Anomalous heat conduction and thermal rectification in weak nonlinear lattices

Heat conduction in one-dimensional system is generally found to be anomalous. However, the scaling behavior of thermal conductivity with system length is still up for debate among theoretical, numerical and experimental results. Here with a devised adjustable reflectivity heat reservoir, we re-address the anomalous heat conduction in one-dimensional Fermi–Pasta–Ulam $$\beta $$ β (FPU- $$\beta $$ β ) lattices under weak nonlinear conditions. Our results show that, the boundary thermal resistance has an important impact on the divergent thermal conductivity of one-dimensional systems with weak nonlinearity. As an application of this concept, we design a thermal rectification model in one material with asymmetric boundary coupling, which is in sharp contrast to the well-known thermal rectifiers composed of two different materials. Our findings shed light on the intrinsic heat conduction in weak nonlinear lattices, which might be helpful to understand the heat transfer experiments of one-dimensional materials, such as carbon nanotubes, nanowires, and polymer chains. Graphical abstract Influence of boundary thermal resistance on anomalous heat conduction in weak nonlinear lattices