The leading Lyapunov exponent in the glasma

TL;DR

This paper investigates the exponential growth of small perturbations in the glasma's boost-invariant color fields, identifying a Lyapunov exponent that relates to entropy production and thermalization in early heavy-ion collisions.

Contribution

It introduces a method to extract the Lyapunov exponent from perturbations in the glasma, revealing a universal growth rate independent of initial conditions.

Findings

Growth rate of perturbations scales as exp(0.4√(g^2μτ)) for SU(2)

Growth rate is insensitive to initial perturbation details

Unstable mode couples to all initial momentum scales

Abstract

We show that small perturbations in the boost-invariant color fields of the glasma exhibit an exponential growth with the square root of time. We interpret this growth rate as a Lyapunov exponent, related to entropy production and the thermalization timescale in the earliest stage of heavy-ion collisions. Working in a regime that is linear in this perturbation, we extract the time dependence of this mode as $\sim \exp(0.4\sqrt{g^2\mu\tau})$ for SU($2$), where $g^2\mu$ is proportional to the saturation scale and the square-root dependence is caused by the boost-invariant expansion of the system. We show that the growth rate of this mode is, unlike its amplitude, remarkably insensitive to the details of how the perturbations are initialized. In particular, we show that the unstable mode couples to all momentum scales present in the initial perturbation.