joint work with Nalini Anantharaman and Clotilde Fermanian-Kammerer.