Nondiffusive fluxes in a Brownian system with Lorentz force

I. Abdoli, H. D. Vuijk, J. U. Sommer, J. M. Brader, and A. Sharma
Phys. Rev. E 101, 012120 – Published 14 January 2020
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Abstract

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.

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  • Received 8 August 2019

DOI:https://doi.org/10.1103/PhysRevE.101.012120

©2020 American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & ThermodynamicsPolymers & Soft Matter

Authors & Affiliations

I. Abdoli1, H. D. Vuijk1, J. U. Sommer1,2, J. M. Brader3, and A. Sharma1,2,*

  • 1Leibniz-Institut für Polymerforschung Dresden, Institut Theorie der Polymere, 01069 Dresden, Germany
  • 2Technische Universität Dresden, Institut für Theoretische Physik, 01069 Dresden, Germany
  • 3Department de Physique, Université de Fribourg, CH-1700 Fribourg, Switzerland

  • *sharma@ipfdd.de

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Issue

Vol. 101, Iss. 1 — January 2020

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