Long-Time Tails and Cage Effect in Driven Granular Fluids

We study the velocity autocorrelation function of a driven granular fluid in the stationary state in three dimensions. As the critical volume fraction of the glass transition in the corresponding elastic system is approached, we observe pronounced cage effects in the velocity autocorrelation function as well as a strong decrease of the diffusion constant, depending on the inelasticity. At moderate densities the velocity autocorrelation function is shown to decay algebraically in time, like t(-3/2), if momentum is conserved locally, and like t(-1), if momentum is not conserved by the driving. A simple scaling argument supports the observed long-time tails.