A Wigner Quasi-distribution Function for Charged Particles in Classical Electromagnetic Fields
A Wigner Quasi-distribution Function for Charged Particles in Classical Electromagnetic Fields
复制标题
经典电磁场中带电粒子的维格纳准分布函数
DOI：
10.1006/aphy.2001.6170
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发表时间：
2001
影响因子：
3
通讯作者：
V. Fleurov
中科院分区：
文献类型：
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作者：
M. Levanda;V. Fleurov
摘要严格推导了经典电磁场中带电粒子的标准不变Wigner准分布函数。讨论了它与轴向规的关系，以及维格纳表示中动能和正则动量的关系。对于任意的经典电磁场，根据“削减”导数和动量，给出了Hamilton-Jacobi和Boltzmann动力学方程的标准不变量子类比。讨论了这些削减量的动力学意义。我们引入了标准不变条件矩，并利用它们导出了一个动量连续性方程。这个方程为我们提供了量子输运过程的流体动力学表示和“碰撞力”的定义。对电子运动的旋转部分应用了流体动力学方程。通过三个实例说明了该理论的应用：磁场中电子的Wigner准分布函数和方程及谐波势；用kq表示周期系统中带电粒子的Wigner拟分布函数电场中重质量极化子的两个Wigner准分布函数。
Abstract A gauge-invariant Wigner quasi-distribution function for charged particles in classical electromagnetic fields is derived in a rigorous way. Its relation to the axial gauge is discussed, as well as the relation between the kinetic and canonical momenta in the Wigner representation. Gauge-invariant quantum analogs of Hamilton–Jacobi and Boltzmann kinetic equations are formulated for arbitrary classical electromagnetic fields in terms of the “slashed” derivatives and momenta, introduced for this purpose. The kinetic meaning of these slashed quantities is discussed. We introduce gauge-invariant conditional moments and use them to derive a kinetic momentum continuity equation. This equation provides us with a hydrodynamic representation for quantum transport processes and a definition of the “collision force.” The hydrodynamic equation is applied for the rotation part of the electron motion. The theory is illustrated by its application in three examples: Wigner quasi-distribution function and equations for an electron in a magnetic field and harmonic potential; Wigner quasi-distribution function for a charged particle in periodic systems using the kq representation; two Wigner quasi-distribution functions for heavy-mass polaron in an electric field.
S. Matsubara：“4. 体内典型和非典型抗精神病药物对多巴胺 D-1、D-2 和血清素 2 受体的占用。”
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