Brownian motion of a charged particle in a magnetic field

J. I, M. Romero-Bastida


In this work we show that Taylor's description of Brownian motion in a magnetic field is equivalent to the situation in which the constant magnetic field is allowed to point along any direction. This can be achieved by means of a rotation of the Langevin equation given in the space of coordinates $ r$, to another space of coordinates $ r^{\prime}$, where the description of the problem is quite similar to that studied by Taylor. We use the over-damping approximation to show why, at equilibrium, the oscillatory behavior inherent in the system is not reflected in the diffusion process across the magnetic field, a fact not studied by Taylor. We also use the large-time approximation to study the effects of colored noise (small correlation time) on the diffusion processes across and along the magnetic field.


(MSD) Mean Square Displacement

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Revista Mexicana de Física E

ISSN: 2683-2216 (on line), 1870-3542 (print)

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