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，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Anderson局域化。(1)利用能级统计的标度性质，研究了强磁场作用下二维无序电子系统的局域-离域转变，即具有么正普适性的量子霍尔系统。得到的发散局域化长度指数与有限尺寸标度分析得到的指数一致。然而，对不同关联长度的无序势的分析表明，这可能是由于随着关联…的增加，临界区变窄所致再长一点。当临界区很窄时，能级统计的标度分析问题有待于进一步研究。(2)对于只有自旋-旋转对称性被破坏的辛系统，通过对波包扩散的模拟，得出了在相变时波函数和能谱中存在分形结构的结论。分维被发现大约是空间维度的一半；对于另外两个普适性类别也是如此。从有限尺寸标度、能级统计、扩散模拟、电导涨落等方面分析了随机磁场中的局域化问题。由于篇幅有限，对结果的详细描述被省略。(4)无论模型如何，三维无序系统在磁场中的局域化指数约为1.35。较少

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

T.Kawarabayashi：“具有对称对称性的三维无序系统中的阿德森转变”物理。