Numerical evidence for the low-mass behavior of the one-dimensional Rayleigh gas with local interaction

Numerical investigations and partial rigorous results suggest that the motion of a tagged particle of mass M on the line R colliding with a free gas of particles of mass m in equilibrium is diffusive. It was conjectured that the diffusion constant D(M), for small mass MQ 0, should approach D(m). (In dimension 1 this is a kind of ‘‘continuity hypothesis.’’) Previous results of computer simulations are inconclusive. We report on some new computer results, which show clearly that there is no continuity, and the limit of D(M) as M tends to 0 is smaller than D(m). We compare with the corresponding results for a similar two-dimensional model, to which the ‘‘continuity argument’’ cannot be applied.