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Critical dynamics and multifractal exponents at the Anderson transition in 3d disordered systems
Author(s) -
Brandes T.,
Huckestein B.,
Schweitzer L.
Publication year - 1996
Publication title -
annalen der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.009
H-Index - 68
eISSN - 1521-3889
pISSN - 0003-3804
DOI - 10.1002/andp.2065080803
Subject(s) - physics , multifractal system , condensed matter physics , critical exponent , electron , dimensionless quantity , scattering , exponent , correlation function (quantum field theory) , critical point (mathematics) , eigenvalues and eigenvectors , quantum mechanics , phase transition , fractal , dielectric , mathematical analysis , linguistics , philosophy , mathematics
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 − D 2 between the correlation dimension D 2 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.