Kinetics of anomalous transport and algebraic correlations in a long-range interacting system

We propose a kinetic description of the Hamiltonian Mean Field model, which is paradigmatic for dynamical systems with long-range interactions. We predict algebraic tails for the momentum autocorrelations and anomalous diffusion for the angles. We derive analytically the corresponding laws in the limit of a large number of particles. We argue that the mechanism for such an anomalous transport does not depend on some complex structure of the phase space: indeed, the transport is anomalous for out-of-equilibrium distributions but also for the equilibrium microcanonical distribution.