Universal Diffusion in Incoherent Black Holes

TL;DR

The paper investigates diffusion in holographic theories with strong momentum relaxation and demonstrates that both charge and energy diffusion constants saturate universal Planckian forms controlled by the butterfly velocity: $D_c\sim C\frac{\hbar v_B^2}{k_B T}$ and $D_e\sim E\frac{\hbar v_B^2}{k_B T}$. Using simple linear axion models and generalized Q-lattice geometries, it shows that in the incoherent regime the diffusion constants depend primarily on the IR scaling exponents and horizon data, yielding a timescale $τ\sim \hbar/(k_B T)$. This provides a concrete holographic realization of diffusion universality in incoherent metals and suggests broad applicability to strongly correlated systems. The work strengthens the connection between quantum chaos (via $v_B$) and transport, and highlights a potential universal bound on diffusion independent of microscopic momentum-relaxation mechanisms.

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 $τ\sim {\hbar}/(k_B T)$ independently of the mechanism of momentum relaxation.

Figures (1)

• Figure 1: Diffusion constants of neutral axion model. The diffusion constants themselves (left) are sensitive to the ratio $k/T$. However, upon dividing by the butterfly velocity $v_B^2$ (right) the universality is evident. In particular note that the energy diffusion constant (red) becomes universal at large $k/T$. The diffusion constants cross at the self-dual point davison$k L^2 = \sqrt{2} r_0$.