Nonlocal wave turbulence in non-Abelian plasmas

TL;DR

This paper studies wave turbulence in non-Abelian plasmas, revealing nonlocal interactions dominate the spectrum, leading to thermalization and a non-steady turbulent cascade with a spectral exponent near -2, supported by numerical simulations.

Contribution

It demonstrates that nonlocal interactions control the gluon spectrum in non-Abelian plasmas, contrasting with universal spectra, and analyzes the effects of inelastic processes on turbulence and thermalization.

Findings

Inelastic processes dominate in the IR, forming a thermal bath.

The turbulent spectrum spreads to UV as t^{1/2}, similar to elastic processes.

Numerical simulations show a spectral exponent close to -2, consistent with classical Yang-Mills results.

Abstract

We investigate driven wave turbulence in non-Abelian plasmas, in the framework of kinetic theory where both elastic and inelastic processes are considered in the small angle approximation. The gluon spectrum, that forms in the presence of a steady source, is shown to be controlled by nonlocal interactions in momentum space, in contrast to the universal Kolmogorov-Zakharov spectra. Assuming strongly nonlocal interactions, we show that inelastic processes are dominant in the IR and cause a thermal bath to form below the forcing scale, as a result of a detailed balance between radiation and absorption of soft gluons by the hard ones. Above the forcing scale, the inelastic collision term reduces to an inhomogeneous diffusion-like equation yielding a spectrum that spreads to the UV as $t^{1/2}$, similarly to elastic processes. Due to nonlocal interactions the non-universal turbulent spectrum is not steady and flattens when time goes on toward the thermal distribution. This analysis is complemented by numerical simulations, where we observe that in the explored time interval the spectral exponent of the nonlocal turbulent cascade is close to $-2$ in agreement with simulations of classical Yang-Mills equations.