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

长期以来，人们一直认为亚伯拉罕等人的局部化的单参数标度理论。描述Anderson本地化的总体功能。它描述了二维的指数局部化。我在这个问题上与阿兹贝尔博士合作，并写了一篇论文，提出在具有非常弱无序的二维无序系统中没有指数局域化。然而，这一理论包含了许多微妙的观点。因此，在目前的研究中，我试图去掉我们理论中的微妙之处，并使其尽可能地严谨。(1)我研究了无序系统的标准紧束缚安德森模型，去掉了“乌姆克拉普过程”和“紫外线截止”。这些都在前一篇论文中。(2)描述一个不等式的唯一假设已经在数值上得到了广泛的检验。这个理论被(1)冲刷了，数值检验给了我们一个肯定的支持。一些时间上的结果已经在Phys.Stat.Sol.1(2004)上给出了。在确认了目前仍在考虑的一个理论观点后，将在其他地方提出结论性的结果。

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.