Granular Brownian motion

TL;DR

This paper investigates the stochastic dynamics of an intruder in a driven granular gas, modeling it with a Langevin equation and analyzing the effects of external and granular baths on its motion.

Contribution

It introduces a Langevin equation framework for intruder dynamics in granular gases, including calculations of drag and diffusion coefficients validated by simulations.

Findings

Langevin equation accurately describes intruder motion

Drag and diffusion coefficients match numerical results

Finite packing and mass effects cause measurable corrections

Abstract

We study the stochastic motion of an intruder in a dilute driven granular gas. All particles are coupled to a thermostat, representing the external energy source, which is the sum of random forces and a viscous drag. The dynamics of the intruder, in the large mass limit, is well described by a linear Langevin equation, combining the effects of the external bath and of the "granular bath". The drag and diffusion coefficients are calculated under few assumptions, whose validity is well verified in numerical simulations. We also discuss the non-equilibrium properties of the intruder dynamics, as well as the corrections due to finite packing fraction or finite intruder mass.