Quantum Limits on product manifolds

Emmanuel Humbert (1) , Yannick Privat (2) , Emmanuel Trélat (3, 4)

1 IDP - Institut Denis Poisson
2 IRMA - Institut de Recherche Mathématique Avancée
3 LJLL (UMR_7598) - Laboratoire Jacques-Louis Lions
4 CaGE - Control And GEometry

We establish some properties of quantum limits on a product manifold, proving for instance that, under appropriate assumptions, the quantum limits on the product of manifolds are absolutely continuous if the quantum limits on each manifolds are absolutely continuous. On a product of Riemannian manifolds satisfying the minimal multiplicity property, we prove that a periodic geodesic can never be charged by a quantum limit.

Domaines: Théorie spectrale [math.SP]

Emmanuel Humbert, Yannick Privat, Emmanuel Trélat. Quantum Limits on product manifolds. Indiana University Mathematics Journal, 2023, 72 (2), pp.757-783. ⟨10.1512/iumj.2023.72.9755⟩. ⟨hal-03562358⟩