论文标题
非权威性自旋1/2费米的自旋玻尔兹曼方程
Spin Boltzmann equation for non-relativistic spin-1/2 fermions
论文作者
论文摘要
我们在具有四边形触点相互作用的非相关模型中得出了自旋1/2费米的自旋玻尔兹曼方程，该模型可以节省自旋的自由度。该模型的一个很大的优点是，可以完全纠正碰撞项中的自旋矩阵元素，并将其放入如此紧凑的形式中，以至于可以清楚地看到如何将旋转耦合在粒子散射中。已经制作了普朗克常数的半古典膨胀，并得出了旋转Boltzmann方程的壳部分，直到近代领先的顺序。在领先地位，可以从旋转密度的碰撞项的消失中获得平衡自旋分布。自旋化学势是自旋保存的自然结果。还讨论了旋转玻尔兹曼方程的脱壳部分。这项工作可以扩展到更复杂的相互作用，例如核力量，以便在低能量下重离子碰撞中应用自旋极化现象。
We derive the spin Boltzmann equations for spin-1/2 fermions in a non-relativistic model with four-fermion contact interaction which conserves spin degrees of freedom. A great advantage of the model is that the spin matrix elements in collision terms can be completely worked out and be put into such a compact form that one can clearly see how spins are coupled in particle scatterings. A semi-classical expansion in the Planck constant has been made and the on-shell part of the spin Boltzmann equation up to the next-to-leading order is derived. At the leading order the equilibrium spin distribution can be obtained from the vanishing of the collision term for the spin density. The spin chemical potential emerges as a natural consequence of spin conservation. The off-shell part of the spin Boltzmann equation is also discussed. The work can be extended to more sophisticated interaction such as nuclear force in order to apply to spin polarization phenomena in heavy-ion collisions at low energies.
