Localization for random block operators

TL;DR

This paper advances the understanding of spectral properties of random block operators by providing new estimates and proving dynamical localization near internal band edges.

Contribution

It introduces an alternative Wegner estimate and improves Lifschitz tail results, enabling proof of dynamical localization using bootstrap multi-scale analysis.

Findings

Established an alternative Wegner estimate.

Improved Lifschitz tail results at internal band edges.

Proved dynamical localization near internal band edges.

Abstract

We continue the investigations of Kirsch, Metzger and the second-named author [J. Stat. Phys. 143, 1035--1054 (2011)] on spectral properties of a certain type of random block operators. In particular, we establish an alternative version of a Wegner estimate and an improved result on Lifschitz tails at the internal band edges. Using these ingredients and the bootstrap multi-scale analysis, we also prove dynamical localization in a neighbourhood of the internal band edges.