Thermalization and viscosity of classical fields

Thermalization time in high-energy heavy-ion collisions is found to be unexpectedly short. Since the systems can be approximately described by the classical Yang-Mills (CYM) fields that are called ”glasma” in the early stages of relativistic heavy ion collisions, classical fields should play important roles to realize early thermalization. Actually, glasma instabilities and chaoticity have been found to promote rapid pressure isotropization and entropy production [1]. Thus it is valuable to study the relaxation of the classical fields around the equilibrium.
In this study, we investigate the viscosity of classical scalar fields [2] by using the Green-Kubo formula. From the correlation function of the energy-momentum tensor in the classical statistical approach, we obtain the shear viscosity using the Green-Kubo formula. We also plan to discuss entropy production of classical fields.

[1] P. Romatschke and R. Venugopalan, Phys. Rev. D 74, 045011 (2006); T. Epelbaum and F. Gelis, Phys. Rev. Lett. 111, 232301 (2013); H. Tsukiji, T. Kunihiro, A. Ohnishi, and T. T. Takahashi, PTEP 2018, 013D02 (2018).
[2] M. M. Homor and A. Jakovac, Phys. Rev D 92, 105011 (2015).