Level Statistics and Anderson Localization in Disordered Electron Systems

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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