Simplicity of eigenvalues in the Anderson model

TL;DR

This paper provides an accessible and clear proof demonstrating that all eigenvalues of the Anderson model within the localization region are simple, enhancing understanding of spectral properties in disordered systems.

Contribution

It introduces a straightforward and intuitive proof establishing the simplicity of eigenvalues in the Anderson model's localized regime, simplifying previous complex arguments.

Findings

Eigenvalues in the Anderson model's localization region are simple.

The proof is transparent and accessible, aiding understanding.

Supports the spectral theory of disordered quantum systems.

Abstract

We give a simple, transparent, and intuitive proof that all eigenvalues of the Anderson model in the region of localization are simple.