基于Chapman-Enskog展开的相对论一阶自旋流体力学
Relativistic first-order spin hydrodynamics via the Chapman-Enskog expansion
摘要：
本文利用Chapman-Enskog方法对\cite{Weickgenannt:2021cuo}中提出的大质量费米子非定域碰撞项进行线性化处理，详细推导了相对论一阶自旋流体动力学方程，该方程较好地描述了碰撞过程中的自旋轨道耦合，对局域自旋极化的研究具有重要意义.基于这个碰撞项，我们对一阶自旋流体力学进行了形式化的讨论，确定了流体变量的运动方程以及对能量动量和自旋张量的非平衡修正。结果表明，在一阶理论下，运动方程与无自旋一阶流体力学没有差别，能量动量张量不受自旋的修正，需要建立自然地考虑自旋-轨道耦合效应的二阶流体理论.
英文摘要：
In this paper, we present a detailed derivation of relativistic first-order spin hydrodynamics using the Chapman-Enskog method to linearize the nonlocal collision term for massive fermions proposed in \cite{Weickgenannt:2021cuo}, which well describes spin-orbit coupling in the collision process and is relevant for the research on local spin polarization. Based on this collisional term, we provide a formal discussion about first-order spin hydrodynamics and determine the motion equations of fluid variables and nonequilibrium corrections to the energy-momentum and spin tensors. The results indicate that the motion equations show no differences compared to spinless first-order hydrodynamics and the energy-momentum tensor receives no corrections from spin as far as first-order theory is concerned, which calls for the construction of second-order theory of fluids naturally incorporating the effect of spin-orbit coupling.
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