Conductivity and Diffusion Constant in Lifshitz Backgrounds

TL;DR

This paper investigates the electrical conductivity and diffusion properties of Lifshitz black branes across various dimensions and dynamical exponents, providing explicit calculations and confirming results with the membrane paradigm.

Contribution

It offers new analytical results for conductivity and diffusion constants in Lifshitz backgrounds with arbitrary parameters, extending previous studies.

Findings

Explicit conductivity and diffusion constant formulas for Lifshitz black branes.

Confirmation of results via the membrane paradigm.

Calculation of real-time correlation functions for a specific case.

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.