Numerical analysis of heat transport in classical one-dimensional systems

Numerical studies of some unidimensional systems suggest that Fourier law is satisfied, where theory predicts a divergence of heat conductivity with the system size. Here, I revisit some such models, finding that in all cases a divergence asymptotically emerges. This includes a variant of the ding-a-ling model, where I find that, contrary to previous claims, the ``anomalous" growth starts already for moderate system sizes. More conceptually interesting is the case of non-binding potentials, whose behavior is well reproduced by assuming that the energy flux across the nonequilibrium stationary state is the sum of two contributions: a diffusive and a hydrodynamic one. This approach, which extends an idea previously formulated for nearly integrable systems, allows to conclude that the asymptotic regime is always dominated by the anomalous hydrodynamic component, but the crossover may occur for extremely long system sizes.