Classical time crystals.

  title={Classical time crystals.},
  author={Alfred Shapere and Frank Wilczek},
  journal={Physical review letters},
  volume={109 16},
We consider the possibility that classical dynamical systems display motion in their lowest-energy state, forming a time analogue of crystalline spatial order. Challenges facing that idea are identified and overcome. We display arbitrary orbits of an angular variable as lowest-energy trajectories for nonsingular Lagrangian systems. Dynamics within orbits of broken symmetry provide a natural arena for formation of time crystals. We exhibit models of that kind, including a model with traveling… 

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