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arXiv · 1007.4343

Dispersion and controllability for the Schr\"odinger equation on negatively curved manifolds

Nalini Anantharaman·Gabriel Riviere
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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.

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Nalini Anantharaman, Gabriel Riviere. 2010-07-25. Dispersion and controllability for the Schr\"odinger equation on negatively curved manifolds. https://arxiv.org/abs/1007.4343

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