Diffusion and Chaos from near AdS$_2$ horizons

TL;DR

The paper examines thermal diffusion and chaos in holographic theories that flow to AdS2 × R^d IR fixed points. By analyzing irrelevant deformations via domain-wall expansions, it shows the same IR mode governs both the specific heat-driven diffusion constant and the chaos-based butterfly velocity, yielding the universal relation $D = E \frac{v_B^2}{2\pi T}$ with $E$ in (1/2,1], and $E=1$ when the leading mode is the universal dilaton with $Δ=2$. In the presence of a scalar with $1<Δ_φ<3/2$, backreaction modifies the IR scalings to $D ≈ T^{3-2Δ_φ}$ and $v_B ≈ T^{2-Δ_φ}$, but the proportionality to $v_B^2/(2π T)$ persists with a coefficient $E(Δ_φ)$. These results generalize and unify earlier observations of diffusion–chaos connections in holographic and SYK-like models, highlighting a deep link between transport and quantum chaos in strongly coupled quantum matter.

Abstract

We calculate the thermal diffusivity $D = κ/c_ρ$ and butterfly velocity $v_B$ in holographic models that flow to AdS$_2 \times R^{d}$ fixed points in the infra-red. We show that both these quantities are governed by the same irrelevant deformation of AdS$_2$ and hence establish a simple relationship between them. When this deformation corresponds to a universal dilaton mode of dimension $Δ= 2$ then this relationship is always given by $D = v_B^2/(2 πT)$.