Memory effects and heat transport in one-dimensional insulators

We study the dynamical correlation functions and heat conduction fur the simplest model of quasi one-dimensional (1d) dielectric crystal i.e. a chain of classical particles coupled by quadratic and cubic intersite potential. Even in the weakly nonlinear regime, numerical simulation on long enough chains reveal sizeable deviations from the perturbative results in the form of a slower decay of correlations in equilibrium. Their origin can be traced back to the subtle nonlinear effects described by mode-coupling theories. Measures of thermal conductivity with nonequilibrium molecular-dynamics method confirm the relevance of such effects for low-dimensional lattices oven at very low temperatures.