Anderson localization for one-frequency quasi-periodic block Jacobi operators

TL;DR

This paper proves Anderson localization for a class of one-frequency quasi-periodic block Jacobi operators with large coupling constants, extending previous results to more general matrix-valued cases.

Contribution

It generalizes existing localization results from band lattice Schrödinger operators to matrix-valued block Jacobi operators with minimal frequency dependence.

Findings

Established Anderson localization for large coupling constants

Extended localization results to matrix-valued quasi-periodic operators

Generalized Bourgain and Jitomirskaya's results to broader operator classes

Abstract

We consider a one-frequency, quasi-periodic, block Jacobi operator, whose blocks are generic matrix-valued analytic functions. We establish Anderson localization for this type of operator under the assumption that the coupling constant is large enough but independent of the frequency. This generalizes a result of J. Bourgain and S. Jitomirskaya on localization for band lattice, quasi-periodic Schroedinger operators.