Conductivity and diffusion constant in Lifshitz backgrounds

We study the DC conductivity and the diffusion constant for asymptotically Lifshitz black branes in (d + 2)-dimensions with arbitrary dynamical exponent z. For a solvable example with z = 2, d = 4, we calculate the real-time correlation functions, from which we can read off the corresponding conductivity and diffusion constant. For black branes with arbitrary z and d, we work out the conductivity and obtain the diffusion constant by making use of the Einstein relation. All the results agree with those obtained via the membrane paradigm.