Metal-Insulator Transition for the Almost Mathieu Operator

We prove that for Diophantine ω and almost every θ, the almost Mathieu operator, (H ω,λ,θ Ψ)(n) = Ψ(n + 1) + Ψ(n -1) + λ cos 2π(ωn + θ)Ψ(n), exhibits localization for λ > 2 and purely absolutely continuous spectrum for λ < 2. This completes the proof of (a correct version of) the Aubry-André conjecture.