Anomalous transport and relaxation in classical one-dimensional models

After reviewing the main features of anomalousenergy transport in 1D systems, we report simulations performed withchains of noisy anharmonic oscillators. The stochastic terms are addedin such a way to conserve total energy and momentum, thus keeping the basic hydrodynamic features of these models. The addition of this "conservative noise" allows to obtain a more efficient estimate of the power-law divergence of heat conductivity κ(L) ∼ Lα in the limit of small noise and large system size L.By comparing the numerical results with rigorous predictions obtained for the harmonic chain, we show how finite-size and time effects can be effectively controlled. For low noise amplitudes, the α values are close to 1/3 for asymmetric potentials and to 0.4 for symmetric ones. These results support the previously conjectured two-universality-classes scenario. © EDP Sciences/Societá Italiana di Fisica/Springer-Verlag 2007.