Molecular dynamics of a classical lattice gas: Transport properties and time correlation functions

A study of the dynamics of a discrete two-dimensional system of classical particles is presented. In this model, dynamics and computations may be done exactly, by definition. The equilibrium state is investigated and the Navier-Stokes hydrodynamical equations are derived. Two hydrodynamical modes exist in the model: the sound waves and a kind of vorticity diffusion. In the Navier-Stokes equations one obtains a transport coefficient which is given by a Green-Kubo formula. The related time correlation function has been calculated in a numerical simulation up to a time of the order of 50 mean free flights. After a short time of exponential decay this time correlation behaves like $t^{-S}$, the exponent being compared to theoretical predictions.