AMY Lorentz invariant parton cascade: the thermal equilibrium case

We introduce the parton cascade Alpaca, which evolves parton ensembles corresponding to single events according to the effective kinetic theory of QCD at high temperature formulated by Arnold, Moore and Yaffe by explicitly simulating elastic scattering, splitting and merging. By taking the ensemble average over many events the phase space density (as evolved by the Boltzmann equation) is recovered, but the parton cascade can go beyond the evolution of the mean because it can be turned into a complete event generator that produces fully exclusive final states including fluctuations and correlations. The parton cascade does not require the phase space density as input (except for the initial condition at the starting time). Rather, effective masses and temperature, which are functions of time and are defined as integrals over expressions involving the distribution function, are estimated in each event from just the parton ensemble of that event. We validate the framework by showing that ensembles sampled from a thermal distribution stay in thermal equilibrium even after running the simulation for a long time. This is a non-trivial result, because it requires all parts of the simulation to intertwine correctly.