# On Mott’s formula for the ac-conductivity in the Anderson model | Annals of Mathematics

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 from above by Cν2(log1ν)d+2 at small frequencies ν. This is to be compared to Mott’s formula, which predicts the leading term to be Cν2(log1ν)d+1.

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### 数学年刊（Annals of Mathematics）

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