{"id":132974,"date":"2025-09-04T19:33:09","date_gmt":"2025-09-04T19:33:09","guid":{"rendered":"https:\/\/www.newsbeep.com\/us\/132974\/"},"modified":"2025-09-04T19:33:09","modified_gmt":"2025-09-04T19:33:09","slug":"space-time-crystals-from-particle-like-topological-solitons","status":"publish","type":"post","link":"https:\/\/www.newsbeep.com\/us\/132974\/","title":{"rendered":"Space-time crystals from particle-like topological solitons"},"content":{"rendered":"<p class=\"c-article-references__text\" id=\"ref-CR1\">Chaikin, P. M. &amp; Lubensky, T. C. Principles of Condensed Matter Physics (Cambridge Univ. Press, 2000).<\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR2\">Yeh, P. &amp; Gu, C. Optics of Liquid Crystal Displays (Wiley, 2010).<\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR3\">Wilczek, F. Quantum time crystals. Phys. Rev. Lett. 109, 160401 (2012).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"pubmed reference\" data-track-action=\"pubmed reference\" href=\"http:\/\/www.ncbi.nlm.nih.gov\/entrez\/query.fcgi?cmd=Retrieve&amp;db=PubMed&amp;dopt=Abstract&amp;list_uids=23215056\" aria-label=\"PubMed reference 3\" target=\"_blank\">PubMed<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 3\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Quantum%20time%20crystals&amp;journal=Phys.%20Rev.%20Lett.&amp;volume=109&amp;publication_year=2012&amp;author=Wilczek%2CF\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR4\">Shapere, A. &amp; Wilczek, F. Classical time crystals. Phys. Rev. Lett. 109, 160402 (2012).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"pubmed reference\" data-track-action=\"pubmed reference\" href=\"http:\/\/www.ncbi.nlm.nih.gov\/entrez\/query.fcgi?cmd=Retrieve&amp;db=PubMed&amp;dopt=Abstract&amp;list_uids=23215057\" aria-label=\"PubMed reference 4\" target=\"_blank\">PubMed<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 4\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Classical%20time%20crystals&amp;journal=Phys.%20Rev.%20Lett.&amp;volume=109&amp;publication_year=2012&amp;author=Shapere%2CA&amp;author=Wilczek%2CF\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR5\">Wilczek, F. Superfluidity and space-time translation symmetry breaking. Phys. Rev. Lett. 111, 250402 (2013).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"pubmed reference\" data-track-action=\"pubmed reference\" href=\"http:\/\/www.ncbi.nlm.nih.gov\/entrez\/query.fcgi?cmd=Retrieve&amp;db=PubMed&amp;dopt=Abstract&amp;list_uids=24483732\" aria-label=\"PubMed reference 5\" target=\"_blank\">PubMed<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 5\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Superfluidity%20and%20space-time%20translation%20symmetry%20breaking&amp;journal=Phys.%20Rev.%20Lett.&amp;volume=111&amp;publication_year=2013&amp;author=Wilczek%2CF\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR6\">Bruno, P. Impossibility of spontaneously rotating time crystals: a no-go theorem. Phys. Rev. Lett. 111, 070402 (2013).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"pubmed reference\" data-track-action=\"pubmed reference\" href=\"http:\/\/www.ncbi.nlm.nih.gov\/entrez\/query.fcgi?cmd=Retrieve&amp;db=PubMed&amp;dopt=Abstract&amp;list_uids=23992051\" aria-label=\"PubMed reference 6\" target=\"_blank\">PubMed<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 6\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Impossibility%20of%20spontaneously%20rotating%20time%20crystals%3A%20a%20no-go%20theorem&amp;journal=Phys.%20Rev.%20Lett.&amp;volume=111&amp;publication_year=2013&amp;author=Bruno%2CP\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR7\">Watanabe, H. &amp; Oshikawa, M. Absence of quantum time crystals. Phys. Rev. Lett. 114, 251603 (2015).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"pubmed reference\" data-track-action=\"pubmed reference\" href=\"http:\/\/www.ncbi.nlm.nih.gov\/entrez\/query.fcgi?cmd=Retrieve&amp;db=PubMed&amp;dopt=Abstract&amp;list_uids=26197119\" aria-label=\"PubMed reference 7\" target=\"_blank\">PubMed<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 7\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Absence%20of%20quantum%20time%20crystals&amp;journal=Phys.%20Rev.%20Lett.&amp;volume=114&amp;publication_year=2015&amp;author=Watanabe%2CH&amp;author=Oshikawa%2CM\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR8\">Sacha, K. &amp; Zakrzewski, J. Time crystals: a review. Rep. Prog. Phys. 81, 016401 (2017).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 8\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Time%20crystals%3A%20a%20review&amp;journal=Rep.%20Prog.%20Phys.&amp;volume=81&amp;publication_year=2017&amp;author=Sacha%2CK&amp;author=Zakrzewski%2CJ\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR9\">Yao, N. Y. &amp; Nayak, C. Time crystals in periodically driven systems. Phys. Today 71, 40\u201347 (2018).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 9\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Time%20crystals%20in%20periodically%20driven%20systems&amp;journal=Phys.%20Today&amp;volume=71&amp;pages=40-47&amp;publication_year=2018&amp;author=Yao%2CNY&amp;author=Nayak%2CC\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR10\">Khemani, V., Moessner, R. &amp; Sondhi, S. L. A brief history of time crystals. Preprint at <a href=\"https:\/\/doi.org\/10.48550\/arXiv.1910.10745\" data-track=\"click_references\" data-track-action=\"external reference\" data-track-value=\"external reference\" data-track-label=\"10.48550\/arXiv.1910.10745\" rel=\"nofollow noopener\" target=\"_blank\">https:\/\/doi.org\/10.48550\/arXiv.1910.10745<\/a> (2019).<\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR11\">Sacha, K. Time Crystals (Springer International Publishing, 2020).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 11\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Time%20Crystals&amp;publication_year=2020&amp;author=Sacha%2CK\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR12\">Guo, L. Phase Space Crystals: Condensed Matter in Dynamical Systems (IOP Publishing, 2021).