Diffusion in a one-dimensional gas of hard point particles

Abstract

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 〈νν(t)〉 ∼ 1/t δ fort large enough, and a crossover from an M ≠ m regime whereδ=2 toδ=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 ofq 2 (t)=〈x(t)4〉/3〈x(t)2〉2. We find thatq(t)→1 (consistent with a normal distribution) in theM →∞ limit (for all timest) and in the t→∞ limit for allM.