  The DC thermoelectric conductivities of holographic systems in which
translational symmetry is broken can be efficiently computed in terms of the
near-horizon data of the dual black hole. By calculating the frequency
dependent conductivities to the first subleading order in the momentum
relaxation rate, we give a physical explanation for these conductivities in the
simplest such example, in the limit of slow momentum relaxation. Specifically,
we decompose each conductivity into the sum of a coherent contribution due to
momentum relaxation and an incoherent contribution, due to intrinsic current
relaxation. This decomposition is different from those previously proposed, and
is consistent with the known hydrodynamic properties in the translationally
invariant limit. This is the first step towards constructing a consistent
theory of charged hydrodynamics with slow momentum relaxation.