<\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR13\">Zaletel, M. P. et al. Colloquium: quantum and classical discrete time crystals. Rev. Mod. Phys. 95, 031001 (2023).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"cas reference\" data-track-action=\"cas reference\" href=\"https:\/\/www.nature.com\/articles\/cas-redirect\/1:CAS:528:DC%2BB3sXitFygtb3O\" aria-label=\"CAS reference 13\" target=\"_blank\">CAS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 13\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Colloquium%3A%20quantum%20and%20classical%20discrete%20time%20crystals&amp;journal=Rev.%20Mod.%20Phys.&amp;volume=95&amp;publication_year=2023&amp;author=Zaletel%2CMP\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR14\">Sacha, K. Modeling spontaneous breaking of time-translation symmetry. Phys. Rev. A 91, 033617 (2015).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 14\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Modeling%20spontaneous%20breaking%20of%20time-translation%20symmetry&amp;journal=Phys.%20Rev.%20A&amp;volume=91&amp;publication_year=2015&amp;author=Sacha%2CK\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR15\">Khemani, V., Lazarides, A., Moessner, R. &amp; Sondhi, S. L. Phase structure of driven quantum systems. Phys. Rev. Lett. 116, 250401 (2016).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"pubmed reference\" data-track-action=\"pubmed reference\" href=\"http:\/\/www.ncbi.nlm.nih.gov\/entrez\/query.fcgi?cmd=Retrieve&amp;db=PubMed&amp;dopt=Abstract&amp;list_uids=27391704\" aria-label=\"PubMed reference 15\" target=\"_blank\">PubMed<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 15\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Phase%20structure%20of%20driven%20quantum%20systems&amp;journal=Phys.%20Rev.%20Lett.&amp;volume=116&amp;publication_year=2016&amp;author=Khemani%2CV&amp;author=Lazarides%2CA&amp;author=Moessner%2CR&amp;author=Sondhi%2CSL\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR16\">Else, D. V., Bauer, B. &amp; Nayak, C. Floquet time crystals. Phys. Rev. Lett. 117, 090402 (2016).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"pubmed reference\" data-track-action=\"pubmed reference\" href=\"http:\/\/www.ncbi.nlm.nih.gov\/entrez\/query.fcgi?cmd=Retrieve&amp;db=PubMed&amp;dopt=Abstract&amp;list_uids=27610834\" aria-label=\"PubMed reference 16\" target=\"_blank\">PubMed<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 16\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Floquet%20time%20crystals&amp;journal=Phys.%20Rev.%20Lett.&amp;volume=117&amp;publication_year=2016&amp;author=Else%2CDV&amp;author=Bauer%2CB&amp;author=Nayak%2CC\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR17\">Yao, N. Y., Potter, A. C., Potirniche, I.-D. &amp; Vishwanath, A. Discrete time crystals: rigidity, criticality, and realizations. Phys. Rev. Lett. 118, 030401 (2017).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"cas reference\" data-track-action=\"cas reference\" href=\"https:\/\/www.nature.com\/articles\/cas-redirect\/1:STN:280:DC%2BC1c3islantw%3D%3D\" aria-label=\"CAS reference 17\" target=\"_blank\">CAS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"pubmed reference\" data-track-action=\"pubmed reference\" href=\"http:\/\/www.ncbi.nlm.nih.gov\/entrez\/query.fcgi?cmd=Retrieve&amp;db=PubMed&amp;dopt=Abstract&amp;list_uids=28157355\" aria-label=\"PubMed reference 17\" target=\"_blank\">PubMed<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 17\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Discrete%20time%20crystals%3A%20rigidity%2C%20criticality%2C%20and%20realizations&amp;journal=Phys.%20Rev.%20Lett.&amp;volume=118&amp;publication_year=2017&amp;author=Yao%2CNY&amp;author=Potter%2CAC&amp;author=Potirniche%2CI-D&amp;author=Vishwanath%2CA\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR18\">Zhang, J. et al. Observation of a discrete time crystal. Nature 543, 217\u2013220 (2017).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"cas reference\" data-track-action=\"cas reference\" href=\"https:\/\/www.nature.com\/articles\/cas-redirect\/1:CAS:528:DC%2BC2sXks1GlsLs%3D\" aria-label=\"CAS reference 18\" target=\"_blank\">CAS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"pubmed reference\" data-track-action=\"pubmed reference\" href=\"http:\/\/www.ncbi.nlm.nih.gov\/entrez\/query.fcgi?cmd=Retrieve&amp;db=PubMed&amp;dopt=Abstract&amp;list_uids=28277505\" aria-label=\"PubMed reference 18\" target=\"_blank\">PubMed<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 18\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Observation%20of%20a%20discrete%20time%20crystal&amp;journal=Nature&amp;volume=543&amp;pages=217-220&amp;publication_year=2017&amp;author=Zhang%2CJ\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR19\">Choi, S. et al. Observation of discrete time-crystalline order in a disordered dipolar many-body system. Nature 543, 221\u2013225 (2017).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"cas reference\" data-track-action=\"cas reference\" href=\"https:\/\/www.nature.com\/articles\/cas-redirect\/1:CAS:528:DC%2BC2sXks1GlsLw%3D\" aria-label=\"CAS reference 19\" target=\"_blank\">CAS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"pubmed reference\" data-track-action=\"pubmed reference\" href=\"http:\/\/www.ncbi.nlm.nih.gov\/entrez\/query.fcgi?cmd=Retrieve&amp;db=PubMed&amp;dopt=Abstract&amp;list_uids=28277511\" aria-label=\"PubMed reference 19\" target=\"_blank\">PubMed<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"pubmed central reference\" data-track-action=\"pubmed central reference\" href=\"http:\/\/www.ncbi.nlm.nih.gov\/pmc\/articles\/PMC5349499\" aria-label=\"PubMed Central reference 19\" target=\"_blank\">PubMed Central<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 19\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Observation%20of%20discrete%20time-crystalline%20order%20in%20a%20disordered%20dipolar%20many-body%20system&amp;journal=Nature&amp;volume=543&amp;pages=221-225&amp;publication_year=2017&amp;author=Choi%2CS\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR20\">Smits, J., Liao, L., Stoof, H. T. C. &amp; van der Straten, P. Observation of a space-time crystal in a superfluid quantum gas. Phys. Rev. Lett. 121, 185301 (2018).