Critical dynamics and multifractal exponents at the Anderson transition in 3d disordered systems

We investigate the dynamics of electrons in the vicinity of the Anderson transition in d = 3 dimensions. Using the exact eigenstates from a numerical diagonalization, a number of quantities related to the critical behavior of the diffusion function are obtained. The relation η = d ? D₂ between the correlation dimension D₂ of the multifractal eigenstates and the exponent η which enters into correlation functions is verified. Numerically, we have η ≈? 1.3. Implications of critical dynamics for experiments are predicted. We investigate the long-time behavior of the motion of a wave packet. Furthermore, electron-electron and electron-phonon scattering rates are calculated. For the latter, we predict a change of the temperature dependence for low T due to η. The electron-electron scattering rate is found to be linear in T and depends on the dimensionless conductance at the critical point.