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Title: Regularizations of time-crystal dynamics

Abstract

We demonstrate herein 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.

Authors:
 [1]; ORCiD logo [2]
+ Show Author Affiliations
  1. Univ. of Kentucky, Lexington, KY (United States)
  2. Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States); Tsung-Dao Lee Inst., Shanghai (China); Shanghai Jiao Tong Univ. (China); Stockholm Univ. (Sweden); Arizona State Univ., Tempe, AZ (United States)
Publication Date:
Research Org.:
Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
Sponsoring Org.:
USDOE Office of Science (SC); National Science Foundation (NSF); European Research Council (ERC); Swedish Research Council (VR)
OSTI Identifier:
1611854
Grant/Contract Number:  
SC0012567; PHY-1214341; 742104; 335-2014-7424
Resource Type:
Accepted Manuscript
Journal Name:
Proceedings of the National Academy of Sciences of the United States of America
Additional Journal Information:
Journal Volume: 116; Journal Issue: 38; Journal ID: ISSN 0027-8424
Publisher:
National Academy of Sciences
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; science & technology - other topics; time crystal; microstructure; Lagrangian

Citation Formats

Shapere, Alfred D., and Wilczek, Frank. Regularizations of time-crystal dynamics. United States: N. p., 2019. Web. doi:10.1073/pnas.1908758116.
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Shapere, Alfred D., & Wilczek, Frank. Regularizations of time-crystal dynamics. United States. https://doi.org/10.1073/pnas.1908758116
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Shapere, Alfred D., and Wilczek, Frank. Wed . "Regularizations of time-crystal dynamics". United States. https://doi.org/10.1073/pnas.1908758116. https://www.osti.gov/servlets/purl/1611854.
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@article{osti_1611854,
title = {Regularizations of time-crystal dynamics},
author = {Shapere, Alfred D. and Wilczek, Frank},
abstractNote = {We demonstrate herein 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.},
doi = {10.1073/pnas.1908758116},
journal = {Proceedings of the National Academy of Sciences of the United States of America},
number = 38,
volume = 116,
place = {United States},
year = {Wed Aug 14 00:00:00 EDT 2019},
month = {Wed Aug 14 00:00:00 EDT 2019}
}
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Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
https://doi.org/10.1073/pnas.1908758116
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Citation Metrics:
Cited by: 10 works
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Figures / Tables:

Fig. 1 Fig. 1: Numerical solution of Eqs. 9 and 10 with µ= 10−5, x(0) = 0.9, ẋ(0) = 0.25 . The upper (gold) curve represents x(t); the middle (red) curve represents y(t); and the lower (blue) curve represents E. The behavior of y(t) exhibits the characteristic temporal microstructure discussed in themore » text, with near-constant velocity often, but briefly, interrupted by small, sudden jumps.« less
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Works referenced in this record:

Space-Time Crystals of Trapped Ions
journal, October 2012

Absolute stability and spatiotemporal long-range order in Floquet systems
journal, August 2016

Phase Structure of Driven Quantum Systems
journal, June 2016

Branched Quantization
journal, November 2012

Time crystals: a review
journal, November 2017

Modeling spontaneous breaking of time-translation symmetry
journal, March 2015

Observation of discrete time-crystalline order in a disordered dipolar many-body system
journal, March 2017

  • Choi, Soonwon; Choi, Joonhee; Landig, Renate
  • Nature, Vol. 543, Issue 7644
  • DOI: 10.1038/nature21426

Canonical structure of higher derivative theories
journal, July 2014

Defining time crystals via representation theory
journal, September 2017

Quantum Time Crystals
journal, October 2012

Floquet Time Crystals
journal, August 2016

Classical Time Crystals
journal, October 2012

Observation of a discrete time crystal
journal, March 2017

  • Zhang, J.; Hess, P. W.; Kyprianidis, A.
  • Nature, Vol. 543, Issue 7644
  • DOI: 10.1038/nature21413

Discrete Time Crystals: Rigidity, Criticality, and Realizations
journal, January 2017

Phase structure of one-dimensional interacting Floquet systems. II. Symmetry-broken phases
journal, June 2016

Space-time crystals of trapped ions
text, January 2012

Branched Quantization
text, January 2012

Discrete time crystals: rigidity, criticality, and realizations
text, January 2016

Observation of a Discrete Time Crystal
text, January 2016

Defining Time Crystals via Representation Theory
text, January 2016

Time crystals: a review
text, January 2017

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    Works referencing / citing this record:

    Time crystal minimizes its energy by performing Sisyphus motion
    journal, August 2019

    • Sacha, Krzysztof; Hannaford, Peter
    • Proceedings of the National Academy of Sciences, Vol. 116, Issue 38
    • DOI: 10.1073/pnas.1913075116
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      Figures / Tables found in this record:

      Fig. 1 (p. 2)figure
      Fig. 2 (p. 2)figure
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      Fig. 6 (p. 4)figure
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