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Anderson localization and the theory of dirty superconductors.

We study the effect of Anderson localization in dirty superconductors. The scale dependence of the diffusion in the vicinity of the mobility edge results in a strong renormalization of the zero-temperature coherence length. This implies the breakdown of the Ginzburg criterion close to the metal-insulator transition and thus the importance of fluctuations in this regime. The upper critical field is calculated and possible experiments are also discussed.