Heat conduction in the nonlinear response regime: Scaling, boundary jumps, and negative differential thermal resistance

We report a numerical study on heat conduction in one-dimensional homogeneous lattices in both the linear and the nonlinear response regime, with a comparison among three prototypical nonlinear lattice models. In the nonlinear response regime, negative differential thermal resistance (NDTR) can occur in both the Frenkel-Kontorova model and the ϕ⁴ model. In the Fermi-Pasta-Ulam- β model, however, only positive differential thermal resistance can be observed, as shown by a monotonous power-law dependence of the heat flux on the applied temperature difference. In general, it was found that NDTR can occur if there is nonlinearity in the onsite potential of the lattice model. It was also found that the regime of NDTR becomes smaller as the system size increases, and eventually vanishes in the thermodynamic limit. For the ϕ⁴ model, a phenomenological description of the size-induced crossover from the existence to the nonexistence of a NDTR regime is provided.