Parametric Instability of Classical Yang-Mills Fields in an Expanding Geometry

TL;DR

This paper studies the parametric instability of classical Yang-Mills fields in an expanding geometry, revealing how fluctuations grow exponentially and potentially influence thermalization in heavy-ion collisions.

Contribution

It introduces a conformal coordinate approach to analyze the instability of Yang-Mills fields in an expanding background, highlighting the growth of fluctuations with finite momenta.

Findings

Finite longitudinal momenta fluctuations grow exponentially due to parametric instability.

Finite transverse momenta fluctuations can also become unstable but are limited to small momenta.

Unstable modes grow early and may impact thermalization in heavy-ion collisions.

Abstract

We investigate the instability of classical Yang-Mills field in an expanding geometry under a color magnetic background field within the linear regime. We consider homogeneous, boost-invariant and time-dependent color magnetic fields simulating the glasma configuration. We introduce the conformal coordinates which enable us to map an expanding problem approximately into a nonexpanding problem. We find that the fluctuations with finite longitudinal momenta can grow exponentially due to parametric instability. Fluctuations with finite transverse momenta can also show parametric instability, but their momenta are restricted to be small. The most unstable modes start to grow exponentially in the early stage of the dynamics and they may affect the thermalization in heavy-ion collisions.