The effect of discrete breathers on heat conduction in nonlinear chains

Intensive studies in the past decades have suggested that the heat conductivity $\kappa$ diverges with the system size $L$ as $\kappa\sim L^{\alpha}$ in one dimensional momentum conserving nonlinear lattices and the value of $\alpha$ is universal. But in the Fermi-Pasta-Ulam-$\beta$ lattices with next-nearest-neighbor interactions we find that $\alpha$ strongly depends on $\gamma$, the ratio of the next-nearest-neighbor coupling to the nearest-neighbor coupling. We relate the $\gamma$-dependent heat conduction to the interactions between the long-wavelength phonons and the randomly distributed discrete breathers. Our results provide an evidence to show that the nonlinear excitations affect the heat transport.