Crossover from Fermi-Pasta-Ulam to normal diffusive behavior in heat conduction through open anharmonic lattices

Abstract

We study heat conduction in one-, two-, and three-dimensional anharmonic lattices connected to stochastic Langevin heat baths. The interatomic potential of the lattices is double-well type, i.e., V(DW)(x)=k(2)x(2)/2+k(4)x(4)/4 with k(2)<0 and k(4)>0. We observe two different temperature regimes of transport: a high-temperature regime where asymptotic length dependence of nonequilibrium steady state heat current is similar to the well-known Fermi-Pasta-Ulam lattices with an interatomic potential, V(FPU)(x)=k(2)x(2)/2+k(4)x(4)/4 with k(2),k(4)>0, and a low-temperature regime where heat conduction is most likely diffusive normal, satisfying Fourier's law. We present our simulation results for different temperature regimes in all dimensions.