Metal-insulator transition for the almost Mathieu operator

1999/11/01 by Svetlana Ya. Jitomirskaya · 1 citation
Mathematics · Physics and Astronomy · #math.SP #math-ph #math.MP

paper · pdf

published as Ann. of Math. (2) 150 (1999), no. 3, 1159-1175 · 17 pages, published version

arxiv created 1999/11/01 · arxiv updated 2016/09/07

Abstract

We prove that for Diophantine \om and almost every þ, the almost Mathieu operator, (H_ω,λ,θΨ)(n)=Ψ(n+1) + Ψ(n-1) + λcos 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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