99-369 Svetlana Jitomirskaya
Metal-Insulator transition for the Almost Mathieu Operator. (536K, postscript) Oct 1, 99
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Abstract. We prove that for Diophantine $\om$ and almost every $\th,$ the almost Mathieu operator, $(H_{\omega,\lambda,\theta}\Psi)(n)=\Psi(n+1) + \Psi(n-1) + \lambda\cos 2\pi(\omega n +\theta)\Psi(n)$, exhibits localization for $\lambda > 2$ and purely absolutely continuous spectrum for $\lambda < 2.$ This completes the proof of (a correct version of) the Aubry-Andre conjecture.

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