Time crystal (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Time crystal" in English language version.

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aps.org

physics.aps.org

Zakrzewski, Jakub (15 October 2012). "Viewpoint: Crystals of Time". physics.aps.org. APS Physics. Archived from the original on 2 February 2017.
Richerme, Phil (January 18, 2017). "How to Create a Time Crystal". Physics. 10. American Physical Society: 5. Bibcode:2017PhyOJ..10....5R. doi:10.1103/Physics.10.5. Retrieved 5 April 2021.
Thomas, Jessica (15 March 2013). "Notes from the Editors: The Aftermath of a Controversial Idea". physics.aps.org. APS Physics. Archived from the original on 2 February 2017.
Yao, N. Y.; Potter, A. C.; Potirniche, I.-D.; Vishwanath, A. (2017). "Discrete Time Crystals: Rigidity, Criticality, and Realizations". Physical Review Letters. 118 (3): 030401. arXiv:1608.02589. Bibcode:2017PhRvL.118c0401Y. doi:10.1103/PhysRevLett.118.030401. ISSN 0031-9007. PMID 28157355. S2CID 206284432.
Gong, Zongping; Ueda, Masahito (2021-07-19). "Time Crystals in Open Systems". Physics. 14: 104. Bibcode:2021PhyOJ..14..104G. doi:10.1103/Physics.14.104. S2CID 244256783.

link.aps.org

Buča, Berislav; Jaksch, Dieter (2019-12-23). "Dissipation Induced Nonstationarity in a Quantum Gas". Physical Review Letters. 123 (26): 260401. arXiv:1905.12880. Bibcode:2019PhRvL.123z0401B. doi:10.1103/PhysRevLett.123.260401. PMID 31951440. S2CID 170079211.
Iemini, F.; Russomanno, A.; Keeling, J.; Schirò, M.; Dalmonte, M.; Fazio, R. (2018-07-16). "Boundary Time Crystals". Physical Review Letters. 121 (3): 035301. arXiv:1708.05014. Bibcode:2018PhRvL.121c5301I. doi:10.1103/PhysRevLett.121.035301. hdl:10023/14492. PMID 30085780. S2CID 51683292.
Keßler, Hans; Kongkhambut, Phatthamon; Georges, Christoph; Mathey, Ludwig; Cosme, Jayson G.; Hemmerich, Andreas (2021-07-19). "Observation of a Dissipative Time Crystal". Physical Review Letters. 127 (4): 043602. arXiv:2012.08885. Bibcode:2021PhRvL.127d3602K. doi:10.1103/PhysRevLett.127.043602. PMID 34355967. S2CID 229210935.
Piazza, Francesco; Ritsch, Helmut (2015-10-15). "Self-Ordered Limit Cycles, Chaos, and Phase Slippage with a Superfluid inside an Optical Resonator". Physical Review Letters. 115 (16): 163601. arXiv:1507.08644. Bibcode:2015PhRvL.115p3601P. doi:10.1103/PhysRevLett.115.163601. PMID 26550874. S2CID 5080527.
Träger, Nick; Gruszecki, Paweł; Lisiecki, Filip; Groß, Felix; Förster, Johannes; Weigand, Markus; Głowiński, Hubert; Kuświk, Piotr; Dubowik, Janusz; Schütz, Gisela; Krawczyk, Maciej (2021-02-03). "Real-Space Observation of Magnon Interaction with Driven Space–Time Crystals". Physical Review Letters. 126 (5): 057201. arXiv:1911.13192. Bibcode:2021PhRvL.126e7201T. doi:10.1103/PhysRevLett.126.057201. PMID 33605763. S2CID 208512720.

archive.today

Zakrzewski, Jakub (15 October 2012). "Viewpoint: Crystals of Time". physics.aps.org. APS Physics. Archived from the original on 2 February 2017.
Wolchover, Natalie (25 April 2013). "Perpetual Motion Test Could Amend Theory of Time". quantamagazine.org. Simons Foundation. Archived from the original on 2 February 2017.
Thomas, Jessica (15 March 2013). "Notes from the Editors: The Aftermath of a Controversial Idea". physics.aps.org. APS Physics. Archived from the original on 2 February 2017.

