Phonon relaxation and heat conduction in one-dimensional Fermiben Pastaben Ulam β lattices by molecular dynamics simulations

The phonon relaxation and heat conduction in one-dimensional Fermi-Pasta-Ulam (FPU) β lattices are studied by using molecular dynamics simulations. The phonon relaxation rate, which dominates the length dependence of the FPU β lattice, is first calculated from the energy autocorrelation function for different modes at various temperatures through equilibrium molecular dynamics simulations. We find that the relaxation rate as a function of wave number k is proportional to k^1.688, which leads to a N^0.41 divergence of the thermal conductivity in the framework of Green-Kubo relation. This is also in good agreement with the data obtained by non-equilibrium molecular dynamics simulations which estimate the length dependence exponent of the thermal conductivity as 0.415. Our results confirm the N^2/5 divergence in one-dimensional FPU β lattices. The effects of the heat flux on the thermal conductivity are also studied by imposing different temperature differences on the two ends of the lattices. We find that the thermal conductivity is insensitive to the heat flux under our simulation conditions. It implies that the linear response theory is applicable towards the heat conduction in one-dimensional FPU β lattices.