论文标题
在非共同相空间中的三维Pauli方程式上
On the Three-Dimensional Pauli Equation in Noncommutative Phase-Space
论文作者
论文摘要
在本文中，我们在非共同相位空间中存在电磁场的情况下获得了三维Pauli方程，以及相应的变形连续性方程，其中考虑了恒定和非恒定磁场的情况。由于在预期的变形连续性方程中没有当前的磁化项，因此我们必须从非交换性Pauli方程本身中提取它，而不修改连续性方程。结果表明，非恒定磁场在Pauli方程和相应的连续性方程中都提高了非征性参数的顺序。但是，我们成功地研究了非销量对电流密度和磁化电流的影响。通过使用经典处理，我们得出了单粒子和N粒子系统的三维Pauli系统的半古典非交通分区功能。然后，我们使用它来计算相应的Helmholtz自由能，然后在交换性和非交通性相位空间中进行磁化和电子的磁敏感性。知道，通过三维BOPP转换转换和Moyal-Weyl产品，我们在所讨论的问题中介绍了相位空间非交通性。
In this paper, we obtained the three-dimensional Pauli equation for a spin-1/2 particle in the presence of an electromagnetic field in noncommutative phase-space, as well the corresponding deformed continuity equation, where the cases of a constant and non-constant magnetic field are considered. Due to the absence of the current magnetization term in the deformed continuity equation as expected, we had to extract it from the noncommutative Pauli equation itself without modifying the continuity equation. It is shown that the non-constant magnetic field lifts the order of the noncommutativity parameter in both the Pauli equation and the corresponding continuity equation. However, we successfully examined the effect of the noncommutativity on the current density and the magnetization current. By using a classical treatment, we derived the semi-classical noncommutative partition function of the three-dimensional Pauli system of the one-particle and N-particle systems. Then, we employed it for calculating the corresponding Helmholtz free energy followed by the magnetization and the magnetic susceptibility of electrons in both commutative and noncommutative phase-spaces. Knowing that with both the three-dimensional Bopp-Shift transformation and the Moyal-Weyl product, we introduced the phase-space noncommutativity in the problems in question.