arxiv.org

Sacha, Krzysztof (2015). "Modeling spontaneous breaking of time-translation symmetry". Physical Review A. 91 (3): 033617. arXiv:1410.3638. Bibcode:2015PhRvA..91c3617S. doi:10.1103/PhysRevA.91.033617. ISSN 1050-2947. S2CID 118627872.
Khemani et al. (2016) Khemani, Vedika; Lazarides, Achilleas; Moessner, Roderich; Sondhi, S. L. (2016). "Phase Structure of Driven Quantum Systems". Physical Review Letters. 116 (25): 250401. arXiv:1508.03344. Bibcode:2016PhRvL.116y0401K. doi:10.1103/PhysRevLett.116.250401. ISSN 0031-9007. PMID 27391704. S2CID 883197.
Else et al. (2016). Else, Dominic V.; Bauer, Bela; Nayak, Chetan (2016). "Floquet Time Crystals". Physical Review Letters. 117 (9): 090402. arXiv:1603.08001. Bibcode:2016PhRvL.117i0402E. doi:10.1103/PhysRevLett.117.090402. ISSN 0031-9007. PMID 27610834. S2CID 1652633.
Sacha, Krzysztof; Zakrzewski, Jakub (1 January 2018). "Time crystals: a review". Reports on Progress in Physics. 81 (1): 016401. arXiv:1704.03735. Bibcode:2018RPPh...81a6401S. doi:10.1088/1361-6633/aa8b38. PMID 28885193. S2CID 28224975.
Else, D. W.; Monroe, C.; Nayak, C.; Yao, N. Y. (March 2020). "Discrete Time Crystals". Annual Review of Condensed Matter Physics. 11: 467–499. arXiv:1905.13232. Bibcode:2020ARCMP..11..467E. doi:10.1146/annurev-conmatphys-031119-050658. S2CID 173188223.
Yao; Nayak (2018). "Time crystals in periodically driven systems". Physics Today. 71 (9): 40–47. arXiv:1811.06657. Bibcode:2018PhT....71i..40Y. doi:10.1063/PT.3.4020. ISSN 0031-9228. S2CID 119433979.
Mi, Xiao; Ippoliti, Matteo; Quintana, Chris; Greene, Ami; Chen, Zijun; Gross, Jonathan; Arute, Frank; Arya, Kunal; Atalaya, Juan; Babbush, Ryan; Bardin, Joseph C. (2022). "Time-Crystalline Eigenstate Order on a Quantum Processor". Nature. 601 (7894): 531–536. arXiv:2107.13571. Bibcode:2022Natur.601..531M. doi:10.1038/s41586-021-04257-w. ISSN 1476-4687. PMC 8791837. PMID 34847568.
Wilczek, Frank (2012). "Quantum Time Crystals". Physical Review Letters. 109 (16): 160401. arXiv:1202.2539. Bibcode:2012PhRvL.109p0401W. doi:10.1103/PhysRevLett.109.160401. ISSN 0031-9007. PMID 23215056. S2CID 1312256.
Shapere, Alfred; Wilczek, Frank (2012). "Classical Time Crystals". Physical Review Letters. 109 (16): 160402. arXiv:1202.2537. Bibcode:2012PhRvL.109p0402S. doi:10.1103/PhysRevLett.109.160402. ISSN 0031-9007. PMID 23215057. S2CID 4506464.
See Li et al. (2012a, 2012b). Li, Tongcang; Gong, Zhe-Xuan; Yin, Zhang-Qi; Quan, H. T.; Yin, Xiaobo; Zhang, Peng; Duan, L.-M.; Zhang, Xiang (2012a). "Space-Time Crystals of Trapped Ions". Physical Review Letters. 109 (16): 163001. arXiv:1206.4772. Bibcode:2012PhRvL.109p3001L. doi:10.1103/PhysRevLett.109.163001. ISSN 0031-9007. PMID 23215073. S2CID 8198228. Li, Tongcang; Gong, Zhe-Xuan; Yin, Zhang-Qi; Quan, H. T.; Yin, Xiaobo; Zhang, Peng; Duan, L.-M.; Zhang, Xiang (2012). "Reply to Comment on "Space–Time Crystals of Trapped Ions"". Unpublished. arXiv:1212.6959. Bibcode:2012arXiv1212.6959L.
See Bruno (2013a) and Bruno (2013b). Bruno, Patrick (2013a). "Comment on 'Quantum Time Crystals'". Physical Review Letters. 110 (11): 118901. arXiv:1210.4128. Bibcode:2013PhRvL.110k8901B. doi:10.1103/PhysRevLett.110.118901. ISSN 0031-9007. PMID 25166585. S2CID 41459498. Bruno, Patrick (2013b). "Comment on "Space-Time Crystals of Trapped Ions"". Physical Review Letters. 111 (2): 029301. arXiv:1211.4792. Bibcode:2013PhRvL.111b9301B. doi:10.1103/PhysRevLett.111.029301. ISSN 0031-9007. PMID 23889455. S2CID 1502258.
See Nozières (2013), Yao et al. (2017), p. 1 and Volovik (2013). Nozières, Philippe (2013). "Time crystals: Can diamagnetic currents drive a charge density wave into rotation?". EPL. 103 (5): 57008. arXiv:1306.6229. Bibcode:2013EL....10357008N. doi:10.1209/0295-5075/103/57008. ISSN 0295-5075. S2CID 118662499. Volovik, G. E. (2013). "On the broken time translation symmetry in macroscopic systems: Precessing states and off-diagonal long-range order". JETP Letters. 98 (8): 491–495. arXiv:1309.1845. Bibcode:2013JETPL..98..491V. doi:10.1134/S0021364013210133. ISSN 0021-3640. S2CID 119100114.
Watanabe, Haruki; Oshikawa, Masaki (2015). "Absence of Quantum Time Crystals". Physical Review Letters. 114 (25): 251603. arXiv:1410.2143. Bibcode:2015PhRvL.114y1603W. doi:10.1103/PhysRevLett.114.251603. ISSN 0031-9007. PMID 26197119. S2CID 312538.
Medenjak, Marko; Buča, Berislav; Jaksch, Dieter (2020-07-20). "Isolated Heisenberg magnet as a quantum time crystal". Physical Review B. 102 (4): 041117. arXiv:1905.08266. Bibcode:2020PhRvB.102d1117M. doi:10.1103/physrevb.102.041117. ISSN 2469-9950. S2CID 160009779.
Khemani, Vedika; Moessner, Roderich; Sondhi, S. L. (23 October 2019). "A Brief History of Time Crystals". arXiv:1910.10745 [cond-mat.str-el].
Uhrich, P.; Defenu, N.; Jafari, R.; Halimeh, J. C. (2020). "Out-of-equilibrium phase diagram of long-range superconductors". Physical Review B. 101 (24): 245148. arXiv:1910.10715. Bibcode:2020PhRvB.101x5148U. doi:10.1103/physrevb.101.245148.
See Wilczek (2013b) and Yoshii et al. (2015). Wilczek, Frank (2013b). "Superfluidity and Space–Time Translation Symmetry Breaking". Physical Review Letters. 111 (25): 250402. arXiv:1308.5949. Bibcode:2013PhRvL.111y0402W. doi:10.1103/PhysRevLett.111.250402. ISSN 0031-9007. PMID 24483732. S2CID 7537145. Yoshii, Ryosuke; Takada, Satoshi; Tsuchiya, Shunji; Marmorini, Giacomo; Hayakawa, Hisao; Nitta, Muneto (2015). "Fulde-Ferrell-Larkin-Ovchinnikov states in a superconducting ring with magnetic fields: Phase diagram and the first-order phase transitions". Physical Review B. 92 (22): 224512. arXiv:1404.3519. Bibcode:2015PhRvB..92v4512Y. doi:10.1103/PhysRevB.92.224512. ISSN 1098-0121. S2CID 118348062.
Sacha, Krzysztof (2015). "Modeling spontaneous breaking of time-translation symmetry". Physical Review A. 91 (3): 033617. arXiv:1410.3638. Bibcode:2015PhRvA..91c3617S. doi:10.1103/PhysRevA.91.033617. ISSN 1050-2947. S2CID 118627872. We show that an ultracold atomic cloud bouncing on an oscillating mirror can reveal spontaneous breaking of a discrete time-translation symmetry
See Khemani et al. (2016) and Else et al. (2016) Khemani, Vedika; Lazarides, Achilleas; Moessner, Roderich; Sondhi, S. L. (2016). "Phase Structure of Driven Quantum Systems". Physical Review Letters. 116 (25): 250401. arXiv:1508.03344. Bibcode:2016PhRvL.116y0401K. doi:10.1103/PhysRevLett.116.250401. ISSN 0031-9007. PMID 27391704. S2CID 883197. Else, Dominic V.; Bauer, Bela; Nayak, Chetan (2016). "Floquet Time Crystals". Physical Review Letters. 117 (9): 090402. arXiv:1603.08001. Bibcode:2016PhRvL.117i0402E. doi:10.1103/PhysRevLett.117.090402. ISSN 0031-9007. PMID 27610834. S2CID 1652633.