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"cas reference\" data-track-action=\"cas reference\" href=\"https:\/\/www.nature.com\/articles\/cas-redirect\/1:CAS:528:DC%2BC1MXlsl2hsb0%3D\" aria-label=\"CAS reference 20\" target=\"_blank\">CAS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"pubmed reference\" data-track-action=\"pubmed reference\" href=\"http:\/\/www.ncbi.nlm.nih.gov\/entrez\/query.fcgi?cmd=Retrieve&amp;db=PubMed&amp;dopt=Abstract&amp;list_uids=30444377\" aria-label=\"PubMed reference 20\" target=\"_blank\">PubMed<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 20\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Observation%20of%20a%20space-time%20crystal%20in%20a%20superfluid%20quantum%20gas&amp;journal=Phys.%20Rev.%20Lett.&amp;volume=121&amp;publication_year=2018&amp;author=Smits%2CJ&amp;author=Liao%2CL&amp;author=Stoof%2CHTC&amp;author=Straten%2CP\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR21\">Liao, L., Smits, J., van der Straten, P. &amp; Stoof, H. T. C. Dynamics of a space-time crystal in an atomic Bose-Einstein condensate. Phys. Rev. A 99, 013625 (2019).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 21\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Dynamics%20of%20a%20space-time%20crystal%20in%20an%20atomic%20Bose-Einstein%20condensate&amp;journal=Phys.%20Rev.%20A&amp;volume=99&amp;publication_year=2019&amp;author=Liao%2CL&amp;author=Smits%2CJ&amp;author=Straten%2CP&amp;author=Stoof%2CHTC\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR22\">Smits, J., Stoof, H. T. C. &amp; van der Straten, P. Spontaneous breaking of a discrete time-translation symmetry. Phys. Rev. A 104, 023318 (2021).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"cas reference\" data-track-action=\"cas reference\" href=\"https:\/\/www.nature.com\/articles\/cas-redirect\/1:CAS:528:DC%2BB3MXitVKktLbI\" aria-label=\"CAS reference 22\" target=\"_blank\">CAS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 22\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Spontaneous%20breaking%20of%20a%20discrete%20time-translation%20symmetry&amp;journal=Phys.%20Rev.%20A&amp;volume=104&amp;publication_year=2021&amp;author=Smits%2CJ&amp;author=Stoof%2CHTC&amp;author=Straten%2CP\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR23\">Randall, J. et al. Many-body\u2013localized discrete time crystal with a programmable spin-based quantum simulator. Science 374, 1474\u20131478 (2021).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"pubmed reference\" data-track-action=\"pubmed reference\" href=\"http:\/\/www.ncbi.nlm.nih.gov\/entrez\/query.fcgi?cmd=Retrieve&amp;db=PubMed&amp;dopt=Abstract&amp;list_uids=34735218\" aria-label=\"PubMed reference 23\" target=\"_blank\">PubMed<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 23\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Many-body%E2%80%93localized%20discrete%20time%20crystal%20with%20a%20programmable%20spin-based%20quantum%20simulator&amp;journal=Science&amp;volume=374&amp;publication_year=2021&amp;author=Randall%2CJ\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR24\">Ke\u00dfler, H. et al. Observation of a dissipative time crystal. Phys. Rev. Lett. 127, 043602 (2021).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"pubmed reference\" data-track-action=\"pubmed reference\" href=\"http:\/\/www.ncbi.nlm.nih.gov\/entrez\/query.fcgi?cmd=Retrieve&amp;db=PubMed&amp;dopt=Abstract&amp;list_uids=34355967\" aria-label=\"PubMed reference 24\" target=\"_blank\">PubMed<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 24\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Observation%20of%20a%20dissipative%20time%20crystal&amp;journal=Phys.%20Rev.%20Lett.&amp;volume=127&amp;publication_year=2021&amp;author=Ke%C3%9Fler%2CH\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR25\">Taheri, H., Matsko, A. B., Maleki, L. &amp; Sacha, K. All-optical dissipative discrete time crystals. Nat. Commun. 13, 848 (2022).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"cas reference\" data-track-action=\"cas reference\" href=\"https:\/\/www.nature.com\/articles\/cas-redirect\/1:CAS:528:DC%2BB38XjsFGns7g%3D\" aria-label=\"CAS reference 25\" target=\"_blank\">CAS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"pubmed reference\" data-track-action=\"pubmed reference\" href=\"http:\/\/www.ncbi.nlm.nih.gov\/entrez\/query.fcgi?cmd=Retrieve&amp;db=PubMed&amp;dopt=Abstract&amp;list_uids=35165273\" aria-label=\"PubMed reference 25\" target=\"_blank\">PubMed<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"pubmed central reference\" data-track-action=\"pubmed central reference\" href=\"http:\/\/www.ncbi.nlm.nih.gov\/pmc\/articles\/PMC8844012\" aria-label=\"PubMed Central reference 25\" target=\"_blank\">PubMed Central<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 25\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=All-optical%20dissipative%20discrete%20time%20crystals&amp;journal=Nat.%20Commun.&amp;volume=13&amp;publication_year=2022&amp;author=Taheri%2CH&amp;author=Matsko%2CAB&amp;author=Maleki%2CL&amp;author=Sacha%2CK\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR26\">Taheri, H., Matsko, A. B., Herr, T. &amp; Sacha, K. Dissipative discrete time crystals in a pump-modulated Kerr microcavity. Commun. Phys. 5, 159 (2022).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 26\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Dissipative%20discrete%20time%20crystals%20in%20a%20pump-modulated%20Kerr%20microcavity&amp;journal=Commun.%20Phys.&amp;volume=5&amp;publication_year=2022&amp;author=Taheri%2CH&amp;author=Matsko%2CAB&amp;author=Herr%2CT&amp;author=Sacha%2CK\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR27\">Mi, X. et al. Time-crystalline eigenstate order on a quantum processor. Nature 601, 531\u2013536 (2022).