Normal energy and stretch diffusion in a one-dimensional momentum conserving lattice with nonlinear bounded kinetic energy

One-dimensional (1D) nonlinear lattices that conserve momentum exhibit anomalous heat conduction, except for the specific case of the 1D coupled rotator lattice. Unlike classical interacting 1D nonlinear lattices such as the Fermi–Pasta–Ulam β (FPU-β) lattice, the 1D coupled rotator lattice has a bounded interaction potential energy. Recently, the 1D coupled rotator lattice with additional bounded kinetic energy has also been found to exhibit normal heat conduction. Here, we study energy diffusion in the 1D momentum-conserving lattice with bounded kinetic energy only. We find that this lattice exhibits normal energy diffusion as well as normal stretch diffusion. This work indicates that bounded energy, whether kinetic or potential, is crucial for normal energy diffusion and heat conduction in 1D momentum-conserving nonlinear lattices.