Yao, N. Y.; Potter, A. C.; Potirniche, I.-D.; Vishwanath, A. (2017). "Discrete Time Crystals: Rigidity, Criticality, and Realizations". Physical Review Letters. 118 (3): 030401. arXiv:1608.02589. Bibcode:2017PhRvL.118c0401Y. doi:10.1103/PhysRevLett.118.030401. ISSN 0031-9007. PMID 28157355. S2CID 206284432.
Choi, Soonwon; Choi, Joonhee; Landig, Renate; Kucsko, Georg; Zhou, Hengyun; Isoya, Junichi; Jelezko, Fedor; Onoda, Shinobu; Sumiya, Hitoshi; Khemani, Vedika; von Keyserlingk, Curt; Yao, Norman Y.; Demler, Eugene; Lukin, Mikhail D. (2017). "Observation of discrete time-crystalline order in a disordered dipolar many-body system". Nature. 543 (7644): 221–225. arXiv:1610.08057. Bibcode:2017Natur.543..221C. doi:10.1038/nature21426. ISSN 0028-0836. PMC 5349499. PMID 28277511.
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. (2017). "Observation of a discrete time crystal". Nature. 543 (7644): 217–220. arXiv:1609.08684. Bibcode:2017Natur.543..217Z. doi:10.1038/nature21413. PMID 28277505. S2CID 4450646.
Iemini, Fernando; Russomanno, Angelo; Keeling, Jonathan; Schirò, Marco; Dalmonte, Marcello; Fazio, Rosario (16 July 2018). "Boundary time crystals". Phys. Rev. Lett. 121 (35301): 035301. arXiv:1708.05014. Bibcode:2018PhRvL.121c5301I. doi:10.1103/PhysRevLett.121.035301. PMID 30085780. S2CID 51683292.
Gong, Zongping; Hamazaki, Ryusuke; Ueda, Masahito (25 January 2018). "Discrete Time-Crystalline Order in Cavity and Circuit QED Systems". Phys. Rev. Lett. 120 (40404): 040404. arXiv:1708.01472. Bibcode:2018PhRvL.120d0404G. doi:10.1103/PhysRevLett.120.040404. PMID 29437420. S2CID 206307409.
Filippo Maria, Gambetta; Carollo, Federico; Marcuzzi, Matteo; Garrahan, Juan P.; Lesanovsky, Igor (8 January 2019). "Discrete Time Crystals in the Absence of Manifest Symmetries or Disorder in Open Quantum Systems". Phys. Rev. Lett. 122 (15701): 015701. arXiv:1807.10161. Bibcode:2019PhRvL.122a5701G. doi:10.1103/PhysRevLett.122.015701. PMID 31012672. S2CID 119187766.
Buča, Berislav; Jaksch, Dieter (2019-12-23). "Dissipation Induced Nonstationarity in a Quantum Gas". Physical Review Letters. 123 (26): 260401. arXiv:1905.12880. Bibcode:2019PhRvL.123z0401B. doi:10.1103/PhysRevLett.123.260401. PMID 31951440. S2CID 170079211.
Iemini, F.; Russomanno, A.; Keeling, J.; Schirò, M.; Dalmonte, M.; Fazio, R. (2018-07-16). "Boundary Time Crystals". Physical Review Letters. 121 (3): 035301. arXiv:1708.05014. Bibcode:2018PhRvL.121c5301I. doi:10.1103/PhysRevLett.121.035301. hdl:10023/14492. PMID 30085780. S2CID 51683292.
Buča, Berislav; Tindall, Joseph; Jaksch, Dieter (2019-04-15). "Non-stationary coherent quantum many-body dynamics through dissipation". Nature Communications. 10 (1): 1730. arXiv:1804.06744. Bibcode:2019NatCo..10.1730B. doi:10.1038/s41467-019-09757-y. ISSN 2041-1723. PMC 6465298. PMID 30988312.
Keßler, Hans; Kongkhambut, Phatthamon; Georges, Christoph; Mathey, Ludwig; Cosme, Jayson G.; Hemmerich, Andreas (2021-07-19). "Observation of a Dissipative Time Crystal". Physical Review Letters. 127 (4): 043602. arXiv:2012.08885. Bibcode:2021PhRvL.127d3602K. doi:10.1103/PhysRevLett.127.043602. PMID 34355967. S2CID 229210935.
Piazza, Francesco; Ritsch, Helmut (2015-10-15). "Self-Ordered Limit Cycles, Chaos, and Phase Slippage with a Superfluid inside an Optical Resonator". Physical Review Letters. 115 (16): 163601. arXiv:1507.08644. Bibcode:2015PhRvL.115p3601P. doi:10.1103/PhysRevLett.115.163601. PMID 26550874. S2CID 5080527.
Dogra, Nishant; Landini, Manuele; Kroeger, Katrin; Hruby, Lorenz; Donner, Tobias; Esslinger, Tilman (2019-12-20). "Dissipation-induced structural instability and chiral dynamics in a quantum gas". Science. 366 (6472): 1496–1499. arXiv:1901.05974. Bibcode:2019Sci...366.1496D. doi:10.1126/science.aaw4465. ISSN 0036-8075. PMID 31857481. S2CID 119283814.
Kozin, Valerii K.; Kyriienko, Oleksandr (2019-11-20). "Quantum Time Crystals from Hamiltonians with Long-Range Interactions". Physical Review Letters. 123 (21): 210602. arXiv:1907.07215. Bibcode:2019PhRvL.123u0602K. doi:10.1103/PhysRevLett.123.210602. ISSN 0031-9007. PMID 31809146. S2CID 197431242.
Khemani, Vedika; Moessner, Roderich; Sondhi, S. L. (2020). "Comment on 'Quantum Time Crystals from Hamiltonians with Long-Range Interactions'". arXiv:2001.11037 [cond-mat.str-el].
Kongkhambut, Phatthamon; Skulte, Jim; Mathey, Ludwig; Cosme, Jayson G.; Hemmerich, Andreas; Keßler, Hans (2022-08-05). "Observation of a continuous time crystal". Science. 377 (6606): 670–673. arXiv:2202.06980. Bibcode:2022Sci...377..670K. doi:10.1126/science.abo3382. ISSN 0036-8075. PMID 35679353. S2CID 246863968.
Autti, S.; Eltsov, V. B.; Volovik, G. E. (May 2018). "Observation of a Time Quasicrystal and Its Transition to a Superfluid Time Crystal". Physical Review Letters. 120 (21): 215301. arXiv:1712.06877. Bibcode:2018PhRvL.120u5301A. doi:10.1103/PhysRevLett.120.215301. PMID 29883148. S2CID 46997186.
Autti, S.; Heikkinen, P. J.; Mäkinen, J. T.; Volovik, G. E.; Zavjalov, V. V.; Eltsov, V. B. (February 2021). "AC Josephson effect between two superfluid time crystals". Nature Materials. 20 (2): 171–174. arXiv:2003.06313. Bibcode:2021NatMa..20..171A. doi:10.1038/s41563-020-0780-y. PMID 32807922. S2CID 212717702.
Träger, Nick; Gruszecki, Paweł; Lisiecki, Filip; Groß, Felix; Förster, Johannes; Weigand, Markus; Głowiński, Hubert; Kuświk, Piotr; Dubowik, Janusz; Schütz, Gisela; Krawczyk, Maciej (2021-02-03). "Real-Space Observation of Magnon Interaction with Driven Space–Time Crystals". Physical Review Letters. 126 (5): 057201. arXiv:1911.13192. Bibcode:2021PhRvL.126e7201T. doi:10.1103/PhysRevLett.126.057201. PMID 33605763. S2CID 208512720.
Kyprianidis, A.; Machado, F.; Morong, W.; Becker, P.; Collins, K. S.; Else, D. V.; Feng, L.; Hess, P. W.; Nayak, C.; Pagano, G.; Yao, N. Y. (2021-06-11). "Observation of a prethermal discrete time crystal". Science. 372 (6547): 1192–1196. arXiv:2102.01695. Bibcode:2021Sci...372.1192K. doi:10.1126/science.abg8102. ISSN 0036-8075. PMID 34112691. S2CID 231786633.
Randall, J.; Bradley, C. E.; van der Gronden, F. V.; Galicia, A.; Abobeih, M. H.; Markham, M.; Twitchen, D. J.; Machado, F.; Yao, N. Y.; Taminiau, T. H. (2021-12-17). "Many-body–localized discrete time crystal with a programmable spin-based quantum simulator". Science. 374 (6574): 1474–1478. arXiv:2107.00736. Bibcode:2021Sci...374.1474R. doi:10.1126/science.abk0603. ISSN 0036-8075. PMID 34735218. S2CID 235727352.
Frey, Philipp; Rachel, Stephan (2022-03-04). "Realization of a discrete time crystal on 57 qubits of a quantum computer". Science Advances. 8 (9): eabm7652. arXiv:2105.06632. Bibcode:2022SciA....8M7652F. doi:10.1126/sciadv.abm7652. ISSN 2375-2548. PMC 8890700. PMID 35235347.

