Energy and momentum diffusion in one-dimensional periodic and asymmetric nonlinear lattices with momentum conservation.

The energy diffusion in one-dimensional (1D) momentum conserving nonlinear lattices usually exhibits anomalous superdiffusion, except the coupled rotator lattice with symmetric and periodic interacting potential which has normal energy diffusion corresponding to normal heat conduction. For nonperiodic 1D lattices with momentum conservation, it has been argued that the asymmetric potential can induce normal heat conduction. Later results indicate the observed normal behavior might be the finite size effect and the anomalous behavior will appear in the thermodynamical limit. Here we propose asymmetric and periodic 1D nonlinear lattices with momentum conservation. The energy and momentum diffusion behaviors will be investigated in detail and the same normal diffusion behaviors for both energy and momentum can be observed. These results confirm that the periodicity is the key for normal transport behavior in 1D momentum conserving lattices, whether the potential is symmetric or asymmetric.