Skip to main content

Introduction

  • Chapter
  • First Online:
Time Crystals

Part of the book series: Springer Series on Atomic, Optical, and Plasma Physics ((SSAOPP,volume 114))

  • 1054 Accesses

Abstract

Periodic motion can be observed everywhere ranging from atomic systems and a clock on a wall to the Solar System and beyond the Milky Way. Periodic evolution in time can be considered as a temporal counterpart of periodic behavior in the space dimensions which is also common because there are solid state crystals. Research of periodic motion of systems as crystalline structures in the time domain is a novel field initiated by Alfred Shapere and Frank Wilczek in the classical systems and by Wilczek himself in the quantum case.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Acebrón, J.A., Bonilla, L.L., Pérez Vicente, C.J., Ritort, F., Spigler, R.: The Kuramoto model: a simple paradigm for synchronization phenomena. Rev. Mod. Phys. 77, 137–185 (2005). https://doi.org/10.1103/RevModPhys.77.137

    Article  ADS  Google Scholar 

  2. Biancalana, F., Amann, A., Uskov, A.V., O’Reilly, E.P.: Dynamics of light propagation in spatiotemporal dielectric structures. Phys. Rev. E 75, 046607 (2007). https://doi.org/10.1103/PhysRevE.75.046607

    Article  ADS  Google Scholar 

  3. Bruno, P.: Comment on “space-time crystals of trapped ions”. Phys. Rev. Lett. 111, 029301 (2013). https://doi.org/10.1103/PhysRevLett.111.029301

    Article  ADS  Google Scholar 

  4. Choi, S., Choi, J., Landig, R., Kucsko, G., Zhou, H., Isoya, J., Jelezko, F., Onoda, S., Sumiya, H., Khemani, V., von Keyserlingk, C., Yao, N.Y., Demler, E., Lukin, M.D.: Observation of discrete time-crystalline order in a disordered dipolar many-body system. Nature 543(7644), 221–225 (2017). Letter. https://doi.org/10.1038/nature21426

  5. Elachi, C.: Waves in active and passive periodic structures: a review. Proc. IEEE 64(12), 1666–1698 (1976). https://doi.org/10.1109/PROC.1976.10409

    Article  ADS  Google Scholar 

  6. Else, D.V., Bauer, B., Nayak, C.: Floquet time crystals. Phys. Rev. Lett. 117, 090402 (2016). https://doi.org/10.1103/PhysRevLett.117.090402

    Article  ADS  Google Scholar 

  7. Giergiel, K., Dauphin, A., Lewenstein, M., Zakrzewski, J., Sacha, K.: Topological time crystals. New J. Phys. 21(5), 052003 (2019). https://doi.org/10.1088/1367-2630/ab1e5f

    Article  ADS  Google Scholar 

  8. Guo, L., Marthaler, M., Schön, G.: Phase space crystals: a new way to create a quasienergy band structure. Phys. Rev. Lett. 111, 205303 (2013). https://doi.org/10.1103/PhysRevLett.111.205303

    Article  ADS  Google Scholar 

  9. Harfoush, F., Taflove, A.: Scattering of electromagnetic waves by a material half-space with a time-varying conductivity. IEEE Trans. Antenn. Propag. 39(7), 898–906 (1991). https://doi.org/10.1109/8.86907

    Article  ADS  Google Scholar 

  10. Holberg, D., Kunz, K.: Parametric properties of fields in a slab of time-varying permittivity. IEEE Trans. Antenn. Propag. 14(2), 183–194 (1966). https://doi.org/10.1109/TAP.1966.1138637

    Article  ADS  Google Scholar 

  11. Khemani, V., Lazarides, A., Moessner, R., Sondhi, S.L.: Phase structure of driven quantum systems. Phys. Rev. Lett. 116, 250401 (2016). https://doi.org/10.1103/PhysRevLett.116.250401

    Article  ADS  Google Scholar 

  12. Kozin, V.K., Kyriienko, O.: Quantum time crystals from Hamiltonians with long-range interactions. Phys. Rev. Lett. 123, 210602 (2019). https://doi.org/10.1103/PhysRevLett.123.210602

    Article  ADS  MathSciNet  Google Scholar 

  13. Kuramoto, Y.: Self-entrainment of a population of coupled non-linear oscillators. In: Araki, H. (ed.) International Symposium on Mathematical Problems in Theoretical Physics, pp. 420–422. Springer, Berlin (1975)

