Classical discrete time crystals

@article{Yao2020ClassicalDT,
  title={Classical discrete time crystals},
  author={Norman Y. Yao and C. Nayak and Leon Balents and Michael P. Zaletel},
  journal={Nature Physics},
  year={2020},
  volume={16},
  pages={438-447}
}
The spontaneous breaking of time-translation symmetry in periodically driven quantum systems leads to a new phase of matter: the discrete time crystal (DTC). This phase exhibits collective subharmonic oscillations that depend upon an interplay of non-equilibrium driving, many-body interactions and the breakdown of ergodicity. However, subharmonic responses are also a well-known feature of classical dynamical systems ranging from predator–prey models to Faraday waves and a.c.-driven charge… 
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A Brief History of Time Crystals.
The idea of breaking time-translation symmetry has fascinated humanity at least since ancient proposals of the perpetuum mobile. Unlike the breaking of other symmetries, such as spatial translation
Classical Many-Body Time Crystals.
TLDR
This work provides a simple and pedagogical framework by which to obtain many-body time crystals using parametrically coupled resonators and presents a clear distinction between single-mode time-translation symmetry breaking and a situation where an extensive number of degrees of freedom undergo the transition.
Classical Prethermal Phases of Matter.
TLDR
Studying the Hamiltonian dynamics of a large three-dimensional lattice of classical spins, this work provides the first numerical proof of prethermal phases of matter in a system with short-range interactions.
Floquet Phases of Matter via Classical Prethermalization.
TLDR
It is demonstrated that the prethermal regime of periodically driven (Floquet), classical many-body systems can host nonequilibrium phases of matter and it is proved that the effective Hamiltonian can host emergent symmetries protected by the discrete time-translation symmetry of the drive.
Supplemental Material for Classical many-body time crystals
Discrete time crystals are a many-body state of matter where the extensive system’s dynamics are slower than the forces acting on it. Nowadays, there is a growing debate regarding the specific
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The results are consistent with the realization of an out-of-equilibrium Floquet phase of matter and introduce a programmable quantum simulator based on solid-state spins for exploring many-body physics.
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