Schrödinger Operators with Potentials Generated by Hyperbolic Transformations: II. Large Deviations and Anderson Localization
arxiv(2024)
摘要
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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