Dispersion and controllability for the Schrödinger equation on negatively curved manifolds

2010/07/25 by Nalini Anantharaman, Anantharaman, Nalini, Gabriel Rivière +1 · 2 citations
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometry and complex manifolds #Quantum chaos and dynamical systems

paper · doi:10.48550/arxiv.1007.4343

openalex publication_date 2010/07/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the time-dependent Schrödinger equation \imath(∂ u)/(∂ t)=-1/2Δu, 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 Schrödinger propagator, and to controllability.

Citations

• Exponential decay for products of Fourier integral operators

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