Diffusion of electrons in two-dimensional disordered symplectic systems

Diffusion of electrons in two-dimensional disordered systems with spin-orbit interactions is investigated numerically. Asymptotic behaviors of the second moment of the wave packet and of the temporal auto-correlation function are examined. At the critical point, the auto-correlation function exhibits the power-law decay with a non-conventional exponent $\alpha$ which is related to the fractal structure in the energy spectrum and in the wave functions. In the metallic regime, the present results imply that transport properties can be described by the diffusion equation for normal metals.