Level Statistics and Anderson Localization in Disordered Electron Systems

无序电子系统中的能级统计和安德森定位

• 批准号: 07640520
• 负责人: ONO Yoshiyuki
• 金额: $ 1.34万
• 依托单位: Toho University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 1995
• 资助国家: 日本
• 起止时间: 1995 至 1996
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-07640520/
• 关键词: level statistics; Gaussian unitary ensemble; level repulsion; Anderson localization; Gaussian symplectic ensemble; level spacing; two level correlation; rigidity of level distribution; 不規則電子系; 量子ホール効果; スピン軌道相互作用

In the present project, the Anderson localization determining transport properties of disordered electron systems have been investigated mainly from the viewpoint of the level statistics. The results were compared with those of finite size scaling analyzes etc., and several useful informations related to the essential properties of the localization phenomena.(1) The localization-delocalization transition in two-dimensional disordered electron systems subject to strong magnetic fields, i.e.the quantum Hall systems, which are typical of the unitary universality class, were studied by using the scaling properties of the level statistics. The obtained exponent of the diverging localization length has been found to be consistent with that obtained from the finite size scaling analyzes. However, the analyzes for different correlation lengths of the disordered potential indicated non-universal behavior, which might be due to the narrowing of the critical region with increasing the correlation … More length. The problem in the scaling analysis of the level statistics when the critical region is very narrow has been left for future studies.(2) For symplectic systems where only the spin-rotation symmetry is broken, the simulations of the wavepacket diffusion led to the conclusion that there exist fractal structures in the wave functions and energy spectra at the transition. The fractal dimension was found to be about half the spatial dimension ; this is the case also for the other two universality classes. The level statistics at the transition point showed a clear difference from those for orthogonal systems.(3) The localization problem in random magnetic fields was analyzed in terms of finite size scaling, level statistics, simulations of diffusion, and conductance fluctuations for two and three dimensions. Detailed description of the results is omitted because of lack of space.(4) The localization exponent for three-dimensional disordered systems in magnetic fields was found to be about 1.35 irrespective of the model. Less

在本项目中，已主要从级别统计数据的角度研究了确定无序电子系统运输特性的安德森本地化。将结果与有限尺寸缩放分析等的结果进行了比较，以及与定位现象的基本特性有关的几个有用信息。（1）在二维无序电子系统中，具有强磁场的定位 - 范围 - 偏置过渡，即使用该级别级别的量级属性研究了量子级典型的量子霍尔系统，这些量子系统是典型的量子级别。已经发现，所获得的分化定位长度的指数与从最终尺寸缩放分析获得的指数一致。但是，对无序潜力的不同相关长度的分析表明非宇宙行为，这可能是由于关键区域的狭窄而增加，随着相关性的增加……更长。当临界区域非常狭窄的情况下，对水平统计的缩放分析中的问题进行了未来的研究。（2）对于仅旋转对称性对称的对称系统，波袋扩散的模拟导致了一个结论，即在过渡中的波函数和能量光谱中存在分形结构。发现分形维度约为空间尺寸的一半。其他两所大学也是如此。过渡点的水平统计数据与正交系统的水平统计数据明显差异。（3）根据有限尺寸缩放，水平统计，差异的模拟以及两个维度和三个维度的电导波动，分析了随机磁场中的定位问题。由于缺乏空间，因此省略了结果的详细描述。（4）发现磁场中三维无序系统的定位指数均约为1.35。较少的

项目成果

Y.Ono: "Scaling Behavior of Level Distribusion in Quantum Hall Regime" J.Phys.Soc.Jpn.65. 1734-1743 (1996)

Y.Ono：“量子霍尔体系中能级分布的标度行为”J.Phys.Soc.Jpn.65。

Y.Ono: "Scaling Behavior of Level Distribution in Quantum Hall Regime" J. Phys. Soc. Jpn.65. 1734-1743 (1996)

Y.Ono：“量子霍尔体系中能级分布的标度行为”J. Phys。

T.Kawarabayashi: "Diffusion of Electrons in Two-Dimensional Disordered Symplectic Systems" Phys.Rev.B. 53. 6975-6978 (1996)

T.Kawarabayashi：“二维无序辛系统中电子的扩散”Phys.Rev.B。

T.Kawarabayashi and T.Ohtsuki: "Anomalous Diffusion at the Anderson Transitions" J.Phys.Soc.Jpn.66. 314-317 (1997)

T.Kawarabayashi 和 T.Ohtsuki：“安德森跃迁处的异常扩散”J.Phys.Soc.Jpn.66。

T.Kawarabayashi: "Anomalous Diffusion at the Anderson Transition" J.Phys.Soc.Jpn.66. 314-317 (1997)

T.Kawarabayashi：“安德森转变时的反常扩散”J.Phys.Soc.Jpn.66。