Classical time crystals

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 fo...

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Bibliographic Details
Published in:Physical review letters 2012-10, Vol.109 (16), p.160402-160402, Article 160402
Main Authors: Shapere, Alfred, Wilczek, Frank
Format: Article
Language:English
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Summary: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.
ISSN:0031-9007
1079-7114
DOI:10.1103/PhysRevLett.109.160402