Localization with Less Larmes: Simply MSA

TL;DR

This paper provides an accessible overview of the fixed-energy Multi-Scale Analysis (MSA) technique for the Anderson model, extending its application to multi-particle systems and serving as an introductory guide.

Contribution

It introduces a straightforward extension of the fixed-energy MSA to multi-particle Anderson models, simplifying the understanding of this analytical method.

Findings

MSA technique can be extended to multi-particle systems

Provides an elementary introduction to fixed-energy MSA

Simplifies the application of MSA in higher dimensions

Abstract

We give a short summary of the fixed-energy Multi-Scale Analysis (MSA) of the Anderson tight binding model in dimension $d\ge 1$ and show that this technique admits a straightforward extension to multi-particle systems. We hope that this short note may serve as an elementary introduction to the MSA.