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Classical Time Crystals

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arxiv 1202.2537 v2 pith:Y44HFIWG submitted 2012-02-12 cond-mat.other gr-qchep-thmath-phmath.MPquant-ph

Alfred Shapere , Frank Wilczek This is my paper · ORCID
classification cond-mat.othergr-qchep-thmath-phmath.MPquant-ph
keywords timeclassicalcrystalsdisplayorbitssystemsanalogueangular
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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.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. The Nature of Phantom Dark Energy and its Relation to Time Crystals

    hep-th 2025-02 reject novelty 5.0 of 10

    Phantom dark energy is claimed to be, at its fundamental level, a fluid of time crystals, with the same non-canonical kinetic conditions producing both.

  2. Dark Energy from Time Crystals

    hep-ph 2025-02 conditional novelty 5.0 of 10

    A time-crystal scalar field is shown to satisfy the phantom dark energy conditions w < -1, c_s^2 > 0, and rho >= 0 inside the crystal region.

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