Dynamical perturbation for classical fluids: A solvable model

We investigate on a one-dimensional model the perturbation to the timedependent correlations in a classical fluid when a small interaction is added to a hard core. Various formulas have already been proposed for this correction. We verify on this model, for which everything can be calculated explicitly, that the expressions proposed by Frisch and Berne yield strongly divergent time integrals for the diffusion coefficient. On the contrary, when all corrections are accounted for, the correction to the velocity time correlation is shown to decay like (Int)/t ₂ at large times, yielding a finite first-order correction to the diffusion coefficient. The extension of this calculation to a gas of hard rods in the case of a perturbation with an infinite range is discussed.