A lower bound on the Lyapunov exponent for the generalized Harper's   model
  We obtain a lower bound for the Lyapunov exponent of a family of discrete Schr\"{o}dinger operators $(Hu)_n=u_{n+1}+u_{n-1}+2a_1\cos2\pi(\theta+n\alpha)u_n+2a_2\cos4\pi(\theta+n\alpha)u_n$, that incorporates both $a_1$ and $a_2,$ thus going beyond the Herman's bound. 
Svetlana Jitomirskaya and Wencai Liu
math-ph math.MP