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

二维随机系统中单电子波函数的非指数局域化

基本信息

批准号：
15540366
负责人：
GODA Masaki
金额：
$ 0.77万
依托单位：
Niigata University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2003
资助国家：
日本
起止时间：
2003 至 2004
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-15540366/
关键词：
Two-dimensional random system Disordered System Absence of exponential localization Scaling theory og localization Rigorous theory Numerical examination Lyapunov exponent Minimum positive Lyapunov exponent 二次元

项目摘要

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.

长期以来，人们一直认为亚伯拉罕等人提出的本地化单参数标度理论。描述了安德森定位的总体特征。它描述了二维指数局部化。我与 Azbel 博士合作解决了这个问题，并写了一篇论文，表明在无序性非常弱的二维无序系统中不存在指数局域化。然而，该理论包含许多微妙之处。因此，在目前的研究中，我试图消除我们理论中的微妙之处，并将其完善为尽可能严格的理论。（1）我研究了无序系统的标准紧束缚安德森模型，以消除“Umklup过程”和“紫外线截止”。这是在上一篇论文中。 (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。该理论被(1)所推翻，数值检验给了我们积极的支持。Phys.Stat.Sol.1(2004)中已经给出了一些时间结果。在确认目前仍在考虑的理论观点后，结论性结果将在其他地方提出。