Propagation estimates in the one-commutator theory
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | GOLENIA, Sylvain | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | MANDICH, Marc-Adrien | |
| dc.date.accessioned | 2024-04-04T03:06:32Z | |
| dc.date.available | 2024-04-04T03:06:32Z | |
| dc.date.created | 2017-03-23 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/193343 | |
| dc.description.abstractEn | 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. | |
| dc.description.sponsorship | Géométrie Spectrale, Graphes et Semiclassique - ANR-13-BS01-0007 | |
| dc.language.iso | en | |
| dc.subject.en | Propagation estimate | |
| dc.subject.en | Mourre theory | |
| dc.subject.en | Mourre estimate | |
| dc.subject.en | Commutator | |
| dc.subject.en | RAGE Theorem | |
| dc.subject.en | Schr\"odinger operators | |
| dc.subject.en | Rajchman measure | |
| dc.title.en | Propagation estimates in the one-commutator theory | |
| dc.type | Document de travail - Pré-publication | |
| dc.subject.hal | Mathématiques [math]/Théorie spectrale [math.SP] | |
| dc.subject.hal | Mathématiques [math]/Physique mathématique [math-ph] | |
| dc.identifier.arxiv | 1703.08042 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| hal.identifier | hal-01494284 | |
| hal.version | 1 | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-01494284v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.au=GOLENIA,%20Sylvain&MANDICH,%20Marc-Adrien&rft.genre=preprint |
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