GOLENIA, Sylvain; MANDICH, Marc-Adrien

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GOLENIA, Sylvain
Institut de Mathématiques de Bordeaux [IMB]

MANDICH, Marc-Adrien
Institut de Mathématiques de Bordeaux [IMB]

Langue

Document de travail - Pré-publication

Résumé en anglais

In the abstract framework of Mourre theory, the propagation of states is understood in terms of a conjugate operator $A$. A powerful estimate has long been known for Hamiltonians having a good regularity with respect to $A$ thanks to the limiting absorption principle (LAP). We study the case where $H$ has less regularity with respect to $A$, specifically in a situation where the LAP and the absence of singularly continuous spectrum have not yet been established. We show that in this case the spectral measure of $H$ is a Rajchman measure and we derive some propagation estimates. One estimate is an application of minimal escape velocities, while the other estimate relies on an improved version of the RAGE formula. Based on several examples, including continuous and discrete Schr\"odinger operators, it appears that the latter propagation estimate is a new result for multi-dimensional Hamiltonians.< Réduire

Mots clés en anglais

Propagation estimate

Mourre theory

Mourre estimate

Commutator

RAGE Theorem

Schr\"odinger operators

Rajchman measure

URI

https://oskar-bordeaux.fr/handle/20.500.12278/193343

Project ANR

Géométrie Spectrale, Graphes et Semiclassique - ANR-13-BS01-0007

Origine

Importé de hal

Unités de recherche

Institut de Mathématiques de Bordeaux (IMB) - UMR 5251