books.google.com

Cao, Tian Yu (25 March 2004). Conceptual Foundations of Quantum Field Theory. Cambridge: Cambridge University Press. ISBN 978-0-521-60272-3. See p. 151.
Wilczek, Frank (16 July 2015). A Beautiful Question: Finding Nature's Deep Design. Penguin Books Limited. ISBN 978-1-84614-702-9. See Ch. 3.
Feng, Duan; Jin, Guojun (2005). Introduction to Condensed Matter Physics. singapore: World Scientific. ISBN 978-981-238-711-0. See p. 18.
Sólyom, Jenö (19 September 2007). Fundamentals of the Physics of Solids: Volume 1: Structure and Dynamics. Springer. ISBN 978-3-540-72600-5. See p. 193.
Sólyom, Jenö (19 September 2007). Fundamentals of the Physics of Solids: Volume 1: Structure and Dynamics. Springer. ISBN 978-3-540-72600-5. See p. 191.

doi.org

Sacha, Krzysztof (2015). "Modeling spontaneous breaking of time-translation symmetry". Physical Review A. 91 (3): 033617. arXiv:1410.3638. Bibcode:2015PhRvA..91c3617S. doi:10.1103/PhysRevA.91.033617. ISSN 1050-2947. S2CID 118627872.
Khemani et al. (2016) Khemani, Vedika; Lazarides, Achilleas; Moessner, Roderich; Sondhi, S. L. (2016). "Phase Structure of Driven Quantum Systems". Physical Review Letters. 116 (25): 250401. arXiv:1508.03344. Bibcode:2016PhRvL.116y0401K. doi:10.1103/PhysRevLett.116.250401. ISSN 0031-9007. PMID 27391704. S2CID 883197.
Else et al. (2016). Else, Dominic V.; Bauer, Bela; Nayak, Chetan (2016). "Floquet Time Crystals". Physical Review Letters. 117 (9): 090402. arXiv:1603.08001. Bibcode:2016PhRvL.117i0402E. doi:10.1103/PhysRevLett.117.090402. ISSN 0031-9007. PMID 27610834. S2CID 1652633.
Richerme, Phil (January 18, 2017). "How to Create a Time Crystal". Physics. 10. American Physical Society: 5. Bibcode:2017PhyOJ..10....5R. doi:10.1103/Physics.10.5. Retrieved 5 April 2021.
Sacha, Krzysztof; Zakrzewski, Jakub (1 January 2018). "Time crystals: a review". Reports on Progress in Physics. 81 (1): 016401. arXiv:1704.03735. Bibcode:2018RPPh...81a6401S. doi:10.1088/1361-6633/aa8b38. PMID 28885193. S2CID 28224975.
Ball, Philip (July 17, 2018). "In search of time crystals". Physics World. 31 (7): 29. Bibcode:2018PhyW...31g..29B. doi:10.1088/2058-7058/31/7/32. S2CID 125917780. Retrieved September 6, 2021. The "discrete" comes from the fact that their periodicity is a discrete, integer multiple of the driving period.
Else, D. W.; Monroe, C.; Nayak, C.; Yao, N. Y. (March 2020). "Discrete Time Crystals". Annual Review of Condensed Matter Physics. 11: 467–499. arXiv:1905.13232. Bibcode:2020ARCMP..11..467E. doi:10.1146/annurev-conmatphys-031119-050658. S2CID 173188223.
Yao; Nayak (2018). "Time crystals in periodically driven systems". Physics Today. 71 (9): 40–47. arXiv:1811.06657. Bibcode:2018PhT....71i..40Y. doi:10.1063/PT.3.4020. ISSN 0031-9228. S2CID 119433979.
Mi, Xiao; Ippoliti, Matteo; Quintana, Chris; Greene, Ami; Chen, Zijun; Gross, Jonathan; Arute, Frank; Arya, Kunal; Atalaya, Juan; Babbush, Ryan; Bardin, Joseph C. (2022). "Time-Crystalline Eigenstate Order on a Quantum Processor". Nature. 601 (7894): 531–536. arXiv:2107.13571. Bibcode:2022Natur.601..531M. doi:10.1038/s41586-021-04257-w. ISSN 1476-4687. PMC 8791837. PMID 34847568.
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gizmodo.com

"A Time Crystal Survived a Whopping 40 Minutes". 6 February 2024.

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hdl.handle.net

Iemini, F.; Russomanno, A.; Keeling, J.; Schirò, M.; Dalmonte, M.; Fazio, R. (2018-07-16). "Boundary Time Crystals". Physical Review Letters. 121 (3): 035301. arXiv:1708.05014. Bibcode:2018PhRvL.121c5301I. doi:10.1103/PhysRevLett.121.035301. hdl:10023/14492. PMID 30085780. S2CID 51683292.

