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

Nalini Anantharaman; Gabriel Riviere

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

Analysis of PDEs 2010-07-27 v1

Authors: Nalini Anantharaman , Gabriel Riviere

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.

Keywords

schrödinger equation anosov geodesic flow semiclassical measures dispersive properties controllability negatively curved manifolds

Cite

@article{arxiv.1007.4343,
  title  = {Dispersion and controllability for the Schr\"odinger equation on negatively curved manifolds},
  author = {Nalini Anantharaman and Gabriel Riviere},
  journal= {arXiv preprint arXiv:1007.4343},
  year   = {2010}
}

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