Direct Scaling Analysis of localization in disordered systems. I. Single-particle models

TL;DR

This paper introduces a simplified multi-scale analysis method for Anderson models, providing direct exponential decay bounds on eigenfunctions, which imply localization properties in disordered lattice systems.

Contribution

A simplified multi-scale analysis approach that directly yields exponential decay bounds for eigenfunctions in disordered systems.

Findings

Uniform exponential bounds on eigenfunction decay in finite lattice subsets

Implication of dynamical localization in the entire lattice

Simplification of existing multi-scale analysis techniques

Abstract

We propose a simplified version of the Multi-Scale Analysis of tight-binding Anderson models with strongly mixing random potentials which leads directly to uniform exponential bounds on decay of eigenfunctions in arbitrarily large finite subsets of a lattice. Naturally, these bounds imply also dynamical localization and exponential decay of eigenfunctions on the entire lattice.