Heat conduction in one dimensional nonintegrable systems

Two classes of 1D nonintegrable systems represented by the Fermi-Pasta-Ulam (FPU) model and the discrete $\phi^4$ model are studied to seek a generic mechanism of energy transport in microscopic level sustaining macroscopic behaviors. The results enable us to understand why the class represented by the $\phi^4$ model has a normal thermal conductivity and the class represented by the FPU model does not even though the temperature gradient can be established.