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Annals of Mathematics, II. Series Vol. 150, No. 3, pp. 11591175 (1999) 

Metalinsulator transition for the almost Mathieu operatorSvetlana Ya. JitomirskayaAbstract: 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 AubryAndré conjecture. Keywords: metalinsulator transition; Mathieu operator; localization; purely absolutely continuous spectrum; AubryAndré conjecture Classification (MSC2000): 47B37 47A10 Full text of the article:
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