Conductivity and Diffusion Constant in Lifshitz Backgrounds

Understand

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.