The dynamics of the Schr\"odinger flow from the point of view of   semiclassical measures
  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. 
Nalini Anantharaman and Fabricio Macia
math.AP math-ph math.MP math.SP