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"cas reference\" data-track-action=\"cas reference\" href=\"https:\/\/www.nature.com\/articles\/cas-redirect\/1:CAS:528:DC%2BB38XhslCns7Y%3D\" aria-label=\"CAS reference 27\" target=\"_blank\">CAS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"pubmed reference\" data-track-action=\"pubmed reference\" href=\"http:\/\/www.ncbi.nlm.nih.gov\/entrez\/query.fcgi?cmd=Retrieve&amp;db=PubMed&amp;dopt=Abstract&amp;list_uids=34847568\" aria-label=\"PubMed reference 27\" target=\"_blank\">PubMed<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 27\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Time-crystalline%20eigenstate%20order%20on%20a%20quantum%20processor&amp;journal=Nature&amp;volume=601&amp;pages=531-536&amp;publication_year=2022&amp;author=Mi%2CX\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR28\">Frey, P. &amp; Rachel, S. Realization of a discrete time crystal on 57 qubits of a quantum computer. Sci. Adv. 8, eabm7652 (2022).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"pubmed reference\" data-track-action=\"pubmed reference\" href=\"http:\/\/www.ncbi.nlm.nih.gov\/entrez\/query.fcgi?cmd=Retrieve&amp;db=PubMed&amp;dopt=Abstract&amp;list_uids=35235347\" aria-label=\"PubMed reference 28\" target=\"_blank\">PubMed<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"pubmed central reference\" data-track-action=\"pubmed central reference\" href=\"http:\/\/www.ncbi.nlm.nih.gov\/pmc\/articles\/PMC8890700\" aria-label=\"PubMed Central reference 28\" target=\"_blank\">PubMed Central<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 28\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Realization%20of%20a%20discrete%20time%20crystal%20on%2057%20qubits%20of%20a%20quantum%20computer&amp;journal=Sci.%20Adv.&amp;volume=8&amp;publication_year=2022&amp;author=Frey%2CP&amp;author=Rachel%2CS\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR29\">Kongkhambut, P. et al. Observation of a continuous time crystal. Science 377, 670\u2013673 (2022).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"cas reference\" data-track-action=\"cas reference\" href=\"https:\/\/www.nature.com\/articles\/cas-redirect\/1:CAS:528:DC%2BB38XitVyqu7rJ\" aria-label=\"CAS reference 29\" target=\"_blank\">CAS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"pubmed reference\" data-track-action=\"pubmed reference\" href=\"http:\/\/www.ncbi.nlm.nih.gov\/entrez\/query.fcgi?cmd=Retrieve&amp;db=PubMed&amp;dopt=Abstract&amp;list_uids=35679353\" aria-label=\"PubMed reference 29\" target=\"_blank\">PubMed<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 29\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Observation%20of%20a%20continuous%20time%20crystal&amp;journal=Science&amp;volume=377&amp;pages=670-673&amp;publication_year=2022&amp;author=Kongkhambut%2CP\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR30\">Liu, T., Ou, J.-Y., MacDonald, K. F. &amp; Zheludev, N. I. Photonic metamaterial analogue of a continuous time crystal. Nat. Phys. 19, 986\u2013991 (2023).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"cas reference\" data-track-action=\"cas reference\" href=\"https:\/\/www.nature.com\/articles\/cas-redirect\/1:CAS:528:DC%2BB3sXosVGiurw%3D\" aria-label=\"CAS reference 30\" target=\"_blank\">CAS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 30\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Photonic%20metamaterial%20analogue%20of%20a%20continuous%20time%20crystal&amp;journal=Nat.%20Phys.&amp;volume=19&amp;pages=986-991&amp;publication_year=2023&amp;author=Liu%2CT&amp;author=Ou%2CJ-Y&amp;author=MacDonald%2CKF&amp;author=Zheludev%2CNI\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR31\">Chen, Y.-H. &amp; Zhang, X. Realization of an inherent time crystal in a dissipative many-body system. Nat. Commun. 14, 6161 (2023).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"cas reference\" data-track-action=\"cas reference\" href=\"https:\/\/www.nature.com\/articles\/cas-redirect\/1:CAS:528:DC%2BB3sXitVygurjK\" aria-label=\"CAS reference 31\" target=\"_blank\">CAS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"pubmed reference\" data-track-action=\"pubmed reference\" href=\"http:\/\/www.ncbi.nlm.nih.gov\/entrez\/query.fcgi?cmd=Retrieve&amp;db=PubMed&amp;dopt=Abstract&amp;list_uids=37789006\" aria-label=\"PubMed reference 31\" target=\"_blank\">PubMed<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"pubmed central reference\" data-track-action=\"pubmed central reference\" href=\"http:\/\/www.ncbi.nlm.nih.gov\/pmc\/articles\/PMC10547780\" aria-label=\"PubMed Central reference 31\" target=\"_blank\">PubMed Central<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 31\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Realization%20of%20an%20inherent%20time%20crystal%20in%20a%20dissipative%20many-body%20system&amp;journal=Nat.%20Commun.&amp;volume=14&amp;publication_year=2023&amp;author=Chen%2CY-H&amp;author=Zhang%2CX\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR32\">Wu, X. et al. Dissipative time crystal in a strongly interacting Rydberg gas. Nat. Phys. 20, 1389\u20131394 (2024).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"cas reference\" data-track-action=\"cas reference\" href=\"https:\/\/www.nature.com\/articles\/cas-redirect\/1:CAS:528:DC%2BB2cXhsV2gs7jF\" aria-label=\"CAS reference 32\" target=\"_blank\">CAS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 32\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Dissipative%20time%20crystal%20in%20a%20strongly%20interacting%20Rydberg%20gas&amp;journal=Nat.%20Phys.&amp;volume=20&amp;pages=1389-1394&amp;publication_year=2024&amp;author=Wu%2CX\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR33\">Greilich, A. et al. Robust continuous time crystal in an electron\u2013nuclear spin system. Nat. Phys. 20, 631\u2013636 (2024).