  In disordered Weyl semimetals, mechanisms of topological origin lead to novel
mechanisms of transport, which manifest themselves in unconventional types of
electromagnetic response. Prominent examples of transport phenomena particular
to the Weyl context include the anomalous Hall effect, the chiral magnetic
effect, and the formation of totally field dominated regimes of transport in
which the longitudinal conductance is proportional to an external magnetic
field. In this paper, we discuss the manifestations of these phenomena at large
length scales including the cases of strong disorder and/or magnetic field
which are beyond the scope of diagrammatic perturbation theory. Our perhaps
most striking finding is the identification of a novel regime of
drift/diffusion transport where diffusion at short scales gives way to
effectively ballistic dynamics at large scales, before a re-entrance to
diffusion takes place at yet larger scales. We will show that this regime plays
a key role in understanding the interplay of the various types of
magnetoresponse of the system. Our results are obtained by describing the
strongly disordered system in terms of an effective field theory of
Chern-Simons type. The paper contains a self-contained derivation of this
theory, and a discussion of both equilibrium and non-equilibrium (noise)
transport phenomena following from it.
