# Nondiffusive Fluxes in Brownian System with Lorentz Force

## TL;DR

This paper investigates how Lorentz force-induced nondiffusive fluxes influence particle density evolution in Brownian systems within inhomogeneous magnetic fields, revealing conditions where these fluxes are significant or negligible.

## Contribution

It demonstrates that nondiffusive fluxes caused by Lorentz force have finite divergence in inhomogeneous magnetic fields, affecting density evolution, unlike in uniform fields.

## Key findings

- Nondiffusive fluxes have finite divergence in inhomogeneous magnetic fields.
- These fluxes influence the density evolution of particles.
- In uniform magnetic fields, fluxes can be ignored.

## Abstract

The Fokker-Planck equation provides 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, can not 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 symmetry as the magnetic field can these fluxes be ignored in the density evolution.