The phonon relaxation and heat conduction of the Femi-Pasta-Ulam β lattice are studied via molecular dynamics simulations. The phonon relaxation rate is calculated from the energy autocorrelation function for different modes at various temperatures through equilibrium molecular dynamics simulations. The relaxation rate as a function of wave vector k is estimated to be proportional to k1.688, which leads to a N0.41 divergence of the thermal conductivity in the framework of Green-Kubo relation. This result is in agreement with that obtained by non-equilibrium molecular dynamics simulations which estimate the length dependence exponent of thermal conductivity as 0.415. Our results confirm the N2/5 divergence in one-dimensional FPU β lattice. The effect of the heat flux on the thermal conductivity is also studied by imposing large temperature differences on the two ends of the lattice in non-equilibrium molecular dynamics simulations. The results indicate that the thermal conductivity is insensitive to the heat flux under our simulation conditions, and the linear response theory is widely applicable.

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