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Else et al. (2016). Else, Dominic V.; Bauer, Bela; Nayak, Chetan (2016). "Floquet Time Crystals". Physical Review Letters. 117 (9): 090402. arXiv:1603.08001. Bibcode:2016PhRvL.117i0402E. doi:10.1103/PhysRevLett.117.090402. ISSN 0031-9007. PMID 27610834. S2CID 1652633.
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Ball, Philip (July 17, 2018). "In search of time crystals". Physics World. 31 (7): 29. Bibcode:2018PhyW...31g..29B. doi:10.1088/2058-7058/31/7/32. S2CID 125917780. Retrieved September 6, 2021. The "discrete" comes from the fact that their periodicity is a discrete, integer multiple of the driving period.
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Yao; Nayak (2018). "Time crystals in periodically driven systems". Physics Today. 71 (9): 40–47. arXiv:1811.06657. Bibcode:2018PhT....71i..40Y. doi:10.1063/PT.3.4020. ISSN 0031-9228. S2CID 119433979.
Mi, Xiao; Ippoliti, Matteo; Quintana, Chris; Greene, Ami; Chen, Zijun; Gross, Jonathan; Arute, Frank; Arya, Kunal; Atalaya, Juan; Babbush, Ryan; Bardin, Joseph C. (2022). "Time-Crystalline Eigenstate Order on a Quantum Processor". Nature. 601 (7894): 531–536. arXiv:2107.13571. Bibcode:2022Natur.601..531M. doi:10.1038/s41586-021-04257-w. ISSN 1476-4687. PMC 8791837. PMID 34847568.
Wilczek, Frank (2012). "Quantum Time Crystals". Physical Review Letters. 109 (16): 160401. arXiv:1202.2539. Bibcode:2012PhRvL.109p0401W. doi:10.1103/PhysRevLett.109.160401. ISSN 0031-9007. PMID 23215056. S2CID 1312256.
Shapere, Alfred; Wilczek, Frank (2012). "Classical Time Crystals". Physical Review Letters. 109 (16): 160402. arXiv:1202.2537. Bibcode:2012PhRvL.109p0402S. doi:10.1103/PhysRevLett.109.160402. ISSN 0031-9007. PMID 23215057. S2CID 4506464.
See Li et al. (2012a, 2012b). Li, Tongcang; Gong, Zhe-Xuan; Yin, Zhang-Qi; Quan, H. T.; Yin, Xiaobo; Zhang, Peng; Duan, L.-M.; Zhang, Xiang (2012a). "Space-Time Crystals of Trapped Ions". Physical Review Letters. 109 (16): 163001. arXiv:1206.4772. Bibcode:2012PhRvL.109p3001L. doi:10.1103/PhysRevLett.109.163001. ISSN 0031-9007. PMID 23215073. S2CID 8198228. Li, Tongcang; Gong, Zhe-Xuan; Yin, Zhang-Qi; Quan, H. T.; Yin, Xiaobo; Zhang, Peng; Duan, L.-M.; Zhang, Xiang (2012). "Reply to Comment on "Space–Time Crystals of Trapped Ions"". Unpublished. arXiv:1212.6959. Bibcode:2012arXiv1212.6959L.
See Bruno (2013a) and Bruno (2013b). Bruno, Patrick (2013a). "Comment on 'Quantum Time Crystals'". Physical Review Letters. 110 (11): 118901. arXiv:1210.4128. Bibcode:2013PhRvL.110k8901B. doi:10.1103/PhysRevLett.110.118901. ISSN 0031-9007. PMID 25166585. S2CID 41459498. Bruno, Patrick (2013b). "Comment on "Space-Time Crystals of Trapped Ions"". Physical Review Letters. 111 (2): 029301. arXiv:1211.4792. Bibcode:2013PhRvL.111b9301B. doi:10.1103/PhysRevLett.111.029301. ISSN 0031-9007. PMID 23889455. S2CID 1502258.
See Nozières (2013), Yao et al. (2017), p. 1 and Volovik (2013). Nozières, Philippe (2013). "Time crystals: Can diamagnetic currents drive a charge density wave into rotation?". EPL. 103 (5): 57008. arXiv:1306.6229. Bibcode:2013EL....10357008N. doi:10.1209/0295-5075/103/57008. ISSN 0295-5075. S2CID 118662499. Volovik, G. E. (2013). "On the broken time translation symmetry in macroscopic systems: Precessing states and off-diagonal long-range order". JETP Letters. 98 (8): 491–495. arXiv:1309.1845. Bibcode:2013JETPL..98..491V. doi:10.1134/S0021364013210133. ISSN 0021-3640. S2CID 119100114.
Watanabe, Haruki; Oshikawa, Masaki (2015). "Absence of Quantum Time Crystals". Physical Review Letters. 114 (25): 251603. arXiv:1410.2143. Bibcode:2015PhRvL.114y1603W. doi:10.1103/PhysRevLett.114.251603. ISSN 0031-9007. PMID 26197119. S2CID 312538.
Medenjak, Marko; Buča, Berislav; Jaksch, Dieter (2020-07-20). "Isolated Heisenberg magnet as a quantum time crystal". Physical Review B. 102 (4): 041117. arXiv:1905.08266. Bibcode:2020PhRvB.102d1117M. doi:10.1103/physrevb.102.041117. ISSN 2469-9950. S2CID 160009779.
Uhrich, P.; Defenu, N.; Jafari, R.; Halimeh, J. C. (2020). "Out-of-equilibrium phase diagram of long-range superconductors". Physical Review B. 101 (24): 245148. arXiv:1910.10715. Bibcode:2020PhRvB.101x5148U. doi:10.1103/physrevb.101.245148.
See Wilczek (2013b) and Yoshii et al. (2015). Wilczek, Frank (2013b). "Superfluidity and Space–Time Translation Symmetry Breaking". Physical Review Letters. 111 (25): 250402. arXiv:1308.5949. Bibcode:2013PhRvL.111y0402W. doi:10.1103/PhysRevLett.111.250402. ISSN 0031-9007. PMID 24483732. S2CID 7537145. Yoshii, Ryosuke; Takada, Satoshi; Tsuchiya, Shunji; Marmorini, Giacomo; Hayakawa, Hisao; Nitta, Muneto (2015). "Fulde-Ferrell-Larkin-Ovchinnikov states in a superconducting ring with magnetic fields: Phase diagram and the first-order phase transitions". Physical Review B. 92 (22): 224512. arXiv:1404.3519. Bibcode:2015PhRvB..92v4512Y. doi:10.1103/PhysRevB.92.224512. ISSN 1098-0121. S2CID 118348062.
Sacha, Krzysztof (2015). "Modeling spontaneous breaking of time-translation symmetry". Physical Review A. 91 (3): 033617. arXiv:1410.3638. Bibcode:2015PhRvA..91c3617S. doi:10.1103/PhysRevA.91.033617. ISSN 1050-2947. S2CID 118627872. We show that an ultracold atomic cloud bouncing on an oscillating mirror can reveal spontaneous breaking of a discrete time-translation symmetry
See Khemani et al. (2016) and Else et al. (2016) Khemani, Vedika; Lazarides, Achilleas; Moessner, Roderich; Sondhi, S. L. (2016). "Phase Structure of Driven Quantum Systems". Physical Review Letters. 116 (25): 250401. arXiv:1508.03344. Bibcode:2016PhRvL.116y0401K. doi:10.1103/PhysRevLett.116.250401. ISSN 0031-9007. PMID 27391704. S2CID 883197. Else, Dominic V.; Bauer, Bela; Nayak, Chetan (2016). "Floquet Time Crystals". Physical Review Letters. 117 (9): 090402. arXiv:1603.08001. Bibcode:2016PhRvL.117i0402E. doi:10.1103/PhysRevLett.117.090402. ISSN 0031-9007. PMID 27610834. S2CID 1652633.
Yao, N. Y.; Potter, A. C.; Potirniche, I.-D.; Vishwanath, A. (2017). "Discrete Time Crystals: Rigidity, Criticality, and Realizations". Physical Review Letters. 118 (3): 030401. arXiv:1608.02589. Bibcode:2017PhRvL.118c0401Y. doi:10.1103/PhysRevLett.118.030401. ISSN 0031-9007. PMID 28157355. S2CID 206284432.
