Weak Disorder Localization and Lifshitz Tails: Continuous Hamiltonians
Weak Disorder Localization and Lifshitz Tails: Continuous Hamiltonians
复制标题
弱无序定位和 Lifshitz 尾部：连续哈密顿量
DOI：
10.1007/s00023-002-8633-6
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发表时间：
2002
期刊：
影响因子：
--
通讯作者：
F. Klopp
中科院分区：
文献类型：
--
作者：
F. Klopp
抽象的。本文致力于研究具有弱随机扰动的连续随机薛定谔算子的带边定位。我们证明，在弱无序状态下，
$ \lambda $ 小，大小邻域内的谱
非简并简单带边的 $ C \cdot \lambda $ 是指数动态局部化的。还获得了这些能量区域中局域长度的上限。当无序度很小时，我们的结果依赖于 Lifshitz 尾部的分析；单点电势不必具有固定符号。
Abstract. This paper is devoted to the study of band edge localization for continuous random Schrödinger operators with weak random perturbations. We prove that, in the weak disorder regime,
$ \lambda $ small, the spectrum in a neighborhood of size
$ C \cdot \lambda $ of a non-degenerate simple band edge is exponentially and dynamically localized. Upper bounds on the localization length in these energy regions are also obtained. Our results rely on the analysis of Lifshitz tails when the disorder is small; the single site potential need not be of fixed sign.