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
Viewpoint
ViewpointCrystals 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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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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