All couplings localization for quasiperiodic operators with Lipschitz monotone potentials

الأصل · EN

We establish Anderson localization for quasiperiodic operator families of the form (H(x)ψ)(m)=ψ(m+1)+ψ(m-1)+λv(x+mα)ψ(m) for all λ>0 and all Diophantine α, 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 Lyapunov exponent is bounded from below.