Solution to a generalized Langevin equation for a charged particle subject to exponentially correlated noise in an AC field

Abstract

The Brownian motion of a charged particle under a sinusoidal electric field is modeled using a generalized Langevin equation. The dissipation effects are expressed in a memory kernel whose exponential decay correlation function is made proportional to the autocorrelation function of the colored stochastic noise, in accordance with the fluctuationdissipation theorem. We calculate the ensemble dynamics and variance in velocity and position exactly and plot the results for several physical regimes. The formulation of the ensemble dynamics in terms of the memory kernel is shown equivalent to a differential equation describing a jerk system.