Energy Transport in a One-Dimensional Granular Gas

We study heat conduction in one-dimensional granular gases. In particular, we consider two mechanisms of viscous dissipation during inter-grain collisions. In one, the dissipative force is proportional to the grain's velocity and dissipates not only energy but also momentum. In the other, the dissipative force is proportional to the relative velocity of the grains and therefore conserves momentum even while dissipating energy. This allows us to explore the role of momentum conservation in the heat conduction properties of this one-dimensional nonlinear system. We find normal thermal conduction whether or not momentum is conserved.