Nonuniversal heat conduction of one-dimensional lattices

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 similar to 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.