Validation and improvement of the ZPC parton cascade inside a box

Abstract

Cascade solutions of the Boltzmann equation suffer from causality violation at large densities and/or scattering cross sections. Although the particle subdivision technique can reduce the causality violation, it alters event-by-event correlations and fluctuations and is also computationally expensive. Here we evaluate and then improve the accuracy of the ZPC parton cascade for elastic scatterings inside a box without using parton subdivision. We first test different collision schemes for the collision times and ordering time and find that the default collision scheme does not accurately describe the equilibrium momentum distribution at large opacities. We then find a specific collision scheme that can describe very accurately the equilibrium momentum distribution as well as the time evolution towards equilibrium, even at large opacities. We also calculate the shear viscosity and the $\eta/s$ ratio of the parton systems and confirm that the new collision scheme is more accurate. In addition, we use a novel parton subdivision method to obtain the "exact" evolution of the system. This subdivision method is valid for such box calculations and is so much more efficient than the standard subdivision method that we use a subdivision factor of $10^6$ in this study.