The Fokker-Planck equation provides a complete statistical description of a particle undergoing random motion in a solvent. In the presence of Lorentz force due to an external magnetic field, the Fokker-Planck equation picks up a tensorial coefficient, which reflects the anisotropy of the particle's motion. This tensor, however, cannot be interpreted as a diffusion tensor; there are antisymmetric terms which give rise to fluxes perpendicular to the density gradients. Here, we show that for an inhomogeneous magnetic field these nondiffusive fluxes have finite divergence and therefore affect the density evolution of the system. Only in the special cases of a uniform magnetic field or carefully chosen initial condition with the same full rotational symmetry as the magnetic field can these fluxes be ignored in the density evolution.

中文翻译：

---

具有洛伦兹力的布朗系统中的非扩散通量。

福克-普朗克方程式提供了在溶剂中经历随机运动的粒子的完整统计描述。在由于外部磁场而产生洛伦兹力的情况下，Fokker-Planck方程将获得一个张量系数，该张量系数反映了粒子运动的各向异性。但是，该张量不能解释为扩散张量。有反对称项会引起垂直于密度梯度的通量。在这里，我们表明，对于非均匀磁场，这些非扩散磁通具有有限的发散度，因此会影响系统的密度演化。只有在均匀磁场或经过精心选择的初始条件（具有与磁场相同的完全旋转对称性）的特殊情况下，这些磁通量才能在密度演化过程中被忽略。