For one-dimensional nonlinear lattices with momentum conserving interparticle interactions, intensive studies have suggested that the heat conductivity $\kappa$ diverges with the system size $L$ as $\kappa \sim L^{\alpha }$ and the value of $\alpha$ is universal. But in the Fermi-Pasta-Ulam-$\beta$ lattices with nearest-neighbor (NN) and next-nearest-neighbor (NNN) coupling, we find that $\alpha$ strongly depends on $\gamma$, the ratio of the NNN coupling to the NN coupling. The correlation between the $\gamma$-dependent heat conduction behavior and the in-band discrete breathers is also analyzed.

• Received 24 August 2011

DOI:https://doi.org/10.1103/PhysRevE.85.020102