Brownian motion of a charged particle driven internally by correlated noise

TL;DR

This paper provides an exact solution for the motion of a charged Brownian particle under correlated noise and magnetic field, revealing transient oscillations and how diffusion is affected by system parameters.

Contribution

It offers a novel exact solution to the generalized Langevin equation with correlated noise and magnetic field, extending previous models to include finite autocorrelation times.

Findings

Transient oscillations in velocity fluctuations due to memory effects

Generalized diffusion coefficients depend on magnetic field and correlation time

Asymptotic results apply to Gaussian stochastic forces with finite autocorrelation

Abstract

We give an exact solution to the generalized Langevin equation of motion of a charged Brownian particle in a uniform magnetic field that is driven internally by an exponentially-correlated stochastic force. A strong dissipation regime is described in which the ensemble-averaged fluctuations of the velocity exhibit transient oscillations that arise from memory effects. Also, we calculate generalized diffusion coefficients describing the transport of these particles and briefly discuss how they are affected by the magnetic field strength and correlation time. Our asymptotic results are extended to the general case of internal driving by correlated Gaussian stochastic forces with finite autocorrelation times.