Pre-Equilibrium Evolution of Conserved Charges with ICCING Initial Conditions

Heavy-ion collisions can be well described through relativistic viscous hydrodynamics, but questions still remain when hydrodynamics is applicable because the initial state may begin very far-from-equilibrium. Thus, a pre-equilibrium evolution phase is used to bridge the gap between the initial state and hydrodynamics. K$\phi$MP$\phi$ST is one such pre-equilibrium model that propagates the energy-momentum tensor by decomposing it into the background and fluctuations around that background, whose evolution is captured by Green's functions. We extend this formalism to include conserved charges and calculate the corresponding non-equilibrium Green's functions in the relaxation time approximation. The ICCING algorithm initializes conserved charges in the initial state by sampling $g \rightarrow q\bar{q}$ splitting probabilities and is, thus, perfectly positioned to implement Green's functions for charge propagation. We show that this method alters the initial state charge geometries and is applicable in central to mid-central collisions.