Scaling property of the heat-current flows across a weak interface

We systematically study heat current J that flows through a few one-dimensional nonlinear lattices, each of which consists of two identical segments that are coupled by a weak interface. Existing theoretical analyses expect that J is generally proportional to the square of the interface strength when the temperature drop is fixed and small. However, we observe two completely different classes in our numerical simulations. One follows the original expectation. In the other class, however, J follows a power-law decay with the strength and the detailed power exponent depends on the details of the lattices and the interface interaction. Further theoretical analyses reveal that in the former class the interface potential energy decays with the interface strength linearly, which is commonly observed. In the latter class, the interface potential energy approaches a constant that is independent of the interaction strength. The detailed power exponents are then well explained.