Anomalous energy diffusion in two-dimensional nonlinear lattices

Heat transport in one-dimensional (1D) momentum-conserved lattices is generally assumed to be anomalous, thus yielding a power-law divergence of thermal conductivity with system length. However, whether heat transport in a two-dimensional (2D) system is anomalous or not is still up for debate because of the difficulties involved in experimental measurements or due to the insufficiently large simulation cell size. Here we simulate energy and momentum diffusion in the 2D nonlinear lattices using the method of fluctuation correlation functions. Our simulations confirm that energy diffusion in the 2D momentum-conserved lattices is anomalous and can be well described by the Lévy-stable distribution. As is expected, we verify that 2D nonlinear lattices with on-site potentials exhibit normal energy diffusion, independent of the dimension. Contrary to the hypothesis of a 1D system, we further clarify that anomalous heat transport in the 2D momentum-conserved system cannot be corroborated by the momentum superdiffusion any longer. Our findings offer some valuable insights into mechanisms of thermal transport in 2D system.