Perturbative and Nonperturbative Kolmogorov Turbulence in a Gluon Plasma

TL;DR

This paper investigates the turbulent spectra in gluon plasmas, analyzing perturbative and nonperturbative processes to explain observed spectral exponents, and proposes scenarios for different cascade behaviors.

Contribution

It provides a detailed analysis of Kolmogorov spectra in gluon plasmas, including nonperturbative effects and potential scaling behaviors beyond perturbation theory.

Findings

Perturbative processes yield a maximum spectral exponent of 5/3.

Nonperturbative effects can lead to larger exponents, up to 5.

A simple scenario for an exponent of 2 is proposed.

Abstract

In numerical simulations of nonabelian plasma instabilities in the hard-loop approximation, a turbulent spectrum has been observed that is characterized by a phase-space density of particles $n(p)\sim p^{-\nu}$ with exponent $\nu\simeq 2$, which is larger than expected from relativistic $2\leftrightarrow 2$ scatterings. Using the approach of Zakharov, L'vov and Falkovich, we analyse possible Kolmogorov coefficients for relativistic $(m \ge 4)$-particle processes, which give at most $\nu=5/3$ perturbatively for an energy cascade. We discuss nonperturbative scenarios which lead to larger values. As an extreme limit we find the result $\nu=5$ generically in an inherently nonperturbative effective field theory situation, which coincides with results obtained by Berges et al.\ in large-$N$ scalar field theory. If we instead assume that scaling behavior is determined by Schwinger-Dyson resummations such that the different scaling of bare and dressed vertices matters, we find that intermediate values are possible. We present one simple scenario which would single out $\nu=2$.