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Dispersion and controllability for the Schrödinger equation on negatively curved manifolds (1007.4343v1)
Published 25 Jul 2010 in math.AP
Abstract: We study the time-dependent Schr\"odinger equation $ \imath\frac{\partial u}{\partial t}=-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 Schr\"odinger propagator, and to controllability.