Sub-exponential decay of eigenfunctions for some discrete schrödinger operators
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | MANDICH, Marc-Adrien | |
| dc.date.accessioned | 2024-04-04T03:10:15Z | |
| dc.date.available | 2024-04-04T03:10:15Z | |
| dc.date.created | 2016-09-10 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/193675 | |
| dc.description.abstractEn | Following the method of Froese and Herbst, we show for a class of potentials V that an eigenfunction ψ with eigenvalue E of the multi-dimensional discrete Schrödinger operator H = ∆ + V on \mathbb{Z}^d decays sub-exponentially whenever the Mourre estimate holds at E. In the one-dimensional case we further show that this eigenfunction decays exponentially with a rate at least of cosh^{−1}((E − 2)/(θ_E − 2)), where θ_E is the nearest threshold of H located between E and 2. A consequence of the latter result is the absence of eigenvalues between 2 and the nearest thresholds above and below this value. The method of Combes-Thomas is also reviewed for the discrete Schrödinger operators. | |
| dc.language.iso | en | |
| dc.title.en | Sub-exponential decay of eigenfunctions for some discrete schrödinger operators | |
| 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.subject.hal | Mathématiques [math]/Analyse fonctionnelle [math.FA] | |
| dc.identifier.arxiv | 1608.04864 | |
| 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-01353783 | |
| hal.version | 1 | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-01353783v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.au=MANDICH,%20Marc-Adrien&rft.genre=preprint |
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