  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 approximation.
