自旋运动论-扩展相空间中的量子运动论
Spin kinetic theory - quantum kinetic theory in extended phase space
摘要：
在相空间扩大的情况下，引入了相空间分布函数及其演化的概念。特别是，我们包括粒子的内禀自旋，并提出了一个标量准分布函数的量子动力学演化方程。在适当的维格纳变换技术，我们希望相应的准分布函数是一个复杂的矩阵，我们引入了一个自旋投影算子的密度矩阵，以获得上述标量准分布函数。这个投影算子和量子光学中广泛使用的胡西米（或Q）函数之间有着密切的对应关系。这样的函数是基于魏格纳函数的高斯拖尾，给出正定分布函数。因此，我们的方法给出了一个Wigner-Husimi准分布函数在扩展相空间中，其中约化分布函数的布洛赫球是严格正的。我们还讨论了规范问题和基于这样的量子动力学理论的流体矩的层次。
英文摘要：
The concept of phase space distribution functions and their evolution is used in the case of en enlarged phase space. In particular, we include the intrinsic spin of particles and present a quantum kinetic evolution equation for a scalar quasi-distribution function. In contrast to the proper Wigner transformation technique, for which we expect the corresponding quasi-distribution function to be a complex matrix, we introduce a spin projection operator for the density matrix in order to obtain the aforementioned scalar quasi-distribution function. There is a close correspondence between this projection operator and the Husimi (or Q) function used extensively in quantum optics. Such a function is based on a Gaussian smearing of a Wigner function, giving a positive definite distribution function. Thus, our approach gives a Wigner-Husimi quasi-distribution function in extended phase space, for which the reduced distribution function on the Bloch sphere is strictly positive. We also discuss the gauge issue and the fluid moment hierarchy based on such a quantum kinetic theory.
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