Generating random thermal momenta

Abstract: Generation of random thermal particle momenta is a basic task in many problems, such as microscopic studies of equilibrium and transport properties of systems, or the conversion of a fluid to particles. In heavy-ion physics, the (in)efficiency of the algorithm matters particularly in hybrid hydrodynamics + hadronic transport calculations. With popular software packages, such as UrQMD 3.3p1 or THERMINATOR, it can still take ten hours to generate particles for a single Pb+Pb "event" at the LHC from fluid dynamics output. Below I describe reasonably efficient simple algorithms using the MPC package, which should help speed momentum generation up by at least one order of magnitude. It is likely that this wheel has been reinvented many times instead of reuse, so there may very well exist older and/or better algorithms that I am not aware of (MPC has been around only since 2000). The main goal here is to encourage practitioners to use available efficient routines, and offer a few practical solutions.