  We study the dynamical correlation functions and heat conduction for 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 even at very low
temperatures.
