Dispersion and controllability for the Schrödinger equation on negatively curved manifolds

Abstract

We study the time-dependent Schrödinger equation $ı\frac{\partial u}{\partial t}=-\frac{1}{2}\Delta u$, on a compact Riemannian manifold on which the geodesic flow has the Anosov property. Using the notion of semiclassical measures, we prove various results related to the dispersive properties of the Schrödinger propagator, and to controllability.