Transport in the Frenkel-Kontorova model. II. The diffusion coefficient

For pt.I see ibid., vol.18, p.4885 (1985). The authors apply the formulae presented in the previous paper of this series to calculate the bulk diffusion coefficient D of the undamped Frenkel-Kontorova model, using molecular dynamics simulation. The calculations are for a single value of the coupling constant, but for a wide range of temperatures and winding number densities. They investigate three methods of determining D, which involve calculating: (i) the equilibrium autocorrelation function of particle flux; (ii) the steady-state response of this flux to an external force; (iii) the single-particle mean square displacement. They show that all three methods provide strong evidence for the existence of D, which has been questioned by previous workers, and that they give numerical results which are in satisfactory agreement with one another. The diffusion coefficient behaves in different ways at low and high temperatures. At low temperatures, it has Arrhenius behaviour, as they expect from kink phenomenology, the activation energy being close to the migration energy for an isolated kink obtained from static calculation.