Correlated motion of two particles in a dense fluid of hard rods

An exact equation describing the stochastic motion of a droplet of neighbouring equal mass hard points with velocities ±c, immerzed in a hard point fluid, is derived. The derivation generalizes Resiboisʹ idea originally applied to the study of self-diffusion. The explicit solution for a two-particle droplet is obtained, showing a rapid relaxation of the interparticle distance to the Poisson distribution, superposed on a slow diffusive motion of the centre of mass of the two particles. An approximate description of the dynamics of N-particle droplets (N> 2) is proposed.