Breakdown of hydrodynamics from holographic pole collision

TL;DR

This paper investigates how hydrodynamic descriptions fail in certain holographic models at low temperatures, revealing different mechanisms of breakdown and confirming bounds on charge diffusion constants.

Contribution

It identifies conditions under which the lowest non-hydrodynamic mode causes hydrodynamic breakdown, including the role of IR modes and slow modes, and explores temperature dependence of convergence radius.

Findings

Hydrodynamic breakdown can be caused by either IR or slow modes.

The upper bound for charge diffusion constant is always satisfied.

Convergence radius depends nontrivially on temperature and gauge coupling.

Abstract

We study the breakdown of diffusive hydrodynamics in holographic systems dual to neutral dilatonic black holes with extremal near horizon geometries conformal to AdS$_2\times\,$R$^2$. We find that at low temperatures by tuning the effective gauge coupling constant in the infra-red, the lowest non-hydrodynamic mode, which collides with the charge diffusive mode and sets the scales at which diffusive hydrodynamics break down, could be either an infra-red mode or a slow mode, resulting in different scaling behaviors of the local equilibrium scales. We confirm that the upper bound for the charge diffusion constant is always satisfied using the velocity and timescale of local equilibration from the pole collision. We also examine the breakdown of hydrodynamics at general temperature and find that the convergence radius has nontrivial dependence on temperature, in addition to the effective gauge coupling constant.