Shear viscosity of classical fields in scalar theory

Hidefumi Matsuda, Teiji Kunihiro, Akira Ohnishi, Toru T. Takahashi

Published 2019-04-04Version 1

We investigate the shear viscosity of classical scalar fields in the $\phi^4$ theory on a lattice by using the Green-Kubo formula. Equilibrium expectation value of the time correlation function of the energy-momentum tensor is evaluated as the ensemble average of the classical field configurations, whose time evolution is obtained by solving the classical equation of motion starting from the initial condition in thermal equilibrium. It is found that there are two distinct damping time scales in the time correlation function, which is found to show damped oscillation behavior in the early stage around a slow monotonous decay with an exponential form, and the slow decay part is found to dominate the shear viscosity. This kind of slow decay is also known to exist in the molecular dynamics simulation, then it may be a generic feature of dense matter. The obtained shear viscosity is smaller than the perturbative estimate in the quantum theory which may well describe the hard sector, and suggests a strong coupling feature of the classical field theory which in turn may well describe the infrared dynamics of the whole quantum theory.