1996/05/10 by Tobias Brandes, Bodo Huckestein, Ludwig Schweitzer
Physics and Astronomy · #cond-mat
published as Ann. Physik 5, 633-651 (1996) · 21 pages, Revtex with epsf, 5 figures included as Postscript files, to appear in Ann. Physik
arxiv created 1996/05/10 · arxiv updated 2009/11/30
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.