Diffusion in a one-dimensional gas of hard point particles

We simulate the classical diffusion of a particle of massM in an infinite one-dimensional system of hard point particles of massm in equilibrium. Each computer run corresponds to about 10⁸ collisions of the diffusive particle. We find that (t) 1/t fort large enough, and a crossover from an M m regime where=2 to=3 forM=m. The diffusion constant has a sharp maximum atM=m. We study moments x(t)² and x(t)⁴, and examine the behavior ofq²(t)=x(t)⁴/3x(t)²². We find thatq(t)1 (consistent with a normal distribution) in theM limit (for all timest) and in the t limit for allM.On sabbatical leave from IVIC-Instituto Venezolano de Investigaciones Cientificas.