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

2024/01/31 by Avila, Artur, Damanik, David, Zhang, Zhenghe · 1 citation
#Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.2402.00215

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.

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