Periodically driven Brownian motion with dry friction and ultrarelativistic Langevin equations

Abstract

We study the periodically driven Brownian motion of a massive particle in one dimension subject to dry (Coulombic) friction. Analytical results are obtained by noticing that the particle velocity obeys the same Langevin equation as the spatial coordinate of an overdamped particle bound to a wedge potential, also in one dimension. The response to an external sinusoidal drive is calculated in linear response theory approximation. The analytical results thus obtained closely compare with the outcome of extensive numerical simulations. Finally we show how this model of Brownian motion can be utilized to characterize the diffusion of ultrarelativistic Brownian particles in the plane, a mechanism recently proposed to model diffusive transport of charge carriers in a graphene sheet.