Additional numerical and graphical evidence to support some Conjectures on discrete Schr{\"o}dinger operators with a more general long range condition

Sylvain Golénia (1) , Marc-Adrien Mandich (2)

1 IMB - Institut de Mathématiques de Bordeaux
2 Chercheur indépendant

This document contains additional numerical and graphical evidence to support some of the conjectures mentioned in \cite{GM3}. We give more evidence for $\kappa=3,4$ in dimension 2. As mentioned in that article we still don't quite understand the sets $\boldsymbol{\mu}_{\kappa}(\Delta)$ and $\boldsymbol{\Theta}_{\kappa}(\Delta)$ on $(0,1/2)$ for $\kappa=3$ in dimension 2. Here we give a bunch more threshold energies for $\kappa = 3$ in dimension 2.

Mots clés: Mourre theory; Chebyshev polynomials; polynomial interpolation; threshold; 2010 Mathematics Subject Classification. 39A70; 81Q10; 47B25; 47A10 discrete Schrödinger operator; long range potential; limiting absorption principle; Mourre theory

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

Sylvain Golénia, Marc-Adrien Mandich. Additional numerical and graphical evidence to support some Conjectures on discrete Schr{\"o}dinger operators with a more general long range condition. 2022. ⟨hal-03499095⟩