The evolving Glasma

TL;DR

This paper investigates the early-time dynamics of the Glasma in heavy-ion collisions by simulating classical Yang-Mills equations, revealing energy transfer among modes and a Kolmogorov-like spectrum.

Contribution

It provides a detailed numerical study of the Glasma's instability growth, energy transfer, and spectral scaling in an expanding system, with systematic parameter analysis.

Findings

Unstable modes grow predominantly in the linear regime.

Energy flows from low to high wave-number modes due to non-linearity.

Energy spectrum approaches a Kolmogorov-like power-law form.

Abstract

We extensively study the growing behavior of the energy and the pressure components depending on the space-time rapidity in the framework of the Glasma, which describes the early-time dynamics in the ultra-relativistic heavy-ion collisions. We simulate the Glasma solving the classical equations of motion in the SU(2) Yang-Mills theory and systematically investigate the dependence of the Glasma instability on the model parameters. We have checked that the transverse and longitudinal grid sizes in our simulation are large enough to handle cutoff effects under control. By comparing the numerical results from several initial conditions with different magnitudes of instability seed and also those with different wave-numbers for rapidity fluctuations, we clearly see that unstable modes dominantly grow up in the linear regime and we also confirm non-linear effects in the time evolution. To extract more detailed information on the evolving Glasma, we decompose the energy into the components in terms of rapidity wave-numbers. We observe an energy flow from low wave-number modes into higher wave-number modes due to non-linearity in the equations of motion. We find that the energy spectrum approaches an asymptotic scaling that is consistent with Kolmogorov's power-law form even in the expanding system of the Glasma.