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Quantum Time Crystals

Frank Wilczek
Phys. Rev. Lett. 109, 160401 – Published 15 October 2012
Physics logo See Viewpoint: Crystals of Time

Abstract

Some subtleties and apparent difficulties associated with the notion of spontaneous breaking of time-translation symmetry in quantum mechanics are identified and resolved. A model exhibiting that phenomenon is displayed. The possibility and significance of breaking of imaginary time-translation symmetry is discussed.

  • Received 29 March 2012

DOI:https://doi.org/10.1103/PhysRevLett.109.160401

© 2012 American Physical Society

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Crystals of Time

Published 15 October 2012

Researchers propose how to realize time crystals, structures whose lowest-energy states are periodic both in time and space.

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Authors & Affiliations

Frank Wilczek

  • Center for Theoretical Physics Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA

Comments & Replies

Comment on “Quantum Time Crystals”

Patrick Bruno
Phys. Rev. Lett. 110, 118901 (2013)

Wilczek Reply:

Frank Wilczek
Phys. Rev. Lett. 110, 118902 (2013)

See Also

Classical Time Crystals

Alfred Shapere and Frank Wilczek
Phys. Rev. Lett. 109, 160402 (2012)

Space-Time Crystals of Trapped Ions

Tongcang Li, Zhe-Xuan Gong, Zhang-Qi Yin, H. T. Quan, Xiaobo Yin, Peng Zhang, L.-M. Duan, and Xiang Zhang
Phys. Rev. Lett. 109, 163001 (2012)

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Issue

Vol. 109, Iss. 16 — 19 October 2012

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