Absolutely continuous spectrum for the Anderson model on a tree: a geometric proof of Klein's theorem

TL;DR

This paper presents a new geometric proof demonstrating the presence of absolutely continuous spectrum in the Anderson model on a Bethe lattice under weak disorder conditions.

Contribution

It provides a novel geometric proof of Klein's theorem regarding the absolutely continuous spectrum for the Anderson model on a tree.

Findings

Confirmed the existence of absolutely continuous spectrum at weak disorder

Provided a new geometric approach to Klein's theorem

Simplified the proof structure for spectral analysis

Abstract

We give a new proof of a version of Klein's theorem on the existence of absolutely continuous spectrum for the Anderson model on the Bethe Lattice at weak disorder.