Physics – Condensed Matter – Disordered Systems and Neural Networks
Scientific paper
2010-04-19
Chapter 4 in "Fifty Years of Anderson localization", ed. E. Abrahams (World Scientific, Singapore, 2010), p. 43; reprinted in
Physics
Condensed Matter
Disordered Systems and Neural Networks
25 pages, 2 figures; published version including corrections
Scientific paper
The self-consistent theory of Anderson localization of quantum particles or classical waves in disordered media is reviewed. After presenting the basic concepts of the theory of Anderson localization in the case of electrons in disordered solids, the regimes of weak and strong localization are discussed. Then the scaling theory of the Anderson localization transition is reviewed. The renormalization group theory is introduced and results and consequences are presented. It is shown how scale-dependent terms in the renormalized perturbation theory of the inverse diffusion coefficient lead in a natural way to a self-consistent equation for the diffusion coefficient. The latter accounts quantitatively for the static and dynamic transport properties except for a region near the critical point. Several recent applications and extensions of the self-consistent theory, in particular for classical waves, are discussed.
Vollhardt Dieter
Wölfle Peter
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