We investigate the shear viscosity of massless classical scalar fields in the |$\phi^4$| theory on a lattice by using the Green–Kubo formula. Based on the scaling property of the classical field, the shear viscosity is represented using a scaling function. The 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 monotonic decay with an exponential form, and the slow decay part is found to dominate the shear viscosity in the massless classical field theory. This kind of slow decay is also known to exist in molecular dynamics simulations, so it may be a generic feature of dense matter.

中文翻译：

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标量理论中无质量经典场的剪切粘度

我们研究| $ \ phi ^ 4 $ |中无质量经典标量场的剪切粘度。通过使用Green-Kubo公式对晶格进行理论计算。基于经典字段的缩放属性，使用缩放函数表示剪切粘度。能量动量张量的时间相关函数的平衡期望值被评估为经典场配置的整体平均值，其时间演化是通过从热平衡的初始条件开始求解经典运动方程而获得的。发现在时间相关函数中有两个截然不同的阻尼时间尺度，发现它们在具有指数形式的缓慢单调衰变的早期显示出阻尼振荡行为，并且发现缓慢衰变部分占主导地位。无质量经典场论中的剪切粘度。