We derive Kubo formulae for first-order spin hydrodynamics based on nonequilibrium statistical operators method. In first-order spin hydrodynamics, there are two new transport coefficients besides the ordinary ones appearing in first-order viscous hydrodynamics. They emerge due to the incorporation of the spin degree of freedom into fluids and the spin-orbital coupling. Zubarev’s nonequilibrium statistical operator method can be well applied to investigate these quantum effects in fluids. The Kubo formulae, based on the method of nonequilibrium statistical operators, are related to equilibrium (imaginary-time) infrared Green’s functions, and all the transport coefficients can be determined when the microscopic theory is specified.

中文翻译：

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一阶自旋流体力学的 Kubo 公式

我们基于非平衡统计算子方法推导出一阶自旋流体动力学的 Kubo 公式。在一阶自旋流体力学中，除了一阶粘性流体力学中出现的普通输运系数之外，还有两个新的输运系数。它们的出现是由于将自旋自由度纳入流体和自旋轨道耦合。Zubarev 的非平衡统计算符方法可以很好地应用于研究流体中的这些量子效应。Kubo公式基于非平衡统计算子的方法，与平衡（虚时间）红外格林函数相关，当指定微观理论时，所有输运系数都可以确定。