Abstract
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 language | English |
|---|---|
| Pages (from-to) | 18772-18776 |
| Number of pages | 5 |
| Journal | Proceedings of the National Academy of Sciences of the United States of America |
| Volume | 116 |
| Issue number | 38 |
| DOIs | |
| State | Published - Sep 17 2019 |
Bibliographical note
Funding Information:ACKNOWLEDGMENTS. We thank Michael Weinstein and Robert V. Kohn for introducing us to the microstructure literature; and Jordan Cotler for helpful discussions. A.D.S. was partially supported by NSF Grant PHY-1214341. F.W.’s work is supported by US Department of Energy Contract DE-SC0012567, European Research Council Grant 742104, and Swedish Research Council Contract 335-2014-7424.
Funding Information:
We thank Michael Weinstein and Robert V. Kohn for introducing us to the microstructure literature; and Jordan Cotler for helpful discussions. A.D.S. was partially supported by NSF Grant PHY-1214341. F.W.?s work is supported by US Department of Energy Contract DE-SC0012567, European Research Council Grant 742104, and Swedish Research Council Contract 335-2014-7424.
Publisher Copyright:
© 2019 National Academy of Sciences. All rights reserved.
Keywords
- Lagrangian
- Microstructure
- Time crystal
ASJC Scopus subject areas
- General