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"cas reference\" data-track-action=\"cas reference\" href=\"https:\/\/www.nature.com\/articles\/cas-redirect\/1:CAS:528:DC%2BB2cXhvFylsrg%3D\" aria-label=\"CAS reference 33\" target=\"_blank\">CAS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 33\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Robust%20continuous%20time%20crystal%20in%20an%20electron%E2%80%93nuclear%20spin%20system&amp;journal=Nat.%20Phys.&amp;volume=20&amp;pages=631-636&amp;publication_year=2024&amp;author=Greilich%2CA\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR34\">Carraro-Haddad, I. et al. Solid-state continuous time crystal in a polariton condensate with a built-in mechanical clock. Science 384, 995\u20131000 (2024).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"cas reference\" data-track-action=\"cas reference\" href=\"https:\/\/www.nature.com\/articles\/cas-redirect\/1:CAS:528:DC%2BB2cXht1WlsrrJ\" aria-label=\"CAS reference 34\" target=\"_blank\">CAS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"pubmed reference\" data-track-action=\"pubmed reference\" href=\"http:\/\/www.ncbi.nlm.nih.gov\/entrez\/query.fcgi?cmd=Retrieve&amp;db=PubMed&amp;dopt=Abstract&amp;list_uids=38815032\" aria-label=\"PubMed reference 34\" target=\"_blank\">PubMed<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 34\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Solid-state%20continuous%20time%20crystal%20in%20a%20polariton%20condensate%20with%20a%20built-in%20mechanical%20clock&amp;journal=Science&amp;volume=384&amp;pages=995-1000&amp;publication_year=2024&amp;author=Carraro-Haddad%2CI\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR35\">Yi, Y., Farrow, M. J., Korblova, E., Walba, D. M. &amp; Furtak, T. E. High-sensitivity aminoazobenzene chemisorbed monolayers for photoalignment of liquid crystals. Langmuir 25, 997\u20131003 (2009).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"cas reference\" data-track-action=\"cas reference\" href=\"https:\/\/www.nature.com\/articles\/cas-redirect\/1:CAS:528:DC%2BD1cXhsFWnsL7O\" aria-label=\"CAS reference 35\" target=\"_blank\">CAS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"pubmed reference\" data-track-action=\"pubmed reference\" href=\"http:\/\/www.ncbi.nlm.nih.gov\/entrez\/query.fcgi?cmd=Retrieve&amp;db=PubMed&amp;dopt=Abstract&amp;list_uids=19093815\" aria-label=\"PubMed reference 35\" target=\"_blank\">PubMed<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 35\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=High-sensitivity%20aminoazobenzene%20chemisorbed%20monolayers%20for%20photoalignment%20of%20liquid%20crystals&amp;journal=Langmuir&amp;volume=25&amp;pages=997-1003&amp;publication_year=2009&amp;author=Yi%2CY&amp;author=Farrow%2CMJ&amp;author=Korblova%2CE&amp;author=Walba%2CDM&amp;author=Furtak%2CTE\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR36\">Landau, L. D. &amp; Lifshitz, E. M. Statistical Physics (Elsevier, 2013).<\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR37\">de Gennes, P. G. &amp; Prost, J. The Physics of Liquid Crystals (Clarendon Press, 1993).<\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR38\">Reichhardt, C., Reichhardt, C. J. O. &amp; Milo\u0161evi\u0107, M. V. Statics and dynamics of skyrmions interacting with disorder and nanostructures. Rev. Mod. Phys. 94, 035005 (2022).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"cas reference\" data-track-action=\"cas reference\" href=\"https:\/\/www.nature.com\/articles\/cas-redirect\/1:CAS:528:DC%2BB38XislSrsrvN\" aria-label=\"CAS reference 38\" target=\"_blank\">CAS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 38\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Statics%20and%20dynamics%20of%20skyrmions%20interacting%20with%20disorder%20and%20nanostructures&amp;journal=Rev.%20Mod.%20Phys.&amp;volume=94&amp;publication_year=2022&amp;author=Reichhardt%2CC&amp;author=Reichhardt%2CCJO&amp;author=Milo%C5%A1evi%C4%87%2CMV\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR39\">Smalyukh, I. I. Review: knots and other new topological effects in liquid crystals and colloids. Rep. Prog. Phys. 83, 106601 (2020).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"pubmed reference\" data-track-action=\"pubmed reference\" href=\"http:\/\/www.ncbi.nlm.nih.gov\/entrez\/query.fcgi?cmd=Retrieve&amp;db=PubMed&amp;dopt=Abstract&amp;list_uids=32721944\" aria-label=\"PubMed reference 39\" target=\"_blank\">PubMed<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 39\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Review%3A%20knots%20and%20other%20new%20topological%20effects%20in%20liquid%20crystals%20and%20colloids&amp;journal=Rep.%20Prog.%20Phys.&amp;volume=83&amp;publication_year=2020&amp;author=Smalyukh%2CII\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR40\">Zhao, H., Tai, J.-S. B., Wu, J.-S. &amp; Smalyukh, I. I. Liquid crystal defect structures with M\u00f6bius strip topology. Nat. Phys. 19, 451\u2013459 (2023).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"cas reference\" data-track-action=\"cas reference\" href=\"https:\/\/www.nature.com\/articles\/cas-redirect\/1:CAS:528:DC%2BB3sXhtFGgtrc%3D\" aria-label=\"CAS reference 40\" target=\"_blank\">CAS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 40\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Liquid%20crystal%20defect%20structures%20with%20M%C3%B6bius%20strip%20topology&amp;journal=Nat.%20Phys.&amp;volume=19&amp;pages=451-459&amp;publication_year=2023&amp;author=Zhao%2CH&amp;author=Tai%2CJ-SB&amp;author=Wu%2CJ-S&amp;author=Smalyukh%2CII\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR41\">Mundoor, H., Senyuk, B. &amp; Smalyukh, I. I. Triclinic nematic colloidal crystals from competing elastic and electrostatic interactions. Science 352, 69\u201373 (2016).