  Recent progress in the holographic approach makes it more transparent that
each conductivity can be decomposed into the coherent contribution due to
momentum relaxation and the incoherent contribution due to intrinsic current
relaxation. In this paper we investigate this decomposition in the framework of
Einstein-Maxwell-dilaton theory. We derive the perturbation equations, which
are decoupled for a large class of background solutions, and then obtain the
analytic results of conductivity with the slow momentum relaxation in low
frequency approximation, which is consistent with the known results from memory
matrix techniques.
