Weickgenannt Nora, Speranza Enrico, Sheng Xin-Li, Wang Qun, Rischke Dirk H
Institute for Theoretical Physics, Goethe University, Max-von-Laue-Straße 1, D-60438 Frankfurt am Main, Germany.
Peng Huanwu Center for Fundamental Theory and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China.
Phys Rev Lett. 2021 Jul 30;127(5):052301. doi: 10.1103/PhysRevLett.127.052301.
We derive the collision term in the Boltzmann equation using the equation of motion for the Wigner function of massive spin-1/2 particles. To next-to-lowest order in ℏ, it contains a nonlocal contribution, which is responsible for the conversion of orbital into spin angular momentum. In a proper choice of pseudogauge, the antisymmetric part of the energy-momentum tensor arises solely from this nonlocal contribution. We show that the collision term vanishes in global equilibrium and that the spin potential is, then, equal to the thermal vorticity. In the nonrelativistic limit, the equations of motion for the energy-momentum and spin tensors reduce to the well-known form for hydrodynamics for micropolar fluids.
我们使用大质量自旋1/2粒子的维格纳函数的运动方程来推导玻尔兹曼方程中的碰撞项。在ħ的次低阶近似下，它包含一个非局域贡献，该贡献负责轨道角动量向自旋角动量的转换。在适当选择的赝规范中，能量 - 动量张量的反对称部分仅源于此非局域贡献。我们表明碰撞项在全局平衡中消失，并且此时自旋势等于热涡度。在非相对论极限下，能量 - 动量张量和自旋张量的运动方程简化为微极流体动力学的熟知形式。
