We analyze numerically the out-of-equilibrium relaxation dynamics of a long-range Hamiltonian system of N fully coupled rotators. For a particular family of initial conditions, this system is known to enter a particular regime in which the dynamic behavior does not agree with thermodynamic predictions. Moreover, there is evidence that in the thermodynamic limit, when N--> infinity is taken prior to t--> infinity, the system will never attain true equilibrium. By analyzing the scaling properties of the two-time autocorrelation function we find that, in that regime, a very complex dynamics unfolds, in which aging phenomena appear. The scaling law strongly suggests that the system behaves in a complex way, relaxing towards equilibrium through intricate trajectories. The present results are obtained for conservative dynamics, where there is no thermal bath in contact with the system.
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