Universal Diffusion in Incoherent Black Holes

TL;DR

This paper demonstrates that in certain holographic models with broken translational symmetry, charge and energy diffusion constants become universal and are governed by fundamental quantum and thermal scales, independent of momentum relaxation mechanisms.

Contribution

It reveals universal diffusion constants in incoherent black holes, linking them to the butterfly velocity and fundamental constants, regardless of momentum relaxation details.

Findings

Diffusion constants scale as $rac{ ext{hbar} v_B^2}{k_B T}$.

Diffusion is controlled by quantum thermal timescale $ au o rac{ ext{hbar}}{k_B T}$.

Results apply to holographic theories with broken translational symmetry.

Abstract

We study charge and energy diffusion in simple holographic theories with broken translational symmetry. We find that when the effects of momentum relaxation are very strong the diffusion constants take universal values $D_{c} \sim D_{e} \sim \hbar v_B^2/(k_B T)$. Here $v_B$ is the velocity of the butterfly effect and the coefficients of proportionality depend only on the scaling exponents of the infra-red fixed point. Our results suggest that diffusion in these incoherent black holes is controlled by $\tau \sim {\hbar}/(k_B T)$ independently of the mechanism of momentum relaxation.