All couplings localization for quasiperiodic operators with monotone potentials

Abstract

We establish Anderson localization for quasiperiodic operator families of the form

for all coupling constants $\lambda >0$ and all Diophantine frequencies $\alpha$, provided that $v$ is a 1-periodic function satisfying a Lipschitz monotonicity condition on [0,1). The localization is uniform on any energy interval on which the Lyapunov exponent is bounded from below.