Regularizations of time-crystal dynamics

Alfred D. Shapere, Frank Wilczek

Research output: Contribution to journalArticlepeer-review

15 Scopus citations


We demonstrate that nonconvex Lagrangians, as contemplated in the theory of time crystals, can arise in the effective description of conventional, physically realizable systems. Such embeddings resolve dynamical singularities which arise in the reduced description. Microstructure featuring intervals of fixed velocity interrupted by quick resets—“Sisyphus dynamics”—is a generic consequence. In quantum mechanics, this microstructure can be blurred, leaving entirely regular behavior.

Original languageEnglish
Pages (from-to)18772-18776
Number of pages5
JournalProceedings of the National Academy of Sciences of the United States of America
Issue number38
StatePublished - Sep 17 2019

Bibliographical note

Publisher Copyright:
© 2019 National Academy of Sciences. All rights reserved.


  • Lagrangian
  • Microstructure
  • Time crystal

ASJC Scopus subject areas

  • General


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