Exponential Dynamical Localization for the Almost–mathieu Operator
نویسنده
چکیده
We prove that the the exponential moments of the position operator stay bounded for the supercritical almost Mathieu operator with Diophantine frequency.
منابع مشابه
Metal - insulator transition for the almost Mathieu operator
We prove that for Diophantine ω and almost every θ, the almost Mathieu operator, (Hω,λ,θΨ)(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.
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