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"cas reference\" data-track-action=\"cas reference\" href=\"https:\/\/www.nature.com\/articles\/cas-redirect\/1:CAS:528:DC%2BC28XlsFSmu7Y%3D\" aria-label=\"CAS reference 41\" target=\"_blank\">CAS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"pubmed reference\" data-track-action=\"pubmed reference\" href=\"http:\/\/www.ncbi.nlm.nih.gov\/entrez\/query.fcgi?cmd=Retrieve&amp;db=PubMed&amp;dopt=Abstract&amp;list_uids=27034368\" aria-label=\"PubMed reference 41\" target=\"_blank\">PubMed<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 41\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Triclinic%20nematic%20colloidal%20crystals%20from%20competing%20elastic%20and%20electrostatic%20interactions&amp;journal=Science&amp;volume=352&amp;pages=69-73&amp;publication_year=2016&amp;author=Mundoor%2CH&amp;author=Senyuk%2CB&amp;author=Smalyukh%2CII\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR42\">Xu, S. &amp; Wu, C. Space-time crystal and space-time group. Phys. Rev. Lett. 120, 096401 (2018).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"cas reference\" data-track-action=\"cas reference\" href=\"https:\/\/www.nature.com\/articles\/cas-redirect\/1:CAS:528:DC%2BC1MXltFSmtLo%3D\" aria-label=\"CAS reference 42\" target=\"_blank\">CAS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"pubmed reference\" data-track-action=\"pubmed reference\" href=\"http:\/\/www.ncbi.nlm.nih.gov\/entrez\/query.fcgi?cmd=Retrieve&amp;db=PubMed&amp;dopt=Abstract&amp;list_uids=29547328\" aria-label=\"PubMed reference 42\" target=\"_blank\">PubMed<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 42\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Space-time%20crystal%20and%20space-time%20group&amp;journal=Phys.%20Rev.%20Lett.&amp;volume=120&amp;publication_year=2018&amp;author=Xu%2CS&amp;author=Wu%2CC\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR43\">Gallego-G\u00f3mez, F., del Monte, F. &amp; Meerholz, K. Optical gain by a simple photoisomerization process. Nat. Mater. 7, 490\u2013497 (2008).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"pubmed reference\" data-track-action=\"pubmed reference\" href=\"http:\/\/www.ncbi.nlm.nih.gov\/entrez\/query.fcgi?cmd=Retrieve&amp;db=PubMed&amp;dopt=Abstract&amp;list_uids=18454152\" aria-label=\"PubMed reference 43\" target=\"_blank\">PubMed<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 43\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Optical%20gain%20by%20a%20simple%20photoisomerization%20process&amp;journal=Nat.%20Mater.&amp;volume=7&amp;pages=490-497&amp;publication_year=2008&amp;author=Gallego-G%C3%B3mez%2CF&amp;author=Monte%2CF&amp;author=Meerholz%2CK\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR44\">Brener, E. A. &amp; Marchenko, V. I. Nonlinear theory of dislocations in smectic crystals: an exact solution. Phys. Rev. E 59, R4752\u2013R4753 (1999).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"cas reference\" data-track-action=\"cas reference\" href=\"https:\/\/www.nature.com\/articles\/cas-redirect\/1:CAS:528:DyaK1MXivV2rs7s%3D\" aria-label=\"CAS reference 44\" target=\"_blank\">CAS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 44\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Nonlinear%20theory%20of%20dislocations%20in%20smectic%20crystals%3A%20an%20exact%20solution&amp;journal=Phys.%20Rev.%20E&amp;volume=59&amp;pages=R4752-R4753&amp;publication_year=1999&amp;author=Brener%2CEA&amp;author=Marchenko%2CVI\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR45\">Sohn, H. R. O. &amp; Smalyukh, I. I. Electrically powered motions of toron crystallites in chiral liquid crystals. Proc. Natl Acad. Sci. USA 117, 6437\u20136445 (2020).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"cas reference\" data-track-action=\"cas reference\" href=\"https:\/\/www.nature.com\/articles\/cas-redirect\/1:CAS:528:DC%2BB3cXlsl2jt78%3D\" aria-label=\"CAS reference 45\" target=\"_blank\">CAS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"pubmed reference\" data-track-action=\"pubmed reference\" href=\"http:\/\/www.ncbi.nlm.nih.gov\/entrez\/query.fcgi?cmd=Retrieve&amp;db=PubMed&amp;dopt=Abstract&amp;list_uids=32161127\" aria-label=\"PubMed reference 45\" target=\"_blank\">PubMed<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"pubmed central reference\" data-track-action=\"pubmed central reference\" href=\"http:\/\/www.ncbi.nlm.nih.gov\/pmc\/articles\/PMC7104241\" aria-label=\"PubMed Central reference 45\" target=\"_blank\">PubMed Central<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 45\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Electrically%20powered%20motions%20of%20toron%20crystallites%20in%20chiral%20liquid%20crystals&amp;journal=Proc.%20Natl%20Acad.%20Sci.%20USA&amp;volume=117&amp;pages=6437-6445&amp;publication_year=2020&amp;author=Sohn%2CHRO&amp;author=Smalyukh%2CII\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR46\">Prigogine, I. Time, structure, and fluctuations. Science 201, 777\u2013785 (1978).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"cas reference\" data-track-action=\"cas reference\" href=\"https:\/\/www.nature.com\/articles\/cas-redirect\/1:STN:280:DC%2BC3cvhvFOgsA%3D%3D\" aria-label=\"CAS reference 46\" target=\"_blank\">CAS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"pubmed reference\" data-track-action=\"pubmed reference\" href=\"http:\/\/www.ncbi.nlm.nih.gov\/entrez\/query.fcgi?cmd=Retrieve&amp;db=PubMed&amp;dopt=Abstract&amp;list_uids=17738519\" aria-label=\"PubMed reference 46\" target=\"_blank\">PubMed<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 46\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Time%2C%20structure%2C%20and%20fluctuations&amp;journal=Science&amp;volume=201&amp;pages=777-785&amp;publication_year=1978&amp;author=Prigogine%2CI\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR47\">Zhang, R. et al. Spatiotemporal control of liquid crystal structure and dynamics through activity patterning. Nat. Mater. 20, 875\u2013882 (2021).