Truncated Lévy distributions in an inelastic gas

We study a one-dimensional model for granular gases, the so-called inelastic Maxwell model. We show theoretically the existence of stationary solutions of the unforced case, that are characterized by an infinite average energy per particle. Moreover, we verify the quasi-stationarity of these states by performing numerical simulations with a finite number of particles, thereby highlighting truncated Lévy distributions for the velocities.