Lifshitz Tails and Localization in 3d Anderson Model
نویسندگان
چکیده
Consider the 3D Anderson model with a zero mean and bounded i.i.d. random potential. Let λ be the coupling constant measuring the strength of the disorder, and σ(E) the self energy of the model at energy E. For any ǫ > 0 and sufficiently small λ, we derive almost sure localization in the band E ≤ −σ(0)−λ4−ǫ. In this energy region, we show that the typical correlation length ξE behaves roughly as O((|E| − σ(E)) −1/2), completing the argument, outlined in the unpublished work of T. Spencer [18].
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