Anderson localization for the completely resonant phases

Abstract

For the almost Mathieu operator $(H_{\lambda ,\alpha ,\theta }u)(n)=u(n+1)+u(n-1)+\lambda v(\theta +n\alpha )u(n)$, Avila and Jitomirskaya guess that for every phase $\theta \in \mathcal{R}\triangleq \{\theta \in \mathbb{R}|2\theta +\alpha \mathbb{Z}\in \mathbb{Z}\}$, $H_{\lambda ,\alpha ,\theta }$ satisfies Anderson localization if $|\lambda |>e^{2\beta }$. In the present paper, we show that for every phase $\theta \in \mathcal{R}$, $H_{\lambda ,\alpha ,\theta }$ satisfies Anderson localization if $|\lambda |>e^{7\beta }$.

arXiv admin note: substantial text overlap with arXiv:1311.0490

References in corpus (1)

• Spectral Gaps of Almost Mathieu Operator in Exponential Regime

Cited by in corpus (6)

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