Bethe格点上Anderson模型的phase diagram中的惊奇
Surprises in the phase diagram of the Anderson model on the Bethe lattice
摘要：
在历史上，Bethe晶格上的安德森模型是第一个可以建立扩展态能量体系和局域态独立体系的模型。在本文中，我们审查最近发现的惊喜的相图。其中之一是，即使在弱无序状态下，扩散输运的机制也远远超出了未扰动模型的能量，进入了Lifshitz尾。正如将要解释的那样，在这种非微扰状态下出现扩展态的机制是无序诱导的共振。我们还提出了剩余的问题有关的结构的本征函数和相关的谱统计问题的贝特格。
英文摘要：
The Anderson model on the Bethe lattice is historically among the first for which an energy regime of extended states and a separate regime of localized states could be established. In this paper, we review recently discovered surprises in the phase diagram. Among them is that even at weak disorder, the regime of diffusive transport extends well beyond energies of the unperturbed model into the Lifshitz tails. As will be explained, the mechanism for the appearance of extended states in this non-perturbative regime are disorder-induced resonances. We also present remaining questions concerning the structure of the eigenfunctions and the associated spectral statistics problem on the Bethe lattice.
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