Direct measurement of correlation functions in a lattice Lorentz gas

Simulations of a two-dimensional ballistic Lorentz gas on a lattice are reported. A moment-propagation technique allows direct measurements of the velocity correlation function and its moments with low relative errors for all times. The predicted 1/t-sq algebraic tails in the velocity correlation function are observed at all studied scatterer densities, unlike what has been reported for continuous systems. In the square lattice a fast oscillation is observed, consistent with the existence of staggered density modes. For the second-rank tensor correlation function, an extremely slow approach to the expected 1/t exp 3 tail is found.