Choi, Soonwon; Choi, Joonhee; Landig, Renate; Kucsko, Georg; Zhou, Hengyun; Isoya, Junichi; Jelezko, Fedor; Onoda, Shinobu; Sumiya, Hitoshi; Khemani, Vedika; von Keyserlingk, Curt; Yao, Norman Y.; Demler, Eugene; Lukin, Mikhail D. (2017). "Observation of discrete time-crystalline order in a disordered dipolar many-body system". Nature. 543 (7644): 221–225. arXiv:1610.08057. Bibcode:2017Natur.543..221C. doi:10.1038/nature21426. ISSN 0028-0836. PMC 5349499. PMID 28277511.
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. (2017). "Observation of a discrete time crystal". Nature. 543 (7644): 217–220. arXiv:1609.08684. Bibcode:2017Natur.543..217Z. doi:10.1038/nature21413. PMID 28277505. S2CID 4450646.
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Gong, Zongping; Hamazaki, Ryusuke; Ueda, Masahito (25 January 2018). "Discrete Time-Crystalline Order in Cavity and Circuit QED Systems". Phys. Rev. Lett. 120 (40404): 040404. arXiv:1708.01472. Bibcode:2018PhRvL.120d0404G. doi:10.1103/PhysRevLett.120.040404. PMID 29437420. S2CID 206307409.
Filippo Maria, Gambetta; Carollo, Federico; Marcuzzi, Matteo; Garrahan, Juan P.; Lesanovsky, Igor (8 January 2019). "Discrete Time Crystals in the Absence of Manifest Symmetries or Disorder in Open Quantum Systems". Phys. Rev. Lett. 122 (15701): 015701. arXiv:1807.10161. Bibcode:2019PhRvL.122a5701G. doi:10.1103/PhysRevLett.122.015701. PMID 31012672. S2CID 119187766.
Buča, Berislav; Jaksch, Dieter (2019-12-23). "Dissipation Induced Nonstationarity in a Quantum Gas". Physical Review Letters. 123 (26): 260401. arXiv:1905.12880. Bibcode:2019PhRvL.123z0401B. doi:10.1103/PhysRevLett.123.260401. PMID 31951440. S2CID 170079211.
Iemini, F.; Russomanno, A.; Keeling, J.; Schirò, M.; Dalmonte, M.; Fazio, R. (2018-07-16). "Boundary Time Crystals". Physical Review Letters. 121 (3): 035301. arXiv:1708.05014. Bibcode:2018PhRvL.121c5301I. doi:10.1103/PhysRevLett.121.035301. hdl:10023/14492. PMID 30085780. S2CID 51683292.
Buča, Berislav; Tindall, Joseph; Jaksch, Dieter (2019-04-15). "Non-stationary coherent quantum many-body dynamics through dissipation". Nature Communications. 10 (1): 1730. arXiv:1804.06744. Bibcode:2019NatCo..10.1730B. doi:10.1038/s41467-019-09757-y. ISSN 2041-1723. PMC 6465298. PMID 30988312.
Keßler, Hans; Kongkhambut, Phatthamon; Georges, Christoph; Mathey, Ludwig; Cosme, Jayson G.; Hemmerich, Andreas (2021-07-19). "Observation of a Dissipative Time Crystal". Physical Review Letters. 127 (4): 043602. arXiv:2012.08885. Bibcode:2021PhRvL.127d3602K. doi:10.1103/PhysRevLett.127.043602. PMID 34355967. S2CID 229210935.
Gong, Zongping; Ueda, Masahito (2021-07-19). "Time Crystals in Open Systems". Physics. 14: 104. Bibcode:2021PhyOJ..14..104G. doi:10.1103/Physics.14.104. S2CID 244256783.
Ball, Philip (September 2021). "Quantum time crystals open up". Nature Materials. 20 (9): 1172. Bibcode:2021NatMa..20.1172B. doi:10.1038/s41563-021-01090-4. ISSN 1476-4660. PMID 34433935. S2CID 237299508.
Piazza, Francesco; Ritsch, Helmut (2015-10-15). "Self-Ordered Limit Cycles, Chaos, and Phase Slippage with a Superfluid inside an Optical Resonator". Physical Review Letters. 115 (16): 163601. arXiv:1507.08644. Bibcode:2015PhRvL.115p3601P. doi:10.1103/PhysRevLett.115.163601. PMID 26550874. S2CID 5080527.
Dogra, Nishant; Landini, Manuele; Kroeger, Katrin; Hruby, Lorenz; Donner, Tobias; Esslinger, Tilman (2019-12-20). "Dissipation-induced structural instability and chiral dynamics in a quantum gas". Science. 366 (6472): 1496–1499. arXiv:1901.05974. Bibcode:2019Sci...366.1496D. doi:10.1126/science.aaw4465. ISSN 0036-8075. PMID 31857481. S2CID 119283814.
Kozin, Valerii K.; Kyriienko, Oleksandr (2019-11-20). "Quantum Time Crystals from Hamiltonians with Long-Range Interactions". Physical Review Letters. 123 (21): 210602. arXiv:1907.07215. Bibcode:2019PhRvL.123u0602K. doi:10.1103/PhysRevLett.123.210602. ISSN 0031-9007. PMID 31809146. S2CID 197431242.
Kongkhambut, Phatthamon; Skulte, Jim; Mathey, Ludwig; Cosme, Jayson G.; Hemmerich, Andreas; Keßler, Hans (2022-08-05). "Observation of a continuous time crystal". Science. 377 (6606): 670–673. arXiv:2202.06980. Bibcode:2022Sci...377..670K. doi:10.1126/science.abo3382. ISSN 0036-8075. PMID 35679353. S2CID 246863968.
LeBlanc, Lindsay J. (2022-08-05). "Unleashing spontaneity in a time crystal". Science. 377 (6606): 576–577. Bibcode:2022Sci...377..576L. doi:10.1126/science.add2015. ISSN 0036-8075. PMID 35926056. S2CID 251349796.
Autti, S.; Eltsov, V. B.; Volovik, G. E. (May 2018). "Observation of a Time Quasicrystal and Its Transition to a Superfluid Time Crystal". Physical Review Letters. 120 (21): 215301. arXiv:1712.06877. Bibcode:2018PhRvL.120u5301A. doi:10.1103/PhysRevLett.120.215301. PMID 29883148. S2CID 46997186.
Autti, S.; Heikkinen, P. J.; Mäkinen, J. T.; Volovik, G. E.; Zavjalov, V. V.; Eltsov, V. B. (February 2021). "AC Josephson effect between two superfluid time crystals". Nature Materials. 20 (2): 171–174. arXiv:2003.06313. Bibcode:2021NatMa..20..171A. doi:10.1038/s41563-020-0780-y. PMID 32807922. S2CID 212717702.
Träger, Nick; Gruszecki, Paweł; Lisiecki, Filip; Groß, Felix; Förster, Johannes; Weigand, Markus; Głowiński, Hubert; Kuświk, Piotr; Dubowik, Janusz; Schütz, Gisela; Krawczyk, Maciej (2021-02-03). "Real-Space Observation of Magnon Interaction with Driven Space–Time Crystals". Physical Review Letters. 126 (5): 057201. arXiv:1911.13192. Bibcode:2021PhRvL.126e7201T. doi:10.1103/PhysRevLett.126.057201. PMID 33605763. S2CID 208512720.
Kyprianidis, A.; Machado, F.; Morong, W.; Becker, P.; Collins, K. S.; Else, D. V.; Feng, L.; Hess, P. W.; Nayak, C.; Pagano, G.; Yao, N. Y. (2021-06-11). "Observation of a prethermal discrete time crystal". Science. 372 (6547): 1192–1196. arXiv:2102.01695. Bibcode:2021Sci...372.1192K. doi:10.1126/science.abg8102. ISSN 0036-8075. PMID 34112691. S2CID 231786633.
Randall, J.; Bradley, C. E.; van der Gronden, F. V.; Galicia, A.; Abobeih, M. H.; Markham, M.; Twitchen, D. J.; Machado, F.; Yao, N. Y.; Taminiau, T. H. (2021-12-17). "Many-body–localized discrete time crystal with a programmable spin-based quantum simulator". Science. 374 (6574): 1474–1478. arXiv:2107.00736. Bibcode:2021Sci...374.1474R. doi:10.1126/science.abk0603. ISSN 0036-8075. PMID 34735218. S2CID 235727352.
Taheri, Hossein; Matsko, Andrey B.; Maleki, Lute; Sacha, Krzysztof (14 February 2022). "All-optical dissipative discrete time crystals". Nature Communications. 13 (1): 848. Bibcode:2022NatCo..13..848T. doi:10.1038/s41467-022-28462-x. ISSN 2041-1723. PMC 8844012. PMID 35165273.
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mpg.de

