The Asymptotic Method Developed from Weak Turbulent Theory and the Nonlinear Permeability and Damping Rate in QGP

TL;DR

This paper develops an asymptotic method based on weak turbulent theory to analyze the nonlinear permeability and damping rates in quark-gluon plasma, highlighting the significance of non-Abelian effects.

Contribution

It introduces a novel asymptotic approach to derive nonlinear permeability tensors and damping rates in QGP, emphasizing the importance of third-order currents and non-Abelian effects.

Findings

Nonlinear permeability tensors for longitudinal color oscillations are derived.

Third-order currents play a crucial role in turbulent QGP.

Numerical damping rates for zero wave vector modes are provided.

Abstract

With asymptotic method developed from weak turbulent theory, the kinetic equations for QGP are expanded in fluctuation field potential $A^T_\mu $. Considering the second-order and third-order currents, we derive the nonlinear permeability tensor function from Yang-Mills field equation, and find that the third-order current is more important in turbulent theory. The nonlinear permeability formulae for longitudinal color oscillations show that the non-Abelian effects are more important than the Abelian-like effects. To compare with other works, we give the numerical result of the damping rate for the modes with zero wave vector.