Localization for Schrodinger operators with random vector potentials

TL;DR

This paper establishes Anderson localization at band edges for magnetic Schrödinger operators with random vector potentials, using new insights into Lifshitz tails and Wegner estimates to analyze spectral properties.

Contribution

It introduces novel results on Lifshitz tails and Wegner estimates for random magnetic Schrödinger operators, enabling localization proofs at band edges.

Findings

Proves Anderson localization at internal band-edges.

Develops new Lifshitz tails behavior results for magnetic operators.

Establishes Wegner estimates for models with random vector potentials.

Abstract

We prove Anderson localization at the internal band-edges for periodic magnetic Schr{\"o}dinger operators perturbed by random vector potentials of Anderson-type. This is achieved by combining new results on the Lifshitz tails behavior of the integrated density of states for random magnetic Schr{\"o}dinger operators, thereby providing the initial length-scale estimate, and a Wegner estimate, for such models.