Observability and quantum limits for the Schrödinger equation on the sphere

2017/02/07 by Fabricio Macià, Macià, Fabricio, Gabriel Rivière +1
Computer Science · Engineering · Mathematics · Physics and Astronomy · #Advanced Mathematical Modeling in Engineering #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical methods in inverse problems #Optimization and Control (math.OC) #Quantum chaos and dynamical systems #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1702.02066

openalex publication_date 2017/02/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note, we describe our recent results on semiclassical measures for the Schrödinger evolution on Zoll manifolds. We focus on the particular case of eigenmodes of the Schrödinger operator on the sphere endowed with its canonical metric. We also recall the relation of this problem with the observability question from control theory. In particular, we exhibit examples of open sets and potentials on the 2-sphere for which observability fails for the evolution problem while it holds for the stationary one. Finally, we give some new results in the case where the Radon transform of the potential identically vanishes.

Citations

• Exact Controllability, Stabilization and Perturbations for Distributed Systems

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