The exact nonlinear driven response of a one-dimensional gas

The exact nonlinear driven response of a one-dimensional gas of hard rods to a time dependent uniform external field is obtained in terms of the single particle Green's function. Limiting cases of very large and very small field are examined and, for the latter, comparison is made between the linear approximation to the exact response and the response obtained from the linear response theory perturbation approximation. Strong disagreement between these results is observed. This supports van Kampen's contention that a macroscopic linear response to an external perturbation is not a manifestation of microscopic linearity.