Universal Charge Diffusion and the Butterfly Effect

TL;DR

This paper reveals a universal relationship between charge diffusion and quantum chaos in holographic theories, linking the diffusion constant to the butterfly velocity and scaling exponents, indicating a deep connection between transport and chaos.

Contribution

It establishes a universal formula for charge diffusion in holographic theories relating it to the butterfly velocity and scaling exponents, highlighting a link between transport and quantum chaos.

Findings

Charge diffusion constant is universally proportional to butterfly velocity squared.

The proportionality constant depends only on IR scaling exponents.

The results connect strong coupling transport with quantum chaos phenomena.

Abstract

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 $D_c = C v_B^2/ (2 \pi T)$ where $v_B$ is the velocity of the butterfly effect. The constant of proportionality, $C$, depends only on the scaling exponents of the infra-red theory. Our results suggest an unexpected connection between transport at strong coupling and quantum chaos.