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

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.

24 pages. Journal referee suggestions included, last section expanded to include more details and a sketch of the proof of localization. To appear in Journal of Functional Analysis