  In the quasi-stationary states of the Hamiltonian Mean-Field model, we
numerically compute correlation functions of momenta and diffusion of angles
with homogeneous initial conditions. This is an example, in a N-body
Hamiltonian system, of anomalous transport properties characterized by non
exponential relaxations and long-range temporal correlations. Kinetic theory
predicts a striking transition between weak anomalous diffusion and strong
anomalous diffusion. The numerical results are in excellent agreement with the
quantitative predictions of the anomalous transport exponents. Noteworthy, also
at statistical equilibrium, the system exhibits long-range temporal
correlations: the correlation function is inversely proportional to time with a
logarithmic correction instead of the usually expected exponential decay,
leading to weak anomalous transport properties.
