Long-time tails in freely cooling granular gases

Abstract

The long-time behavior of the current auto-correlation functions for the velocity, the shear stress and the heat flux is investigated in freely cooling granular gases. It is found that the correlation functions for the velocity and the shear stress have the long-time tails obeying $\tau^{-d/2}$, while the correlation function of heat flux decays as $\tau^{-(d+2)/2} \exp(-\zeta^* \tau)$ with the dimensionless cooling rate $\zeta^*$, the spatial dimension $d$ and the scaled time $\tau$ in terms of the collision frequency. The result of our numerical simulation of the freely cooling granular gases is consistent with the theoretical prediction.