Large Deviations of the Lyapunov Exponent and Localization for the 1D Anderson Model
Large Deviations of the Lyapunov Exponent and Localization for the 1D Anderson Model
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DOI：
10.1007/s00220-019-03502-8
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发表时间：
2019-08-01
影响因子：
2.4
通讯作者：
Zhu, Xiaowen
中科院分区：
文献类型：
--
作者：
Jitomirskaya, Svetlana;Zhu, Xiaowen
1987年，Carmona-Klein-Martinelli给出了一维任意无序（如Bernoulli）安德森模型的安德森局部化的证明，该证明部分基于多尺度分析。后来，在90年代，人们意识到，对于具有正李雅普诺夫指数的一维模型，多尺度分析的某些部分可以被涉及相应上循环的次谐性和大偏差估计的考虑所取代，从而导致一维准周期模型的非微扰证明。在本文中，我们提出了一个简短的证明沿着这些路线，为安德森模型。为了证明动态本地化，我们还开发了一个统一版本的克雷格-西蒙的约束，工程的高度普遍性，可能是独立的利益。
The proof of Anderson localization for the 1D Anderson model with arbitrary (e.g. Bernoulli) disorder, originally given by Carmona-Klein-Martinelli in 1987, is based in part on the multi-scale analysis. Later, in the 90s, it was realized that for one-dimensional models with positive Lyapunov exponents some parts of multi-scale analysis can be replaced by considerations involving subharmonicity and large deviation estimates for the corresponding cocycle, leading to nonperturbative proofs for 1D quasiperiodic models. In this paper we present a short proof along these lines, for the Anderson model. To prove dynamical localization we also develop a uniform version of Craig-Simon's bound that works in high generality and may be of independent interest.