Chromoelectric oscillations in a dynamically evolving anisotropic background

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 which 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 integrodifferential evolution equation for the chromoelectric field. We present numerical solutions to this integrodifferential 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 nontrivial time-dependent momentum-space anisotropic background and the effect of collisional damping for the first time.