We introduce a theoretical framework for computing transport coefficients for
complex materials. As a first example, we resolve long-standing inconsistencies
between experiment and theory pertaining to the conductivity and Hall mobility
for amorphous silicon and show that the Hall sign anomaly is a consequence of
localized states. Next, we compute the AC conductivity of amorphous
polyanaline. The formalism is applicable to complex materials involving defects
and band-tail states originating from static topological disorder and extended
states. The method may be readily integrated with current \textit{ab initio}
methods.Comment: 4 pages, 2 figures, submitted to Phys. Rev. Let