of the critical exponent for three symmetry classes (orthogonal, unitary, and symplectic) are different. We have also estimated the scaling beta function for the quasi-1D localization length, which indicates that the finite size scaling of the quasi-1D localization length depends on the symmetry in the metallic and critical regions, but not in the strongly localized region.

We also report numerical study of the Anderson transition in systems with spin-orbit coupling in 2D and below. Such systems are an exception to the prediction of Abrahams et. al. that there is no metallic phase in 2D and below. We have estimated the critical exponent for the 2D Anderson transition in systems with spin-orbit coupling, and then studied the quantum transport property in the 2D metallic phase. Our results in the 2D metallic region support the Hikami-Larkin-Nagaoka's prediction that the 2D metals have perfect conductivity. We have also investigated the possibility of an Anderson transition below 2D. Our simulations on the Sierpinski carpet suggest that an Anderson transition occurs even below 2D in the presence of spin-orbit coupling. The lower critical dimension might be between 1D and 2D.