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 proportional to 1/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 agreement with our theoretic predictions. Possible experimental tests are discussed. Copyright (C) EPLA, 2007.