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

2022/01/24 by Golénia, Sylvain, Mandich, Marc-Adrien
#FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Mathematical Physics (math-ph) #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.2201.09547

Abstract

This document contains additional numerical and graphical evidence to support some of the conjectures mentioned in \citeGM3. We give more evidence for κ=3,4 in dimension 2. As mentioned in that article we still don't quite understand the sets \boldsymbolμ_κ(Δ) and \boldsymbolΘ_κ(Δ) on (0,1/2) for κ=3 in dimension 2. Here we give a bunch more threshold energies for κ= 3 in dimension 2.

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