Correlation in the velocity of a Brownian particle induced by frictional anisotropy and magnetic field

TL;DR

This paper investigates how anisotropic friction and magnetic fields induce velocity correlations in charged Brownian particles, revealing non-trivial relaxation behaviors depending on magnetic field strength.

Contribution

It introduces the analysis of velocity correlations caused by combined effects of magnetic fields and anisotropic friction in Brownian motion, highlighting new dynamical phenomena.

Findings

Velocity correlation appears due to anisotropic friction and magnetic field.

Correlation relaxation is non-oscillating at low magnetic fields.

Relaxation becomes oscillating at higher magnetic fields.

Abstract

We study the motion of charged Brownian particles in an external magnetic field. It is found that a correlation appears between the components of particle velocity in the case of anisotropic friction, approaching asymptotically zero in the stationary limit. If magnetic field is smaller compared to the critical value, determined by frictional anisotropy, the relaxation of the correlation is non-oscillating in time. However, in a larger magnetic field this relaxation becomes oscillating. The phenomenon is related to the statistical dependence of the components of transformed random force caused by the simultaneous influence of magnetic field and anisotropic dissipation.