Fabricio Macia (Madrid)
Dispersion and observability for completely integrable Schrödinger flows
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.