Direct measurement of correlation functions in a lattice Lorentz gas

We report simulations of a two-dimensional ballistic Lorentz gas on a lattice. A moment-propagation technique allows direct measurements of the velocity correlation function and its moments with low relative errors for all times. We observe the predicted ${\mathit{t}}^{\mathrm{-}2}$ algebraic tails in the velocity correlation function at all studied scatterer densities, unlike what has been reported for continuous systems. In the square lattice a fast [(-1${)}^{\mathit{t}}$] oscillation is observed, consistent with the existence of staggered density modes. For the second-rank tensor correlation function we find an extremely slow approach to the expected ${\mathit{t}}^{\mathrm{-}3}$ tail.