CRITICAL-DYNAMICS AND MULTIFRACTAL EXPONENTS AT THE ANDERSON TRANSITION IN 3D DISORDERED-SYSTEMS

We investigate the dynamics of electrons in the vicinity of the Anders on transition in d = 3 dimensions. Using the exact eigenstates from a numerical diagonalization, a number of quantities related to the criti cal behavior of the diffusion function are obtained. The relation eta = d - D-2 between the correlation dimension D-2 Of the multifractal ei genstates and the exponent eta which enters into correlation functions is verified. Numerically, we have eta approximate to 1.3. Implication s of critical dynamics for experiments are predicted. We investigate t he long-time behavior of the motion of a wave packet. Furthermore, ele ctron-electron and electron-phonon scattering rates are calculated. Fo r the latter, we predict a change of the temperature dependence for lo w T due to eta. The electron-electron scattering rate is found to be l inear in T and depends on the dimensionless conductance at the critica l point.