  The relation between relaxation and diffusion is investigated in a
Hamiltonian system of globally coupled rotators. Diffusion is anomalous if and
only if the system is going towards equilibrium. The anomaly in diffusion is
not anomalous diffusion taking a power-type function, but is a transient
anomaly due to non-stationarity. Contrary to previous claims, in
quasi-stationary states, diffusion can be explained by a stretched exponential
correlation function, whose stretching exponent is almost constant and
correlation time is linear as functions of degrees of freedom. The full time
evolution is characterized by varying stretching exponent and correlation time.
