The dynamics of the Schrödinger flow from the point of view of semiclassical measures

Details The dynamics of the Schrödinger flow from the point of view of semiclassical measures The dynamics of the Schrödinger flow from the point of view of semiclassical measures

2011-02-04

arxiv.org/abs/1102.0970v2

Mathematics

Analysis of PDEs

Survey article; 24 pages. References and a Section 1.4 added

Scientific paper

On a compact Riemannian manifold, we study the various dynamical properties of the Schr\"odinger flow $(e^{it\Delta/2})$, through the notion of semiclassical measures and the quantum-classical correspondence between the Schr\"odinger equation and the geodesic flow. More precisely, we are interested in its high-frequency behavior, as well as its regularizing and unique continuation-type properties. We survey a variety of results illustrating the difference between positive, negative and vanishing curvature.

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