title: Classical time crystals.
abstract: 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 density waves.
authors.affiliation: Department of Physics and Astronomy, University of Kentucky, Lexington, Kentucky 40502, USA.
authors.forename: Alfred
authors.initials: A
authors.lastname: Shapere
authors.forename: Frank
authors.initials: F
authors.lastname: Wilczek