The trimmed Anderson model at strong disorder: localisation and its breakup

TL;DR

This paper investigates the conditions under which Anderson localization occurs or fails in a discrete random Schrödinger operator with potential supported on a sub-lattice at strong disorder, revealing new insights into localization phenomena.

Contribution

It establishes new criteria for localization and identifies cases where localization can be ruled out in models with sub-lattice supported potentials.

Findings

Localization occurs under specific sub-lattice conditions at strong disorder

Examples where localization is absent are provided

New criteria for Anderson localization in sub-lattice models

Abstract

We explore the properties of discrete random Schroedinger operators in which the random part of the potential is supported on a sub-lattice. In particular, we provide new conditions on the sub-lattice under which Anderson localisation happens at strong disorder, and provide examples in which it can be ruled out.