All couplings localization for quasiperiodic operators with monotone potentials (Q1731781)

Summary: We establish Anderson localization for quasiperiodic operator families of the form \[ (H(x)\psi)(m)=\psi(m+1)+\psi(m-1)+\lambda v(x+m\alpha)\psi(m) \] 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.