DIFFUSION AND CORRELATIONS IN LATTICE-GAS AUTOMATA

We present an analysis of diffusion in terms of the spontaneous densit y fluctuations in a nonthermal two-species fluid modeled by a lattice- gas automaton. The power spectrum of the density-correlation function is computed with statistical-mechanical methods, analytically in the h ydrodynamic limit, and numerically from a Boltzmann expression for sho rter time and space scales. In particular, we define an observable-the weighted difference of the species densities-whose fluctuation correl ations yield the diffusive mode independently of the other modes, so t hat the corresponding power spectrum provides a measure of diffusion d ynamics solely. Automaton simulations are performed to obtain measurem ents of the spectral density over the complete range of wavelengths (f rom the microscopic scale to the macroscopic scale of the automaton un iverse). Comparison of the theoretical results with the numerical expe riments data yields the following results: (i) the spectral functions of the lattice-gas fluctuations are in accordance with those of a clas sical ''nonthermal'' fluid; (ii) the Landau-Placzek theory, obtained a s the hydrodynamic limit of the Boltzmann theory, describes the spectr a correctly in the long wavelength limit; and (iii) at shorter wavelen gths and at moderate densities the complete Boltzmann theory provides good agreement with the simulation data. These results offer convincin g validation of lattice-gas automata as a microscopic approach to diff usion phenomena in fluid systems.