Dispersion and controllability for the Schrödinger equation on negatively curved manifolds

Details Dispersion and controllability for the Schrödinger equation on negatively curved manifolds Dispersion and controllability for the Schrödinger equation on negatively curved manifolds

2010-07-25

arxiv.org/abs/1007.4343v1

Mathematics

Analysis of PDEs

Scientific paper

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.

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