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Anderson Localization

Anderson 1958

One could argue that in disordered media, the phases of the interference terms are so random that their sum vanishes on average. That assumption would bring us back to the diffusion model of metallic conductance.
But that neglect of interferences is not always justified

The first answers came from the work of Larry Fleishman and Anderson in 1980. At low enough temperatures, they argued, repulsive interactions neither destroy the localized electronic states nor induce thermally excited hopping. Conductance should still vanish at low temperatures. Around the same time, Boris Altshuler and coworkers found (right ref?) that interactions between electrons destroy the constructive interferences and thus lead to a finite, almost diffusive conductance. Recent work by Denis Basko, Altshuler, and colleagues combined the two results and concludes that repulsive interactions, together with disorder in the potential energy landscape, lead to a metal–insulator transition at some intermediate, finite temperature.

1982 Density of states and screening near the mobility edge


Here we report the measurement of the mobility edge for ultracold atoms in a disordered potential created by laser speckles


Distribution of the local density of states as a criterion for Anderson localization:
Numerically exact results for various lattices in dimensions D = 2 and 3