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We investigate thermalization of gluons in spatially homogeneous systems using the Boltzmann equation in diffusion approximation. A complete picture on thermalization is obtained for both initially under- and over-populated systems. In an initially under-populated system, we find that its soft sector undergoes three stages: overheating, cooling/overcooling and reheating before full thermalization is achieved. In an initially over-populated system, we find that its soft sector only undergoes two stages towards full thermalization: overheating and cooling. The cooling stage is consistently driven by momentum broadening due to multiple elastic collisions, manifest as a non-thermal scaling solution.
Cabodevila et al. (Fri,) studied this question.