Perturbative and Nonperturbative Kolmogorov Turbulence in a Gluon Plasma

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 $\nu =2$.

published version

References in corpus (8)

• Non-thermal fixed points: effective weak-coupling for strongly correlated systems far from equilibrium
• Nonthermal fixed points and the functional renormalization group
• Turbulence in nonabelian gauge theory
• Non-abelian plasma instabilities for strong anisotropy
• Non-Abelian plasma instabilities: SU(3) vs. SU(2)
• Strong versus weak wave-turbulence in relativistic field theory
• On Kolmogorov Wave Turbulence in QCD
• Real time statistical field theory

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