Positivity of the Lyapunov exponent for analytic quasiperiodic operators with arbitrary finite-valued background

Abstract

We study lower bounds on the Lyapunov exponent associated with one-frequency quasiperiodic Schrödinger operators with an added finite valued background potential. We prove that, for sufficiently large coupling constant, the Lyapunov exponent is positive with a uniform (in energy and background) minoration.

arXiv comment8 pages. Comments welcome! Revision: we added details to the proof of lemma 2.1 and theorem 1.1. We also corrected a typo in equation (2) and updated the acknowledgements