论文标题
对安德森紧密结合模型中状态综合密度的尖锐估计
Sharp estimates for the integrated density of states in Anderson tight-binding models
论文作者
论文摘要
最近的工作[G. David，M。Filoche和S. Mayboroda，Arxiv：1909.10558 [Adv。数学。 （待发表）]]] []]已经证明了整个频谱中施罗丁运营商的综合密度（IDOS）的综合密度（IDOS）的存在，称为景观定律。这些界限涉及尺寸常数，其最佳值尚未确定。在这里，我们研究了具有二元或统一随机分布的1D和2D紧密结合模型中景观定律的准确性。我们特别表明，在1D中，可以通过涉及非常简单的乘法移动的单个公式来近似IDO。在2D中，同样的想法适用，但必须在频谱的底部和顶部之间更改预制剂。
Recent work [G. David, M. Filoche, and S. Mayboroda, arXiv:1909.10558[Adv. Math. (to be published)]] has proved the existence of bounds from above and below for the Integrated Density of States (IDOS) of the Schrödinger operator throughout the spectrum, called the landscape law. These bounds involve dimensional constants whose optimal values are yet to be determined. Here, we investigate the accuracy of the landscape law in 1D and 2D tight-binding Anderson models, with binary or uniform random distributions. We show, in particular, that in 1D, the IDOS can be approximated with high accuracy through a single formula involving a remarkably simple multiplicative energy shift. In 2D, the same idea applies but the prefactor has to be changed between the bottom and top parts of the spectrum.
