  We study a homogeneously driven granular gas of inelastic hard particles with
rough surfaces subject to Coulomb friction. The stationary state as well as the
full dynamic evolution of the translational and rotational granular
temperatures are investigated as a function of the three parameters of the
friction model. Four levels of approximation to the (velocity-dependent)
tangential restitution are introduced and used to calculate translational and
rotational temperatures in a mean field theory. When comparing these
theoretical results to numerical simulations of a randomly driven mono-layer of
particles subject to Coulomb friction, we find that already the simplest model
leads to qualitative agreement, but only the full Coulomb friction model is
able to reproduce/predict the simulation results quantitatively for all
magnitudes of friction. In addition, the theory predicts two relaxation times
for the decay to the stationary state. One of them corresponds to the
equilibration between the translational and rotational degrees of freedom. The
other one, which is slower in most cases, is the inverse of the common
relaxation rate of translational and rotational temperatures.
