Propagation estimates in the one-commutator theory
Language
en
Document de travail - Pré-publication
English Abstract
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 ...Read more >
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.Read less <
English Keywords
Propagation estimate
Mourre theory
Mourre estimate
Commutator
RAGE Theorem
Schr\"odinger operators
Rajchman measure
ANR Project
Géométrie Spectrale, Graphes et Semiclassique - ANR-13-BS01-0007
Origin
Hal imported