Thermal conduction in a chain of colliding harmonic oscillators revisited

Thermal conduction in a chain of colliding harmonic oscillators, sometimes called the ding-dong model, is investigated. We first argue that this system is equivalent to the Dawson plasma sheet model. Next we show the Lyapunov analysis for this system to characterize its dynamical property. Finally, we reconsider the numerical study of thermal conduction for this system using the Green-Kubo relation and the direct simulation of Fourier law. Both show that thermal conduction is normal in that $\kappa \mathrm{}(N,T)\mathrm{}\propto N^0,$ at least, at low temperature in a large system.