Delone-Anderson算子的遍历性和动力学局部化
Ergodicity and dynamical localization for Delone-Anderson operators
摘要：
利用随机着色Delone集和Delone动力系统的框架，研究了Delone-Anderson算子的遍历性.特别是，我们证明了存在的综合密度的状态，并根据一些假设的几何复杂性的基础Delone集，我们获得的信息几乎肯定的频谱的家庭的随机运营商。然后，我们利用这些结果来研究的Lifshitz尾行为的积分态密度的德龙-安德森运营商在底部的频谱。此外，我们使用Lifshitz-tail估计作为多尺度分析的输入来证明动力学局部化。
英文摘要：
We study the ergodic properties of Delone-Anderson operators, using the framework of randomly coloured Delone sets and Delone dynamical systems. In particular, we show the existence of the integrated density of states and, under some assumptions on the geometric complexity of the underlying Delone sets, we obtain information on the almost-sure spectrum of the family of random operators. We then exploit these results to study the Lifshitz-tail behaviour of the integrated density of states of a Delone-Anderson operator at the bottom of the spectrum. Furthermore, we use Lifshitz-tail estimates as an input for the multi-scale analysis to prove dynamical localization.
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