On high-energy tails in inelastic gases

We study the formation of high-energy tails in a one-dimensional kinetic model for granular gases, the so-called Inelastic Maxwell Model. We introduce a time-discretized version of the stochastic process, and show that continuous time implies larger fluctuations of the particles energies. This is due to a statistical relation between the number of inelastic collisions undergone by a particle and its average energy. This feature is responsible for the high-energy tails in the model, as shown by computer simulations and by analytical calculations on a linear Lorentz model.