关于Anderson模型中交流电导率的Mott公式
On Mott's formula for the ac-conductivity in the Anderson model
摘要：
本文在遍历磁薛定谔算子的一般框架下研究了线性响应理论中的交流电导率。对于Anderson模型，如果费米能级处于局域化区域，我们证明了在小频率$ν$处交流电导率受$C ν^2 (\log \frac 1 ν)^{d+2}$的约束.这是比较莫特的公式，它预测的主导项是$C ν^2 (\log \frac 1 ν)^{d+1}$。
英文摘要：
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 $C ν^2 (\log \frac 1 ν)^{d+2}$ at small frequencies $ν$. This is to be compared to Mott's formula, which predicts the leading term to be $C ν^2 (\log \frac 1 ν)^{d+1}$.
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