Title :

Concentration and non concentration for the Schrödinger equation on Zoll manifolds

Author(s) :

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

English keyword(s) :

Semiclassical analysis
Integrable Hamiltonian systems
Semiclassical measures
Zoll manifolds
Schrödinger equation

HAL domain(s) :

Mathématiques [math]/Equations aux dérivées partielles [math.AP]
Mathématiques [math]/Physique mathématique [math-ph]
Mathématiques [math]/Théorie spectrale [math.SP]

English abstract : [en]

We study the long time dynamics of the Schrödinger equation on Zoll man-ifolds. We establish criteria under which the solutions of the Schrödinger equation can or cannot concentrate on a given closed geodesic. As an ...
Show more >We study the long time dynamics of the Schrödinger equation on Zoll man-ifolds. We establish criteria under which the solutions of the Schrödinger equation can or cannot concentrate on a given closed geodesic. As an application, we derive some results on the set of semiclassical measures for eigenfunctions of Schrödinger operators: we prove that adding a potential to the Laplacian on the sphere results on the existence of geodesics $\gamma$ such that $\delta_{\Gamma}$ cannot be obtained as a semiclassical measure for some sequence of eigenfunctions. We also show that the same phenomenon occurs for the free Laplacian on certain Zoll surfaces.Show less >

Language :

Anglais

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL

Submission date :

2025-01-24T18:23:36Z