Additional numerical and graphical evidence to support some Conjectures on discrete Schrödinger operators with a more general long range condition

preprint2022arXivOpen access

Abstract

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

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