Non-Exponential Localization of One-Electron Wave-Function in Two-Dimensional Random Systems

长期以来，人们一直认为Abraham等人的单参数定域标度理论描述了安德森定域的总体特征。它描述了二维指数局部化。我与Azbel博士合作研究了这个问题，并写了一篇论文，提出了在二维无序系统中没有指数局域化的问题。然而，这个理论包含了许多微妙之处。因此，在目前的研究中，我试图从我们的理论中去除微妙的地方，并将其打磨得尽可能严谨。(1)I研究了无序系统的标准紧束缚安德森模型，以去除“乌姆克鲁普过程”和“紫外截止”。“这是在以前的文件。（2）描述不等式的唯一假设已经在数值上得到了广泛的检验。本文的理论得到了（1）的进一步发展，数值实验也为我们提供了积极的支持，一些时间结果已发表在Phys.Stat.Sol.1（2004）中。结论性的结果将在其他地方提出后，确认一个理论点，这仍然是在考虑。

It has long been believed that the one-parameter scaling theory of localization by Abraham et al. describes an overall feature of the Anderson localization. It describes exponential localization in two-dimension. I collaborated with Dr.Azbel on this problem and wrote a paper suggesting absence of exponential localization in two-dimensional disordered system with very weak disorder. However, the theory contained many subtle points. Thus in the present research I tried to remove the subtle points from our theory and to polish it to be the one as rigorous as possible.(1)I have studied the standard tightly-binding Anderson model of disordered systems, to remove an "Umklup process" and an "ultra-violet cut-off." which were in the previous paper. (2)The only assumption describing an inequality has numerically been examined extensively. The theory was blushed up by (1), and the numerical examination gave us a positive support.Some temporal results has been presented in Phys.Stat.Sol.1(2004). Conclusive results will be presented elsewhere after confirming a theoretical point which is still now in consideration.