Abdoli I, Vuijk H D, Sommer J U, Brader J M, Sharma A
Leibniz-Institut für Polymerforschung Dresden, Institut Theorie der Polymere, 01069 Dresden, Germany.
Technische Universität Dresden, Institut für Theoretische Physik, 01069 Dresden, Germany.
Phys Rev E. 2020 Jan;101(1-1):012120. doi: 10.1103/PhysRevE.101.012120.
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.
福克 - 普朗克方程提供了对在溶剂中做随机运动的粒子的完整统计描述。在存在外部磁场产生的洛伦兹力的情况下，福克 - 普朗克方程会出现一个张量系数，它反映了粒子运动的各向异性。然而，这个张量不能被解释为扩散张量；存在反对称项，会产生垂直于密度梯度的通量。在此，我们表明对于非均匀磁场，这些非扩散通量具有有限散度，因此会影响系统的密度演化。只有在均匀磁场的特殊情况或具有与磁场相同的完全旋转对称性的精心选择的初始条件下，这些通量在密度演化中才可以被忽略。
