Agenda

Résumé : Limit-cycle or time-crystal phases, in which the order parameter retains a periodic motion in time, are non-equilibrium phases. They are therefore expected to display phenomena that fall beyond equilibrium classifications. We study such phenomena in paradigmatic O(N) models. Once suitably driven out of equilibrium, they develop instabilities towards limit-cycle long-range orders, which emerge in driven quantum systems and solid-state platforms, as well as nonreciprocal active matter. I will discuss realization in existing platforms, but also new implementations in driven magnets. I will describe the complete phase diagram beyond mean-field, which hosts new type of phase transitions towards limit cycles, associated to new non-equilibrium universality classes. Finally, I will discuss why such phases generically display the Kardar-Parisi-Zhang physics and generalization of it.