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H. Schulz-Baldes, J. Bellissard
Anomalous transport: a mathematical framework
ABSTRACT. We develop a mathematical framework allowing to study
anomalous transport in homogeneous solids. The main tools
characterizing the anomalous transport properties are spectral and
diffusion exponents associated to the covariant Hamiltonians describing
these media. The diffusion exponents characterize the spectral measures
entering in Kubo's formula for the conductivity and hence lead to
anomalies in Drude's formula. We give several formulas allowing to
calculate these exponents and treat, as an example, Wegner's
$n$-orbital model as well as the Anderson model in coherent potential