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Sub-exponential decay of eigenfunctions for some discrete schrödinger operators

hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorMANDICH, Marc-Adrien
dc.date.accessioned2024-04-04T03:10:15Z
dc.date.available2024-04-04T03:10:15Z
dc.date.created2016-09-10
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/193675
dc.description.abstractEnFollowing 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.isoen
dc.title.enSub-exponential decay of eigenfunctions for some discrete schrödinger operators
dc.typeDocument de travail - Pré-publication
dc.subject.halMathématiques [math]/Théorie spectrale [math.SP]
dc.subject.halMathématiques [math]/Physique mathématique [math-ph]
dc.subject.halMathématiques [math]/Analyse fonctionnelle [math.FA]
dc.identifier.arxiv1608.04864
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
hal.identifierhal-01353783
hal.version1
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-01353783v1
bordeaux.COinSctx_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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