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 acconductivity is bounded from above by Cv2(log 1/v)d+2 at small frequencies v. This is to be compared to Mott's formula, which predicts the leading term to be Cv2(log 1/v)d+1.