Roundabout Relaxation: Collective Excitation Requires a Detour to Equilibrium

Relaxation to equilibrium after strong and collective excitation is studied by using a Hamiltonian dynamical system of a one-dimensional $XY$ model. After an excitation of a domain of $K$ elements, the excitation is concentrated to fewer elements, which are made farther away from equilibrium, and the excitation intensity increases logarithmically with $K$. Equilibrium is reached only after taking this roundabout route, with the time for relaxation diverging asymptotically as $K^{\gamma }$ with $\gamma \approx 4.2$.