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nih.gov

pubmed.ncbi.nlm.nih.gov

Khemani et al. (2016) Khemani, Vedika; Lazarides, Achilleas; Moessner, Roderich; Sondhi, S. L. (2016). "Phase Structure of Driven Quantum Systems". Physical Review Letters. 116 (25): 250401. arXiv:1508.03344. Bibcode:2016PhRvL.116y0401K. doi:10.1103/PhysRevLett.116.250401. ISSN 0031-9007. PMID 27391704. S2CID 883197.
Else et al. (2016). Else, Dominic V.; Bauer, Bela; Nayak, Chetan (2016). "Floquet Time Crystals". Physical Review Letters. 117 (9): 090402. arXiv:1603.08001. Bibcode:2016PhRvL.117i0402E. doi:10.1103/PhysRevLett.117.090402. ISSN 0031-9007. PMID 27610834. S2CID 1652633.
Sacha, Krzysztof; Zakrzewski, Jakub (1 January 2018). "Time crystals: a review". Reports on Progress in Physics. 81 (1): 016401. arXiv:1704.03735. Bibcode:2018RPPh...81a6401S. doi:10.1088/1361-6633/aa8b38. PMID 28885193. S2CID 28224975.
Mi, Xiao; Ippoliti, Matteo; Quintana, Chris; Greene, Ami; Chen, Zijun; Gross, Jonathan; Arute, Frank; Arya, Kunal; Atalaya, Juan; Babbush, Ryan; Bardin, Joseph C. (2022). "Time-Crystalline Eigenstate Order on a Quantum Processor". Nature. 601 (7894): 531–536. arXiv:2107.13571. Bibcode:2022Natur.601..531M. doi:10.1038/s41586-021-04257-w. ISSN 1476-4687. PMC 8791837. PMID 34847568.
Wilczek, Frank (2012). "Quantum Time Crystals". Physical Review Letters. 109 (16): 160401. arXiv:1202.2539. Bibcode:2012PhRvL.109p0401W. doi:10.1103/PhysRevLett.109.160401. ISSN 0031-9007. PMID 23215056. S2CID 1312256.
Shapere, Alfred; Wilczek, Frank (2012). "Classical Time Crystals". Physical Review Letters. 109 (16): 160402. arXiv:1202.2537. Bibcode:2012PhRvL.109p0402S. doi:10.1103/PhysRevLett.109.160402. ISSN 0031-9007. PMID 23215057. S2CID 4506464.
See Li et al. (2012a, 2012b). Li, Tongcang; Gong, Zhe-Xuan; Yin, Zhang-Qi; Quan, H. T.; Yin, Xiaobo; Zhang, Peng; Duan, L.-M.; Zhang, Xiang (2012a). "Space-Time Crystals of Trapped Ions". Physical Review Letters. 109 (16): 163001. arXiv:1206.4772. Bibcode:2012PhRvL.109p3001L. doi:10.1103/PhysRevLett.109.163001. ISSN 0031-9007. PMID 23215073. S2CID 8198228. Li, Tongcang; Gong, Zhe-Xuan; Yin, Zhang-Qi; Quan, H. T.; Yin, Xiaobo; Zhang, Peng; Duan, L.-M.; Zhang, Xiang (2012). "Reply to Comment on "Space–Time Crystals of Trapped Ions"". Unpublished. arXiv:1212.6959. Bibcode:2012arXiv1212.6959L.
See Bruno (2013a) and Bruno (2013b). Bruno, Patrick (2013a). "Comment on 'Quantum Time Crystals'". Physical Review Letters. 110 (11): 118901. arXiv:1210.4128. Bibcode:2013PhRvL.110k8901B. doi:10.1103/PhysRevLett.110.118901. ISSN 0031-9007. PMID 25166585. S2CID 41459498. Bruno, Patrick (2013b). "Comment on "Space-Time Crystals of Trapped Ions"". Physical Review Letters. 111 (2): 029301. arXiv:1211.4792. Bibcode:2013PhRvL.111b9301B. doi:10.1103/PhysRevLett.111.029301. ISSN 0031-9007. PMID 23889455. S2CID 1502258.
Watanabe, Haruki; Oshikawa, Masaki (2015). "Absence of Quantum Time Crystals". Physical Review Letters. 114 (25): 251603. arXiv:1410.2143. Bibcode:2015PhRvL.114y1603W. doi:10.1103/PhysRevLett.114.251603. ISSN 0031-9007. PMID 26197119. S2CID 312538.
See Wilczek (2013b) and Yoshii et al. (2015). Wilczek, Frank (2013b). "Superfluidity and Space–Time Translation Symmetry Breaking". Physical Review Letters. 111 (25): 250402. arXiv:1308.5949. Bibcode:2013PhRvL.111y0402W. doi:10.1103/PhysRevLett.111.250402. ISSN 0031-9007. PMID 24483732. S2CID 7537145. Yoshii, Ryosuke; Takada, Satoshi; Tsuchiya, Shunji; Marmorini, Giacomo; Hayakawa, Hisao; Nitta, Muneto (2015). "Fulde-Ferrell-Larkin-Ovchinnikov states in a superconducting ring with magnetic fields: Phase diagram and the first-order phase transitions". Physical Review B. 92 (22): 224512. arXiv:1404.3519. Bibcode:2015PhRvB..92v4512Y. doi:10.1103/PhysRevB.92.224512. ISSN 1098-0121. S2CID 118348062.
See Khemani et al. (2016) and Else et al. (2016) Khemani, Vedika; Lazarides, Achilleas; Moessner, Roderich; Sondhi, S. L. (2016). "Phase Structure of Driven Quantum Systems". Physical Review Letters. 116 (25): 250401. arXiv:1508.03344. Bibcode:2016PhRvL.116y0401K. doi:10.1103/PhysRevLett.116.250401. ISSN 0031-9007. PMID 27391704. S2CID 883197. Else, Dominic V.; Bauer, Bela; Nayak, Chetan (2016). "Floquet Time Crystals". Physical Review Letters. 117 (9): 090402. arXiv:1603.08001. Bibcode:2016PhRvL.117i0402E. doi:10.1103/PhysRevLett.117.090402. ISSN 0031-9007. PMID 27610834. S2CID 1652633.
Yao, N. Y.; Potter, A. C.; Potirniche, I.-D.; Vishwanath, A. (2017). "Discrete Time Crystals: Rigidity, Criticality, and Realizations". Physical Review Letters. 118 (3): 030401. arXiv:1608.02589. Bibcode:2017PhRvL.118c0401Y. doi:10.1103/PhysRevLett.118.030401. ISSN 0031-9007. PMID 28157355. S2CID 206284432.
Choi, Soonwon; Choi, Joonhee; Landig, Renate; Kucsko, Georg; Zhou, Hengyun; Isoya, Junichi; Jelezko, Fedor; Onoda, Shinobu; Sumiya, Hitoshi; Khemani, Vedika; von Keyserlingk, Curt; Yao, Norman Y.; Demler, Eugene; Lukin, Mikhail D. (2017). "Observation of discrete time-crystalline order in a disordered dipolar many-body system". Nature. 543 (7644): 221–225. arXiv:1610.08057. Bibcode:2017Natur.543..221C. doi:10.1038/nature21426. ISSN 0028-0836. PMC 5349499. PMID 28277511.
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. (2017). "Observation of a discrete time crystal". Nature. 543 (7644): 217–220. arXiv:1609.08684. Bibcode:2017Natur.543..217Z. doi:10.1038/nature21413. PMID 28277505. S2CID 4450646.
Iemini, Fernando; Russomanno, Angelo; Keeling, Jonathan; Schirò, Marco; Dalmonte, Marcello; Fazio, Rosario (16 July 2018). "Boundary time crystals". Phys. Rev. Lett. 121 (35301): 035301. arXiv:1708.05014. Bibcode:2018PhRvL.121c5301I. doi:10.1103/PhysRevLett.121.035301. PMID 30085780. S2CID 51683292.
Gong, Zongping; Hamazaki, Ryusuke; Ueda, Masahito (25 January 2018). "Discrete Time-Crystalline Order in Cavity and Circuit QED Systems". Phys. Rev. Lett. 120 (40404): 040404. arXiv:1708.01472. Bibcode:2018PhRvL.120d0404G. doi:10.1103/PhysRevLett.120.040404. PMID 29437420. S2CID 206307409.
Filippo Maria, Gambetta; Carollo, Federico; Marcuzzi, Matteo; Garrahan, Juan P.; Lesanovsky, Igor (8 January 2019). "Discrete Time Crystals in the Absence of Manifest Symmetries or Disorder in Open Quantum Systems". Phys. Rev. Lett. 122 (15701): 015701. arXiv:1807.10161. Bibcode:2019PhRvL.122a5701G. doi:10.1103/PhysRevLett.122.015701. PMID 31012672. S2CID 119187766.
Buča, Berislav; Jaksch, Dieter (2019-12-23). "Dissipation Induced Nonstationarity in a Quantum Gas". Physical Review Letters. 123 (26): 260401. arXiv:1905.12880. Bibcode:2019PhRvL.123z0401B. doi:10.1103/PhysRevLett.123.260401. PMID 31951440. S2CID 170079211.
Iemini, F.; Russomanno, A.; Keeling, J.; Schirò, M.; Dalmonte, M.; Fazio, R. (2018-07-16). "Boundary Time Crystals". Physical Review Letters. 121 (3): 035301. arXiv:1708.05014. Bibcode:2018PhRvL.121c5301I. doi:10.1103/PhysRevLett.121.035301. hdl:10023/14492. PMID 30085780. S2CID 51683292.
Buča, Berislav; Tindall, Joseph; Jaksch, Dieter (2019-04-15). "Non-stationary coherent quantum many-body dynamics through dissipation". Nature Communications. 10 (1): 1730. arXiv:1804.06744. Bibcode:2019NatCo..10.1730B. doi:10.1038/s41467-019-09757-y. ISSN 2041-1723. PMC 6465298. PMID 30988312.
Keßler, Hans; Kongkhambut, Phatthamon; Georges, Christoph; Mathey, Ludwig; Cosme, Jayson G.; Hemmerich, Andreas (2021-07-19). "Observation of a Dissipative Time Crystal". Physical Review Letters. 127 (4): 043602. arXiv:2012.08885. Bibcode:2021PhRvL.127d3602K. doi:10.1103/PhysRevLett.127.043602. PMID 34355967. S2CID 229210935.
Ball, Philip (September 2021). "Quantum time crystals open up". Nature Materials. 20 (9): 1172. Bibcode:2021NatMa..20.1172B. doi:10.1038/s41563-021-01090-4. ISSN 1476-4660. PMID 34433935. S2CID 237299508.
Piazza, Francesco; Ritsch, Helmut (2015-10-15). "Self-Ordered Limit Cycles, Chaos, and Phase Slippage with a Superfluid inside an Optical Resonator". Physical Review Letters. 115 (16): 163601. arXiv:1507.08644. Bibcode:2015PhRvL.115p3601P. doi:10.1103/PhysRevLett.115.163601. PMID 26550874. S2CID 5080527.
Dogra, Nishant; Landini, Manuele; Kroeger, Katrin; Hruby, Lorenz; Donner, Tobias; Esslinger, Tilman (2019-12-20). "Dissipation-induced structural instability and chiral dynamics in a quantum gas". Science. 366 (6472): 1496–1499. arXiv:1901.05974. Bibcode:2019Sci...366.1496D. doi:10.1126/science.aaw4465. ISSN 0036-8075. PMID 31857481. S2CID 119283814.
Kozin, Valerii K.; Kyriienko, Oleksandr (2019-11-20). "Quantum Time Crystals from Hamiltonians with Long-Range Interactions". Physical Review Letters. 123 (21): 210602. arXiv:1907.07215. Bibcode:2019PhRvL.123u0602K. doi:10.1103/PhysRevLett.123.210602. ISSN 0031-9007. PMID 31809146. S2CID 197431242.
Kongkhambut, Phatthamon; Skulte, Jim; Mathey, Ludwig; Cosme, Jayson G.; Hemmerich, Andreas; Keßler, Hans (2022-08-05). "Observation of a continuous time crystal". Science. 377 (6606): 670–673. arXiv:2202.06980. Bibcode:2022Sci...377..670K. doi:10.1126/science.abo3382. ISSN 0036-8075. PMID 35679353. S2CID 246863968.
LeBlanc, Lindsay J. (2022-08-05). "Unleashing spontaneity in a time crystal". Science. 377 (6606): 576–577. Bibcode:2022Sci...377..576L. doi:10.1126/science.add2015. ISSN 0036-8075. PMID 35926056. S2CID 251349796.
Autti, S.; Eltsov, V. B.; Volovik, G. E. (May 2018). "Observation of a Time Quasicrystal and Its Transition to a Superfluid Time Crystal". Physical Review Letters. 120 (21): 215301. arXiv:1712.06877. Bibcode:2018PhRvL.120u5301A. doi:10.1103/PhysRevLett.120.215301. PMID 29883148. S2CID 46997186.
Autti, S.; Heikkinen, P. J.; Mäkinen, J. T.; Volovik, G. E.; Zavjalov, V. V.; Eltsov, V. B. (February 2021). "AC Josephson effect between two superfluid time crystals". Nature Materials. 20 (2): 171–174. arXiv:2003.06313. Bibcode:2021NatMa..20..171A. doi:10.1038/s41563-020-0780-y. PMID 32807922. S2CID 212717702.
Träger, Nick; Gruszecki, Paweł; Lisiecki, Filip; Groß, Felix; Förster, Johannes; Weigand, Markus; Głowiński, Hubert; Kuświk, Piotr; Dubowik, Janusz; Schütz, Gisela; Krawczyk, Maciej (2021-02-03). "Real-Space Observation of Magnon Interaction with Driven Space–Time Crystals". Physical Review Letters. 126 (5): 057201. arXiv:1911.13192. Bibcode:2021PhRvL.126e7201T. doi:10.1103/PhysRevLett.126.057201. PMID 33605763. S2CID 208512720.
Kyprianidis, A.; Machado, F.; Morong, W.; Becker, P.; Collins, K. S.; Else, D. V.; Feng, L.; Hess, P. W.; Nayak, C.; Pagano, G.; Yao, N. Y. (2021-06-11). "Observation of a prethermal discrete time crystal". Science. 372 (6547): 1192–1196. arXiv:2102.01695. Bibcode:2021Sci...372.1192K. doi:10.1126/science.abg8102. ISSN 0036-8075. PMID 34112691. S2CID 231786633.
Randall, J.; Bradley, C. E.; van der Gronden, F. V.; Galicia, A.; Abobeih, M. H.; Markham, M.; Twitchen, D. J.; Machado, F.; Yao, N. Y.; Taminiau, T. H. (2021-12-17). "Many-body–localized discrete time crystal with a programmable spin-based quantum simulator". Science. 374 (6574): 1474–1478. arXiv:2107.00736. Bibcode:2021Sci...374.1474R. doi:10.1126/science.abk0603. ISSN 0036-8075. PMID 34735218. S2CID 235727352.
Taheri, Hossein; Matsko, Andrey B.; Maleki, Lute; Sacha, Krzysztof (14 February 2022). "All-optical dissipative discrete time crystals". Nature Communications. 13 (1): 848. Bibcode:2022NatCo..13..848T. doi:10.1038/s41467-022-28462-x. ISSN 2041-1723. PMC 8844012. PMID 35165273.
Frey, Philipp; Rachel, Stephan (2022-03-04). "Realization of a discrete time crystal on 57 qubits of a quantum computer". Science Advances. 8 (9): eabm7652. arXiv:2105.06632. Bibcode:2022SciA....8M7652F. doi:10.1126/sciadv.abm7652. ISSN 2375-2548. PMC 8890700. PMID 35235347.

