Any classical translation-invariant spin system possesses a class of periodic trajectories with all spins pointing in the same direction at any moment. Such trajectories differ 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 stabilize to perpetually quasiperiodic or aperiodic but non-ergodic motion. The latter depends non-trivially on 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.
Igor Ermakov received his Ph.D. in 2022 at Skoltech. The title of his Ph.D. thesis is "Dynamics of exceptional states in many-body systems". Currently Igor is a researcher at Steklov Institute of mathematics and Russian Quantum Center.
Seminar by the NYU-ECNU Institute of Physics at NYU Shanghai