Temperature dependence of thermal conductivity in 1D nonlinear lattices

We examine the temperature dependence of thermal conductivity of one dimensional nonlinear (anharmonic) lattices with and without on-site potential. It is found from computer simulation that the heat conductivity depends on temperature via the strength of nonlinearity. Based on this correlation, we make a conjecture in the effective phonon theory that the mean-free-path of the effective phonon is inversely proportional to the strength of nonlinearity. We demonstrate analytically and numerically that the temperature behavior of the heat conductivity $\kappa\propto1/T$ is not universal for 1D harmonic lattices with a small nonlinear perturbation. The computer simulations of temperature dependence of heat conductivity in general 1D nonlinear lattices are in good agreements with our theoretic predictions. Possible experimental test is discussed.