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Article overview
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Critical dynamics and multifractal exponents at the Anderson transition in 3d disordered systems | Tobias Brandes
; Bodo Huckestein
; Ludwig Schweitzer
; | Date: |
10 May 1996 | Journal: | Ann. Physik 5, 633-651 (1996) | Subject: | cond-mat | Affiliation: | Gakushuin Univ.), Bodo Huckestein (Univ. Cologne), Ludwig Schweitzer (PTB | Abstract: | 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 $eta = d-D_{2}$ between the correlation dimension $D_{2}$ of the multifractal eigenstates and the exponent $eta$ which enters into correlation functions is verified. Numerically, we have $etaapprox 1.3$. 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 $eta$. The electron-electron scattering rate is found to be linear in $T$ and depends on the dimensionless conductance at the critical point. | Source: | arXiv, cond-mat/9605062 | Services: | Forum | Review | PDF | Favorites |
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