Tracer's Diffusion: Swimming Through the Grains

In this chapter I consider the stochastic dynamics of an intruder in a granular fluid. Under the same assumptions used to derive the Boltzmann equation, a Master Equation for the intruder's velocity is derived. In the limit of large intruder's mass, the dynamics is described by an Ornstein-Uhlenbeck process. I discuss the effects of collisions' inelasticity and of non-Gaussian properties of the surrounding gas. When the shape of the intruder breaks some spatial symmetry, part of the energy dissipated in collisions can be converted in useful work. A granular Brownian motor is then realized.