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We study charge diffusion in holographic scaling theories with a particle-hole symmetry. We show that these theories have a universal regime in which the diffusion constant is given by D₂=Cv₁^2/ (2πT), where v₁ is the velocity of the butterfly effect. The constant of proportionality C depends only on the scaling exponents of the infrared theory. Our results suggest an unexpected connection between transport at strong coupling and quantum chaos.
Mike Blake (Tue,) studied this question.