Anomalous transport for anharmonic chains has been first confirmed almost twenty years ago. The resulting scaling behaviour of time correlations in thermal equilibrium is a more recent activity. We discuss how nonlinear fluctuating hydrodynamics is used as an effective tool. Also handled are fluctuations of time-integrated local currents. Building a bridge towards one-dimensional quantum system the discrete nonlinear Schroedinger equation is further example of interest.

Technical University Munich, Germany