On Mott's formula for the ac-conductivity in the Anderson model

Abstract

We study the ac-conductivity in linear response theory in the general framework of ergodic magnetic Schrödinger operators. For the Anderson model, if the Fermi energy lies in the localization regime, we prove that the ac-conductivity is bounded by $C{\nu }^2(\log \frac{1}{\nu }{)}^{d+2}$ at small frequencies $\nu$. This is to be compared to Mott's formula, which predicts the leading term to be $C{\nu }^2(\log \frac{1}{\nu }{)}^{d+1}$.

29 pages, 1 figure; misprints corrected, references updated, Remark 3.2 on gauge equivalence added; to appear in the Annals of Mathematics

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