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"cas reference\" data-track-action=\"cas reference\" href=\"https:\/\/www.nature.com\/articles\/cas-redirect\/1:CAS:528:DC%2BB3MXkvValt7g%3D\" aria-label=\"CAS reference 47\" target=\"_blank\">CAS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"pubmed reference\" data-track-action=\"pubmed reference\" href=\"http:\/\/www.ncbi.nlm.nih.gov\/entrez\/query.fcgi?cmd=Retrieve&amp;db=PubMed&amp;dopt=Abstract&amp;list_uids=33603187\" aria-label=\"PubMed reference 47\" target=\"_blank\">PubMed<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"pubmed central reference\" data-track-action=\"pubmed central reference\" href=\"http:\/\/www.ncbi.nlm.nih.gov\/pmc\/articles\/PMC8404743\" aria-label=\"PubMed Central reference 47\" target=\"_blank\">PubMed Central<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 47\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Spatiotemporal%20control%20of%20liquid%20crystal%20structure%20and%20dynamics%20through%20activity%20patterning&amp;journal=Nat.%20Mater.&amp;volume=20&amp;pages=875-882&amp;publication_year=2021&amp;author=Zhang%2CR\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR48\">Zhao, H., Malomed, B. A. &amp; Smalyukh, I. I. Topological solitonic macromolecules. Nat. Commun. 14, 4581 (2023).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"cas reference\" data-track-action=\"cas reference\" href=\"https:\/\/www.nature.com\/articles\/cas-redirect\/1:CAS:528:DC%2BB3sXhsF2htb%2FM\" aria-label=\"CAS reference 48\" target=\"_blank\">CAS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"pubmed reference\" data-track-action=\"pubmed reference\" href=\"http:\/\/www.ncbi.nlm.nih.gov\/entrez\/query.fcgi?cmd=Retrieve&amp;db=PubMed&amp;dopt=Abstract&amp;list_uids=37516736\" aria-label=\"PubMed reference 48\" target=\"_blank\">PubMed<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"pubmed central reference\" data-track-action=\"pubmed central reference\" href=\"http:\/\/www.ncbi.nlm.nih.gov\/pmc\/articles\/PMC10387112\" aria-label=\"PubMed Central reference 48\" target=\"_blank\">PubMed Central<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 48\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Topological%20solitonic%20macromolecules&amp;journal=Nat.%20Commun.&amp;volume=14&amp;publication_year=2023&amp;author=Zhao%2CH&amp;author=Malomed%2CBA&amp;author=Smalyukh%2CII\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR49\">Lee, Y.-H. et al. Recent progress in Pancharatnam\u2013Berry phase optical elements and the applications for virtual\/augmented realities. Opt. Data Process. Storage 3, 79\u201388 (2017).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 49\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Recent%20progress%20in%20Pancharatnam%E2%80%93Berry%20phase%20optical%20elements%20and%20the%20applications%20for%20virtual%2Faugmented%20realities&amp;journal=Opt.%20Data%20Process.%20Storage&amp;volume=3&amp;pages=79-88&amp;publication_year=2017&amp;author=Lee%2CY-H\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR50\">Cohen, E. et al. Geometric phase from Aharonov\u2013Bohm to Pancharatnam\u2013Berry and beyond. Nat. Rev. Phys. 1, 437\u2013449 (2019).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 50\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Geometric%20phase%20from%20Aharonov%E2%80%93Bohm%20to%20Pancharatnam%E2%80%93Berry%20and%20beyond&amp;journal=Nat.%20Rev.%20Phys.&amp;volume=1&amp;pages=437-449&amp;publication_year=2019&amp;author=Cohen%2CE\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR51\">Lyubarov, M. et al. Amplified emission and lasing in photonic time crystals. Science 377, 425\u2013428 (2022).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"cas reference\" data-track-action=\"cas reference\" href=\"https:\/\/www.nature.com\/articles\/cas-redirect\/1:CAS:528:DC%2BB38XhvV2rtrjM\" aria-label=\"CAS reference 51\" target=\"_blank\">CAS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"pubmed reference\" data-track-action=\"pubmed reference\" href=\"http:\/\/www.ncbi.nlm.nih.gov\/entrez\/query.fcgi?cmd=Retrieve&amp;db=PubMed&amp;dopt=Abstract&amp;list_uids=35679355\" aria-label=\"PubMed reference 51\" target=\"_blank\">PubMed<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 51\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Amplified%20emission%20and%20lasing%20in%20photonic%20time%20crystals&amp;journal=Science&amp;volume=377&amp;pages=425-428&amp;publication_year=2022&amp;author=Lyubarov%2CM\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR52\">Chang, T. et al. Cellulose nanocrystal chiral photonic micro-flakes for multilevel anti-counterfeiting and identification. Chem. Eng. J. 446, 136630 (2022).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"cas reference\" data-track-action=\"cas reference\" href=\"https:\/\/www.nature.com\/articles\/cas-redirect\/1:CAS:528:DC%2BB38XhtlWltLzM\" aria-label=\"CAS reference 52\" target=\"_blank\">CAS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 52\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Cellulose%20nanocrystal%20chiral%20photonic%20micro-flakes%20for%20multilevel%20anti-counterfeiting%20and%20identification&amp;journal=Chem.%20Eng.%20J.&amp;volume=446&amp;publication_year=2022&amp;author=Chang%2CT\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR53\">Huang, W. &amp; Mow, W. H. PiCode: 2D barcode with embedded picture and ViCode: 3D barcode with embedded video. In Proc. 19th Annual International Conference on Mobile Computing &amp; Networking 139\u2013142 (ACM, 2013).<\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR54\">Chang, S. et al. Electrical tuning of branched flow of light. Nat. Commun. 15, 197 (2024).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"cas reference\" data-track-action=\"cas reference\" href=\"https:\/\/www.nature.com\/articles\/cas-redirect\/1:CAS:528:DC%2BB2cXkt1WntA%3D%3D\" aria-label=\"CAS reference 54\" target=\"_blank\">CAS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"pubmed reference\" data-track-action=\"pubmed reference\" href=\"http:\/\/www.ncbi.nlm.nih.gov\/entrez\/query.fcgi?cmd=Retrieve&amp;db=PubMed&amp;dopt=Abstract&amp;list_uids=38172091\" aria-label=\"PubMed reference 54\" target=\"_blank\">PubMed<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"pubmed central reference\" data-track-action=\"pubmed central reference\" href=\"http:\/\/www.ncbi.nlm.nih.gov\/pmc\/articles\/PMC10764866\" aria-label=\"PubMed Central reference 54\" target=\"_blank\">PubMed Central<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 54\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Electrical%20tuning%20of%20branched%20flow%20of%20light&amp;journal=Nat.