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

本项目主要从能级统计的角度研究了决定无序电子系统输运性质的安德森局域化。将所得结果与有限尺度尺度分析等结果进行了比较，并提供了有关局部化现象本质性质的一些有用信息。(1)利用能级统计量的标度性质，研究了强磁场作用下二维无序电子系统（即典型的酉普适类量子霍尔系统）的定域-离域跃迁。得到的发散局部化长度指数与有限尺寸标度分析的结果一致。然而，对不同相关长度的无序势的分析显示出不普遍的行为，这可能是由于随着相关长度的增加，临界区域变窄。当临界区域很窄时，水平统计量的标度分析问题有待进一步研究。(2)对于仅自旋对称性被破缺的辛系统，通过对波包扩散的模拟，得出了跃迁处的波函数和能谱存在分形结构的结论。分形维数约为空间维数的一半；另外两个普适性类也是如此。过渡点的水平统计量与正交系统的水平统计量明显不同。(3)从有限尺寸标度、能级统计、扩散模拟、二维和三维电导波动等方面分析了随机磁场中的局部化问题。由于篇幅所限，对结果的详细描述就省略了。(4)三维无序系统在磁场中的局部化指数与模型无关，均约为1.35。少

项目成果

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。

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。

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: "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: "Anderson Transition in Three-Dimensional Disordered Systems with Symplectic Symmetry" Phys.Rev.Lett.77. 3593-3596 (1996)

T.Kawarabayashi：“具有辛对称性的三维无序系统中的安德森跃迁”Phys.Rev.Lett.77。