Brownian motion of a charged particle in a magnetic field

Abstract

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.