Boltzmann approximation of transport properties in thermal lattice gases

The transport properties of the Grosfils, Boon, and Lallemand model, a two-dimensional isotropic thermal lattice-gas, are evaluated in the Boltzmann approximation. This includes the (self)-diffusion, for which we have introduced an additional and passive color label to the otherwise identical particles in the system. Independently, those results are confirmed by the use of the decay of the velocity autocorrelation function. The theoretical predictions of the dynamical structure factors and results obtained by simulations show an excellent agreement up to fairly large wave vectors. In the hydrodynamic limit of small wave vectors, the Landau-Placzek formulas form an alternative and satisfactory description.