Schrödinger Operators with Potentials Generated by Hyperbolic Transformations: II. Large Deviations and Anderson Localization

Abstract

We consider discrete one-dimensional Schrödinger operators whose potentials are generated by Hölder continuous sampling along the orbits of a uniformly hyperbolic transformation. For any ergodic measure satisfying a suitable bounded distortion property, we establish a uniform large deviation estimate in a large energy region provided that the sampling function is locally constant or has small supremum norm. We also prove full spectral Anderson localization for the operators in question.

arXiv comment36 pages