Localization on the quantum graph connecting the points of the lattice ${\mathbb{Z}}^d$

Abstract

We consider the graph whose edges connect all nearest neighbours of the lattice ${\mathbb{Z}}^d$. We prove several theorems establishing localization of eigenfunctions of the Schrödinger operator on this graph. The energies for which we establish the localization belong to specific intervals whose union is an unbounded subset of the real line.