EVENT DETAILS AND ABSTRACT

Title: Resonances and semiclassical measures for the Schrödinger flow on the torus
Speaker: Fabricio Macià
Speaker Info: Universidad Politécnica de Madrid
Brief Description:
Special Note:
Abstract:

We present some recent joint work with Nalini Anantharaman on the structure of the set of semiclassical measures for sequences of solutions to the linear Schrödinger equation on the flat torus. In particular, we show that their projection on the position variable is absolutely continuous with respect to the Lebesgue measure and we give an explicit propagation law for their Radon-Nikodym derivative. In the proof of our results we exploit in a decisive way the dynamics of the Schrödinger flow, as well as a description of two-microlocal concentration effects around resonant linear manifolds in phase space.