Heat Transport Behaviour in One-Dimensional Lattice Models with Damping

We investigate the heat transport behaviours of two typical lattice models, the Fermi--Pasta--Ulam-β model and the Ф⁴ lattice model, in the presence of damping which imitates the effect of the thermal radiation and the thermal diffusion to the surroundings through the sample boundary. It is found that the damping does not affect the thermal conductivity, but can change the heat flux dumped into the lattice chain. We also discuss possible applications under the heuristic guidance of our numerical results. In particular, we suggest a way to measure the thermal conductivity experimentally in the presence of large energy loss arisen from the radiation and the diffusion.