Аннотация:
Any classical translation-invariant spin system possesses a class of periodic trajectories with all spins pointing in the same direction at any moment of time. Such trajectories are different from a generic many-body trajectory in many more ways than one might think. We show that initially a periodic trajectory, if close to a single-body separatrix, loses memory about its initial conditions significantly faster than a generic one. On the contrary away from the separatrix motion may stabilise to perpetually quasiperiodic, or to aperiodic but non-ergodic motion. The latter depends non-trivially on the the system size. We also demonstrate that such trajectories have a profound impact on the dynamics of the corresponding quantum spin system: When the latter is initialized in a product state with all spins pointing in the same direction, its relaxation is accompanied by oscillations and takes a time considerably larger than a typical relaxation time.
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