%20Commun.&amp;volume=15&amp;publication_year=2024&amp;author=Chang%2CS\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR55\">Poy, G. et al. Interaction and co-assembly of optical and topological solitons. Nat. Photon. 16, 454\u2013461 (2022).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"cas reference\" data-track-action=\"cas reference\" href=\"https:\/\/www.nature.com\/articles\/cas-redirect\/1:CAS:528:DC%2BB38XhsVSntbvM\" aria-label=\"CAS reference 55\" target=\"_blank\">CAS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 55\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Interaction%20and%20co-assembly%20of%20optical%20and%20topological%20solitons&amp;journal=Nat.%20Photon.&amp;volume=16&amp;pages=454-461&amp;publication_year=2022&amp;author=Poy%2CG\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR56\">Martinez, A., Mireles, H. C. &amp; Smalyukh, I. I. Large-area optoelastic manipulation of colloidal particles in liquid crystals using photoresponsive molecular surface monolayers. Proc. Natl Acad. Sci. USA 108, 20891\u201320896 (2011).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"cas reference\" data-track-action=\"cas reference\" href=\"https:\/\/www.nature.com\/articles\/cas-redirect\/1:CAS:528:DC%2BC38XnvVCrsg%3D%3D\" aria-label=\"CAS reference 56\" target=\"_blank\">CAS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"pubmed reference\" data-track-action=\"pubmed reference\" href=\"http:\/\/www.ncbi.nlm.nih.gov\/entrez\/query.fcgi?cmd=Retrieve&amp;db=PubMed&amp;dopt=Abstract&amp;list_uids=22160673\" aria-label=\"PubMed reference 56\" target=\"_blank\">PubMed<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"pubmed central reference\" data-track-action=\"pubmed central reference\" href=\"http:\/\/www.ncbi.nlm.nih.gov\/pmc\/articles\/PMC3248499\" aria-label=\"PubMed Central reference 56\" target=\"_blank\">PubMed Central<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 56\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Large-area%20optoelastic%20manipulation%20of%20colloidal%20particles%20in%20liquid%20crystals%20using%20photoresponsive%20molecular%20surface%20monolayers&amp;journal=Proc.%20Natl%20Acad.%20Sci.%20USA&amp;volume=108&amp;pages=20891-20896&amp;publication_year=2011&amp;author=Martinez%2CA&amp;author=Mireles%2CHC&amp;author=Smalyukh%2CII\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n<p class=\"c-article-references__text\" id=\"ref-CR57\">Lee, T., Trivedi, R. P. &amp; Smalyukh, I. I. Multimodal nonlinear optical polarizing microscopy of long-range molecular order in liquid crystals. Opt. Lett. 35, 3447\u20133449 (2010).<\/p>\n<p class=\"c-article-references__links u-hide-print\"><a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"cas reference\" data-track-action=\"cas reference\" href=\"https:\/\/www.nature.com\/articles\/cas-redirect\/1:CAS:528:DC%2BC3cXhsFSrs73M\" aria-label=\"CAS reference 57\" target=\"_blank\">CAS<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" rel=\"nofollow noopener\" data-track-label=\"link\" data-track-item_id=\"link\" data-track-value=\"pubmed reference\" data-track-action=\"pubmed reference\" href=\"http:\/\/www.ncbi.nlm.nih.gov\/entrez\/query.fcgi?cmd=Retrieve&amp;db=PubMed&amp;dopt=Abstract&amp;list_uids=20967095\" aria-label=\"PubMed reference 57\" target=\"_blank\">PubMed<\/a>\u00a0<br \/>\n    <a data-track=\"click_references\" data-track-action=\"google scholar reference\" data-track-value=\"google scholar reference\" data-track-label=\"link\" data-track-item_id=\"link\" rel=\"nofollow noopener\" aria-label=\"Google Scholar reference 57\" href=\"http:\/\/scholar.google.com\/scholar_lookup?&amp;title=Multimodal%20nonlinear%20optical%20polarizing%20microscopy%20of%20long-range%20molecular%20order%20in%20liquid%20crystals&amp;journal=Opt.%20Lett.&amp;volume=35&amp;pages=3447-3449&amp;publication_year=2010&amp;author=Lee%2CT&amp;author=Trivedi%2CRP&amp;author=Smalyukh%2CII\" target=\"_blank\"><br \/>\n                    Google Scholar<\/a>\u00a0\n                <\/p>\n","protected":false},"excerpt":{"rendered":"Chaikin, P. M. &amp; Lubensky, T. C. Principles of Condensed Matter Physics (Cambridge Univ. Press, 2000). Yeh, P.&hellip;\n","protected":false},"author":2,"featured_media":132975,"comment_status":"","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[49],"tags":[26297,2365,257,31205,2528,15767,2529,199,79,35791],"class_list":{"0":"post-132974","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","7":"category-physics","8":"tag-biomaterials","9":"tag-condensed-matter-physics","10":"tag-general","11":"tag-liquid-crystals","12":"tag-materials-science","13":"tag-nanotechnology","14":"tag-optical-and-electronic-materials","15":"tag-physics","16":"tag-science","17":"tag-topological-defects"},"_links":{"self":[{"href":"https:\/\/www.newsbeep.com\/us\/wp-json\/wp\/v2\/posts\/132974","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.newsbeep.com\/us\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.newsbeep.com\/us\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.newsbeep.com\/us\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.newsbeep.com\/us\/wp-json\/wp\/v2\/comments?post=132974"}],"version-history":[{"count":0,"href":"https:\/\/www.newsbeep.com\/us\/wp-json\/wp\/v2\/posts\/132974\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.newsbeep.com\/us\/wp-json\/wp\/v2\/media\/132975"}],"wp:attachment":[{"href":"https:\/\/www.newsbeep.com\/us\/wp-json\/wp\/v2\/media?parent=132974"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.newsbeep.com\/us\/wp-json\/wp\/v2\/categories?post=132974"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.newsbeep.com\/us\/wp-json\/wp\/v2\/tags?post=132974"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}