Metal-insulator transition for the almost Mathieu operator

Abstract

We prove that for Diophantine $\omega$ and almost every $\theta$, 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-André conjecture.

DOI
https://doi.org/10.2307/121066

Authors

Svetlana Jitomirskaya