Role of conserved quantities in normal heat transport in one dimenison

Although one-dimensional systems that exhibit translational symmetry are generally believed to exhibit anomalous heat transport, previous work has shown that the model of coupled rotators on a one-dimensional lattice constitute a possible exception. We investigate the equilibrium spatiotemporal correlations of energy and momentum of the rotator model, and find that both these fields diffuse normally. The normal diffusion is explained within the framework of stochastic hydrodynamics by observing that the angle variables do not constitute a conserved field, which leads to the absence of long-wavelength currents in the system. As an outcome of our analysis, we propose some general criteria for normal transport based on the existence of conservation laws.