Conductivity and Diffusion Constant in Lifshitz Backgrounds

Abstract

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.

18 pages, no figures, references added, to appear in JHEP

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