Chromoelectric oscillations in a dynamically evolving anisotropic background

TL;DR

This paper investigates chromoelectric field oscillations within a dynamically evolving anisotropic plasma background, deriving novel equations that incorporate time-dependent anisotropy and collisional damping, and providing numerical solutions under various conditions.

Contribution

It introduces a new set of dynamical equations for chromoelectric oscillations in anisotropic backgrounds, including collisional damping effects and time-dependent anisotropy, with numerical analysis.

Findings

Equations include time-dependent anisotropy and damping effects.

Numerical solutions show behavior under different initial conditions.

Reproduces viscous hydrodynamics in specific limits.

Abstract

We study the oscillations of a uniform longitudinal chromoelectric field in a dynamically-evolving momentum-space anisotropic background in the weak field limit. Evolution equations for the background are derived by taking moments of the Boltzmann equation in two cases: (i) a fixed relaxation time and (ii) a relaxation time that is proportional to the local inverse transverse momentum scale of the plasma. The second case allows us to reproduce 2nd-order viscous hydrodynamical dynamics in the limit of small shear viscosity to entropy ratio. We then linearize the Boltzmann-Vlasov equation in a dynamically-evolving background and obtain an integro-differential evolution equation for the chromoelectric field. We present numerical solutions to this integro-differential equation for a variety of different initial conditions and shear viscosity to entropy density ratios. The dynamical equations obtained are novel in that they include a non-trivial time-dependent momentum-space anisotropic background and the effect of collisional damping for the first time.