ncbi.nlm.nih.gov

Mi, Xiao; Ippoliti, Matteo; Quintana, Chris; Greene, Ami; Chen, Zijun; Gross, Jonathan; Arute, Frank; Arya, Kunal; Atalaya, Juan; Babbush, Ryan; Bardin, Joseph C. (2022). "Time-Crystalline Eigenstate Order on a Quantum Processor". Nature. 601 (7894): 531–536. arXiv:2107.13571. Bibcode:2022Natur.601..531M. doi:10.1038/s41586-021-04257-w. ISSN 1476-4687. PMC 8791837. PMID 34847568.
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springer.com

link.springer.com

Sacha, Krzysztof (2020). Time Crystals. Springer Series on Atomic, Optical, and Plasma Physics. Vol. 114. Springer. doi:10.1007/978-3-030-52523-1. ISBN 978-3-030-52522-4. S2CID 240770955.

technologyreview.com

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theconversation.com

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uni-hamburg.de

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Sacha, Krzysztof (2015). "Modeling spontaneous breaking of time-translation symmetry". Physical Review A. 91 (3): 033617. arXiv:1410.3638. Bibcode:2015PhRvA..91c3617S. doi:10.1103/PhysRevA.91.033617. ISSN 1050-2947. S2CID 118627872.
Khemani et al. (2016) Khemani, Vedika; Lazarides, Achilleas; Moessner, Roderich; Sondhi, S. L. (2016). "Phase Structure of Driven Quantum Systems". Physical Review Letters. 116 (25): 250401. arXiv:1508.03344. Bibcode:2016PhRvL.116y0401K. doi:10.1103/PhysRevLett.116.250401. ISSN 0031-9007. PMID 27391704. S2CID 883197.
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Yao; Nayak (2018). "Time crystals in periodically driven systems". Physics Today. 71 (9): 40–47. arXiv:1811.06657. Bibcode:2018PhT....71i..40Y. doi:10.1063/PT.3.4020. ISSN 0031-9228. S2CID 119433979.
Mi, Xiao; Ippoliti, Matteo; Quintana, Chris; Greene, Ami; Chen, Zijun; Gross, Jonathan; Arute, Frank; Arya, Kunal; Atalaya, Juan; Babbush, Ryan; Bardin, Joseph C. (2022). "Time-Crystalline Eigenstate Order on a Quantum Processor". Nature. 601 (7894): 531–536. arXiv:2107.13571. Bibcode:2022Natur.601..531M. doi:10.1038/s41586-021-04257-w. ISSN 1476-4687. PMC 8791837. PMID 34847568.
Wilczek, Frank (2012). "Quantum Time Crystals". Physical Review Letters. 109 (16): 160401. arXiv:1202.2539. Bibcode:2012PhRvL.109p0401W. doi:10.1103/PhysRevLett.109.160401. ISSN 0031-9007. PMID 23215056. S2CID 1312256.
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Watanabe, Haruki; Oshikawa, Masaki (2015). "Absence of Quantum Time Crystals". Physical Review Letters. 114 (25): 251603. arXiv:1410.2143. Bibcode:2015PhRvL.114y1603W. doi:10.1103/PhysRevLett.114.251603. ISSN 0031-9007. PMID 26197119. S2CID 312538.
Medenjak, Marko; Buča, Berislav; Jaksch, Dieter (2020-07-20). "Isolated Heisenberg magnet as a quantum time crystal". Physical Review B. 102 (4): 041117. arXiv:1905.08266. Bibcode:2020PhRvB.102d1117M. doi:10.1103/physrevb.102.041117. ISSN 2469-9950. S2CID 160009779.
See Wilczek (2013b) and Yoshii et al. (2015). Wilczek, Frank (2013b). "Superfluidity and Space–Time Translation Symmetry Breaking". Physical Review Letters. 111 (25): 250402. arXiv:1308.5949. Bibcode:2013PhRvL.111y0402W. doi:10.1103/PhysRevLett.111.250402. ISSN 0031-9007. PMID 24483732. S2CID 7537145. Yoshii, Ryosuke; Takada, Satoshi; Tsuchiya, Shunji; Marmorini, Giacomo; Hayakawa, Hisao; Nitta, Muneto (2015). "Fulde-Ferrell-Larkin-Ovchinnikov states in a superconducting ring with magnetic fields: Phase diagram and the first-order phase transitions". Physical Review B. 92 (22): 224512. arXiv:1404.3519. Bibcode:2015PhRvB..92v4512Y. doi:10.1103/PhysRevB.92.224512. ISSN 1098-0121. S2CID 118348062.
Sacha, Krzysztof (2015). "Modeling spontaneous breaking of time-translation symmetry". Physical Review A. 91 (3): 033617. arXiv:1410.3638. Bibcode:2015PhRvA..91c3617S. doi:10.1103/PhysRevA.91.033617. ISSN 1050-2947. S2CID 118627872. We show that an ultracold atomic cloud bouncing on an oscillating mirror can reveal spontaneous breaking of a discrete time-translation symmetry
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zenodo.org

See Bruno (2013a) and Bruno (2013b). Bruno, Patrick (2013a). "Comment on 'Quantum Time Crystals'". Physical Review Letters. 110 (11): 118901. arXiv:1210.4128. Bibcode:2013PhRvL.110k8901B. doi:10.1103/PhysRevLett.110.118901. ISSN 0031-9007. PMID 25166585. S2CID 41459498. Bruno, Patrick (2013b). "Comment on "Space-Time Crystals of Trapped Ions"". Physical Review Letters. 111 (2): 029301. arXiv:1211.4792. Bibcode:2013PhRvL.111b9301B. doi:10.1103/PhysRevLett.111.029301. ISSN 0031-9007. PMID 23889455. S2CID 1502258.