Journal of Spectral Theory


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Volume 5, Issue 1, 2015, pp. 89–112
DOI: 10.4171/JST/92

Published online: 2015-04-20

Anderson localization for the almost Mathieu operator in the exponential regime

Wencai Liu[1] and Xiaoping Yuan[2]

(1) Fudan University, Shanghai, China
(2) Fudan University, Shanghai, China

For the almost Mathieu operator $$(H_{\lambda,\alpha,\theta}u)_n=u_{n+1}+u_{n-1}+2\lambda \mathrm {cos}2\pi(\theta+n\alpha)u_n$,$$ Avila and Jitomirskaya verify this for $|\lambda| > e^{{\frac{16}{9}} \beta}$. In the present paper, we extend their result to the regime $ |\lambda| > e^{\frac{3}{2} \beta}$.

Keywords: Anderson localization, almost Mathieu operator

Liu Wencai, Yuan Xiaoping: Anderson localization for the almost Mathieu operator in the exponential regime. J. Spectr. Theory 5 (2015), 89-112. doi: 10.4171/JST/92