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Periodically driven quantum many-body systems can spontaneously reorganize their motion and start moving with a period different than the driving period. These are ``discrete time crystals'' and they have been realized already in the laboratory. It turns out that systems from the same class can spontaneously reveal quasicrystalline structures in time. The interaction between the particles forces them into a quasicrystal pattern in the time domain, in spite of the fact that the driving is periodic.
Giergiel et al. (Tue,) studied this question.
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