ANOMALOUS TRANSPORT - A MATHEMATICAL FRAMEWORK

We develop a mathematical framework allowing to study anomalous transp ort 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 ex ponents characterize the spectral measures entering in Kubo's formula for the conductivity and hence lead to anomalies in Drude's formula. W e give several formulas allowing to calculate these exponents and trea t, as an example, Wegner's n-orbital model as well as the Anderson mod el in coherent potential approximation.