    Chapter  Google Scholar 

  14. Kuramoto, Y., Nishikawa, I.: Statistical macrodynamics of large dynamical systems. case of a phase transition in oscillator communities. J. Statist. Phys. 49(3), 569–605 (1987). https://doi.org/10.1007/BF01009349

  15. Lustig, E., Sharabi, Y., Segev, M.: Topological aspects of photonic time crystals. Optica 5(11), 1390–1395 (2018). https://doi.org/10.1364/OPTICA.5.001390. http://www.osapublishing.org/optica/abstract.cfm?URI=optica-5-11-1390

  16. Mierzejewski, M., Giergiel, K., Sacha, K.: Many-body localization caused by temporal disorder. Phys. Rev. B 96, 140201 (2017). https://doi.org/10.1103/PhysRevB.96.140201

    Article  ADS  Google Scholar 

  17. Morgenthaler, F.R.: Velocity modulation of electromagnetic waves. IRE Trans. Microw. Theory Tech. 6(2), 167–172 (1958). https://doi.org/10.1109/TMTT.1958.1124533

    Article  ADS  Google Scholar 

  18. Sacha, K.: Anderson localization and Mott insulator phase in the time domain. Sci. Rep. 5, 10787 (2015). https://doi.org/http://dx.doi.org/10.1038/srep1078710.1038/srep10787. https://www.nature.com/articles/srep10787

  19. Sacha, K.: Modeling spontaneous breaking of time-translation symmetry. Phys. Rev. A 91, 033617 (2015). https://doi.org/10.1103/PhysRevA.91.033617

    Article  ADS  Google Scholar 

  20. Sacha, K., Zakrzewski, J.: Time crystals: a review. Rep. Prog. Phys. 81(1), 016401 (2017). https://doi.org/10.1088/1361-6633/aa8b38

    Article  ADS  MathSciNet  Google Scholar 

  21. Shapere, A., Wilczek, F.: Classical time crystals. Phys. Rev. Lett. 109, 160402 (2012). https://doi.org/10.1103/PhysRevLett.109.160402

    Article  ADS  Google Scholar 

  22. Syrwid, A., Zakrzewski, J., Sacha, K.: Time crystal behavior of excited eigenstates. Phys. Rev. Lett. 119, 250602 (2017). https://doi.org/10.1103/PhysRevLett.119.250602

    Article  ADS  Google Scholar 

  23. Watanabe, H., Oshikawa, M.: Absence of quantum time crystals. Phys. Rev. Lett. 114, 251603 (2015). https://doi.org/10.1103/PhysRevLett.114.251603

    Article  ADS  MathSciNet  Google Scholar 

  24. Watanabe, H., Oshikawa, M., Koma, T.: Proof of the absence of long-range temporal orders in Gibbs states. J. Stat. Phys. 178(4), 926–935 (2020). https://doi.org/10.1007/s10955-019-02471-5

    Article  ADS  MathSciNet  Google Scholar 

  25. Wilczek, F.: Quantum time crystals. Phys. Rev. Lett. 109, 160401 (2012). https://doi.org/10.1103/PhysRevLett.109.160401

    Article  ADS  Google Scholar 

  26. Witthaut, D., Timme, M.: Kuramoto dynamics in Hamiltonian systems. Phys. Rev. E 90, 032917 (2014). https://doi.org/10.1103/PhysRevE.90.032917

    Article  ADS  Google Scholar 

  27. Zhang, J., Hess, P.W., Kyprianidis, A., Becker, P., Lee, A., Smith, J., Pagano, G., Potirniche, I.D., Potter, A.C., Vishwanath, A., Yao, N.Y., Monroe, C.: Observation of a discrete time crystal. Nature 543(7644), 217–220 (2017). Letter. https://doi.org/10.1038/nature21413

  28. Zurita-Sánchez, J.R., Halevi, P., Cervantes-González, J.C.: Reflection and transmission of a wave incident on a slab with a time-periodic dielectric function 𝜖(t). Phys. Rev. A 79, 053821 (2009). https://doi.org/10.1103/PhysRevA.79.053821

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Sacha, K. (2020). Introduction. In: Time Crystals. Springer Series on Atomic, Optical, and Plasma Physics, vol 114. Springer, Cham. https://doi.org/10.1007/978-3-030-52523-1_1

Download citation

Publish with us

Policies and ethics