Transport in the Frenkel-Kontorova model. III. Thermal conductivity

For pt.II see ibid., vol.18, p.4903 (1985). The authors use molecular dynamics simulation to study the thermal conductivity lambda of the undamped Frenkel-Kontorova model. The aims of the work are to provide evidence for the existence of lambda in this one-dimensional system, to investigate a variety of simulation techniques for calculating it, and to obtain numerical results for lambda as a function of temperature and winding number. They have examined three techniques: (i) direct determination of the energy flux caused by a temperature gradient; (ii) use of the Kubo formula to obtain lambda from the autocorrelation function of the energy flux; (iii) the calculation of lambda from the response of the energy flux to a suitable chosen uniform external perturbation. They show that the results given by the three approaches support the existence of lambda and are in satisfactory agreement with each other. The dependence of lambda on temperature and winding number can be explained by simple physical arguments.