Friction and diffusion of a Brownian particle in a mesoscopic solvent

The friction and diffusion coefficients of a massive Brownian particle in a mesoscopic solvent are computed from the force and the velocity autocorrelation functions. The mesoscopic solvent is described in terms of free streaming of the solvent molecules, interrupted at discrete time intervals by multiparticle collisions that conserve mass, momentum, and energy. The Brownian particle interacts with the solvent molecules through repulsive Lennard-Jones forces. The decays of the force and velocity autocorrelation functions are analyzed in the microcanonical ensemble as a function of the number N of solvent molecules and Brownian particle mass and diameter. The simulations are carried out for large system sizes and long times to assess the N dependence of the friction coefficient. The decay rates of these correlations are confirmed to vary as N(-1) in accord with earlier predictions. Hydrodynamic effects on the velocity autocorrelation function and diffusion coefficient are studied as a function of Brownian particle mass and diameter.