SUB-EXPONENTIAL LOWER BOUNDS FOR EMBEDDED EIGENFUNCTIONS OF SOME DISCRETE SCHRÖDINGER OPERATORS

Marc-Adrien Mandich (1)

1 IMB - Institut de Mathématiques de Bordeaux

Following the method of Froese and Herbst, we show for a class of potentials V that an embedded eigenfunction ψ with eigenvalue E of the multi-dimensional discrete Schrödinger operator H= ∆ + V on 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 threshold to 2 on either side.

Domaines: Théorie spectrale [math.SP]; Physique mathématique [math-ph]; Analyse fonctionnelle [math.FA]

Marc-Adrien Mandich. SUB-EXPONENTIAL LOWER BOUNDS FOR EMBEDDED EIGENFUNCTIONS OF SOME DISCRETE SCHRÖDINGER OPERATORS. 2016. ⟨hal-01353783v2⟩