论文标题
Anderson本地化的算术版本通过降低
Arithmetic version of Anderson localization via reducibility
论文作者
论文摘要
Anderson本地化的算术版本，即在本地化频率和本地化阶段具有明确的算术描述，首先由Jitomirskaya \ Cite \ cite {J}给出了几乎Mathieu操作员（AMO）。后来，结果由Bourgain和Jitomirskaya \ Cite {BJ02}推广到一类{\ IT尺寸} Quasi-Periodic长距离运算符。在本文中，我们提出了一种基于Aubry二元性算术版本和定量降低性的新方法。我们的方法使我们能够证明{\ IT dimensions}中的Quasi-Periodic远程运算符等级的结果，其中包括\ cite {j，bj02}作为特殊情况。
The arithmetic version of Anderson localization (AL), i.e., AL with explicit arithmetic description on both the localization frequency and the localization phase, was first given by Jitomirskaya \cite{J} for the almost Mathieu operators (AMO). Later, the result was generalized by Bourgain and Jitomirskaya \cite{bj02} to a class of {\it one dimensional} quasi-periodic long-range operators. In this paper, we propose a novel approach based on an arithmetic version of Aubry duality and quantitative reducibility. Our method enables us to prove the same result for the class of quasi-periodic long-range operators in {\it all dimensions}, which includes \cite{J, bj02} as special cases.
