Titre :

Observability and quantum limits for the Schrödinger equation on the sphere

Auteur(s) :

Macià, Fabricio [Auteur]
Universidad Politécnica de Madrid [UPM]
Riviere, Gabriel [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]

Mot(s)-clé(s) en anglais :

Schrödinger Equation
Controllability
Observability
Quantum limits
Eigenvalue distribution
Zoll manifolds

Discipline(s) HAL :

Mathématiques [math]/Equations aux dérivées partielles [math.AP]
Mathématiques [math]/Physique mathématique [math-ph]
Mathématiques [math]/Optimisation et contrôle [math.OC]

Résumé en anglais : [en]

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 ...
Lire la suite >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.Lire moins >

Langue :

Anglais

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL

Date de dépôt :

2025-01-24T17:51:34Z