Granular Brownian motion

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 a 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.