Aging in an infinite-range Hamiltonian system of coupled rotators

TL;DR

This paper numerically investigates aging phenomena in a long-range Hamiltonian system of coupled rotators, revealing complex out-of-equilibrium dynamics and slow relaxation behavior in the thermodynamic limit.

Contribution

It is the first study to observe aging in a Hamiltonian system with conservative dynamics, demonstrating complex relaxation processes in such long-range interacting models.

Findings

Aging phenomena appear in the system's out-of-equilibrium dynamics.

The system exhibits complex relaxation trajectories towards equilibrium.

Scaling laws suggest intricate relaxation behavior in the thermodynamic limit.

Abstract

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 $N\to \infty$ is taken prior to $t\to \infty$, 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 {\em 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. This is the first time that aging is observed in such Hamiltonian systems.