Level Statistics and Anderson Localization in Disordered Electron Systems
Project/Area Number  07640520 
Research Category 
GrantinAid for Scientific Research (C)

Section  一般 
Research Field 
物性一般(含基礎論)

Research Institution  Toho University 
Principal Investigator 
ONO Yoshiyuki Toho Univ., Dept.Phys., Professor, 理学部, 教授 (30011761)

CoInvestigator(Kenkyūbuntansha) 
OHTSUKI Tomi Sophia Univ., Dept.Phys., Associate Professor, 理工学部, 助教授 (50201976)

Project Fiscal Year 
1995 – 1996

Project Status 
Completed(Fiscal Year 1996)

Budget Amount *help 
¥2,100,000 (Direct Cost : ¥2,100,000)
Fiscal Year 1996 : ¥800,000 (Direct Cost : ¥800,000)
Fiscal Year 1995 : ¥1,300,000 (Direct Cost : ¥1,300,000)

Keywords  level statistics / Gaussian unitary ensemble / level repulsion / Anderson localization / Gaussian symplectic ensemble / level spacing / two level correlation / rigidity of level distribution / 準位統計 / ガウスユニタリー集団 / 準位反発 / アンダーソン局在 / ガウスシンプレクティック集団 / 準位間隔 / 二準位相関 / 準位分布の剛性度 / 不規則電子系 / 量子ホール効果 / スピン軌道相互作用 
Research Abstract 
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 localizationdelocalization transition in twodimensional 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 nonuniversal behavior, which might be due to the narrowing of the critical region with increasing the correlation
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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 spinrotation 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 threedimensional disordered systems in magnetic fields was found to be about 1.35 irrespective of the model. 3.ランダム磁場中の局在問題も有限サイズスケーリングや準位統計、拡散のシミュレーション、伝導度揺らぎ等によって二、三次元の場合に解析し、詳細な知見を得た。 4.磁場中の三次元不規則電子系のアンダーソン転移については、量子ホール系を何層も重ねたモデルと、強束縛電子モデルにパイエルス因子を導入したもので有限サイズスケーリングの解析を行い、どちらの場合も局在長の指数が1.35程度になることを確かめた。 Less

Report
(4results)
Research Output
(20results)