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

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

2005-08-01

arxiv.org/abs/math-ph/0508007v2

Ann. Math. (2) 166, 551-579 (2007)

Physics

Mathematical Physics

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

Scientific paper

We study the ac-conductivity in linear response theory in the general framework of ergodic magnetic Schr\"odinger 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 $C \nu^2 (\log \frac 1 \nu)^{d+1}$.

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