论文标题
古典杨米尔斯田地的剪切粘度
Shear viscosity of classical Yang-Mills field
论文作者
论文摘要
我们通过使用绿色kubo公式研究了晶格上经典阳米尔（CYM）字段的剪切粘度$η$，在该公式中，剪切粘度是根据平衡中能量摩托张量的时间相关函数计算得出的。剪切粘度$η（g，t）$的依赖性在耦合$ g $和温度$ t $上由缩放函数$f_η（g^2t）$表示为$η（g，t）=tf_η（g^2t）$，这是由于cym的缩放属性属性。 The explicit functional form of $f_η(g^2T)$ is successfully determined from the calculated shear viscosity: It turns out that $η(g,T)$ of the CYM field is proportional to $1/g^{1.10-1.88}$ at weak coupling, which is a weaker dependence on $g$ than that in the leading-order perturbation theory but consistent with that of the "anomalous viscosity" $η\ propto 1/g^{1.5} $在强大的领域下。还发现，获得的剪切粘度与通过分析在扩展的几何形状中使用流体动力方程式在扩展几何形状中的压力的各向异性分析而大致一致。
We investigate the shear viscosity $η$ of the classical Yang-Mills (CYM) field on a lattice by using the Green-Kubo formula, where the shear viscosity is calculated from the time-correlation function of the energy-momentum tensor in equilibrium. Dependence of the shear viscosity $η(g,T)$ on the coupling $g$ and temperature $T$ is represented by a scaling function $f_η(g^2T)$ as $η(g,T)=Tf_η(g^2T)$ due to the scaling-invariant property of the CYM. The explicit functional form of $f_η(g^2T)$ is successfully determined from the calculated shear viscosity: It turns out that $η(g,T)$ of the CYM field is proportional to $1/g^{1.10-1.88}$ at weak coupling, which is a weaker dependence on $g$ than that in the leading-order perturbation theory but consistent with that of the "anomalous viscosity" $η\propto 1/g^{1.5}$ under the strong disordered field. The obtained shear viscosity is also found to be roughly consistent with that estimated through the analysis of the anisotropy of the pressure of the CYM dynamics in the expanding geometry with recourse to a hydrodynamic equation.
