The repulsion between localization centers in the Anderson model

TL;DR

This paper demonstrates that in the Anderson model, localization centers tend to be far apart when their associated energies are close, using advanced results in random Schrödinger operators.

Contribution

It provides a quantitative estimate of the repulsion between localization centers in the Anderson model based on deep theoretical results.

Findings

Localization centers become far apart as energies approach each other

Quantitative bounds on the distance between localization centers

Application of advanced random Schrödinger operator theory

Abstract

In this note we show that, a simple combination of deep results in the theory of random Schr\"odinger operators yields a quantitative estimate of the fact that the localization centers become far apart, as corresponding energies are close together.