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Annals of Mathematics, II. Series, Vol. 150, No. 3, pp. 1159-1175, 1999
EMIS ELibM Electronic Journals Annals of Mathematics, II. Series
Vol. 150, No. 3, pp. 1159-1175 (1999)

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Metal-insulator transition for the almost Mathieu operator

Svetlana Ya. Jitomirskaya

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.

Keywords: metal-insulator transition; Mathieu operator; localization; purely absolutely continuous spectrum; Aubry-André conjecture

Classification (MSC2000): 47B37 47A10

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Electronic fulltext finalized on: 8 Sep 2001. This page was last modified: 23 Jan 2002.

© 2001 Johns Hopkins University Press
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