Svetlana Jitomirskaya
Metal-Insulator transition for the Almost Mathieu Operator.
(536K, postscript)
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.