AC spectrum for a class of random operators at small disorder

TL;DR

This paper proves the existence of absolutely continuous spectrum in a class of Anderson-type operators with non-stationary random potentials at small disorder, expanding understanding of spectral properties in higher-dimensional lattices.

Contribution

It introduces a new class of Anderson operators with non-stationary potentials and demonstrates pure absolutely continuous spectrum at small disorder levels.

Findings

Pure absolutely continuous spectrum exists in the middle of the band

Applicable to non-stationary, non-decaying potentials on odd-dimensional lattices

Spectral properties are established for small disorder regimes

Abstract

In this paper we present a class of Anderson type operators with independent, non-stationary (non-decaying) random potentials supported on a subset of positive density in the odd-dimensional lattice and prove the existence of pure absolutely continuous spectrum in the middle of the band for small disorder.