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Heat conduction in one-dimensional (1D) scattering models is studied based on numerical simulations and an analytical S-matrix method which is developed in the mesoscopic electronic transport theory. In the models, it is found that the heat conduction is closely related to a spatial correlation of particle motions: if the correlation exists, the heat conduction is abnormal; otherwise (i.e. if the correlation vanishes), the heat conduction is normal. The randomization of scatterers in the models is found to determine the existence of correlation. Our simulations are in agreement with the theoretical expectations. We generalize the result and study the property of heat conduction by directly analysing the correlation in general 1D dynamical systems.

Heat conduction and long-range spatial correlation in 1D models