- journal article metadata
European Mathematical Society Publishing House
2016-09-19 17:05:14
Journal of Spectral Theory
J. Spectr. Theory
JST
1664-039X
1664-0403
Quantum theory
10.4171/JST
http://www.ems-ph.org/doi/10.4171/JST
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European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society
5
2015
1
Anderson localization for the almost Mathieu operator in the exponential regime
Wencai
Liu
Fudan University, SHANGHAI, CHINA
Xiaoping
Yuan
Fudan University, SHANGHAI, CHINA
Anderson localization, almost Mathieu operator
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}$.
Ordinary differential equations
Operator theory
89
112
10.4171/JST/92
http://www.ems-ph.org/doi/10.4171/JST/92