  We study transport properties of discrete quantum dynamical systems on the
lattice, in particular Coined Quantum Walks and the Chalker--Coddington model.
We prove existence of a non trivial charge transport and that the absolutely
continuous spectrum covers the whole unit circle under mild assumptions. For
Quantum Walks we exhibit explicit constructions of coins which imply existence
of stable directed quantum currents along classical curves. The results are of
topological nature and independent of the details of the model.
