# 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 from above 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 $C \nu^2 (\log \frac 1 \nu)^{d+1}$.

## Authors

Abel Klein

Department of Mathematics, University of California, Irvine, CA 92697, United States

Olivier Lenoble

Department of Mathematics, University of California, Irvine, CA 92697, United States

Peter Müller

Department of Mathematics, University of California, Irvine, CA 92697, United States