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dc.contributor.authorPizzi, Andrea
dc.contributor.authorNunnenkamp, Andreas
dc.contributor.authorKnolle, Johannes
dc.date.accessioned2021-02-16T16:18:07Z
dc.date.available2021-02-16T16:18:07Z
dc.date.issued2021-02-16
dc.date.submitted2020-07-02
dc.identifier.issn2041-1723
dc.identifier.others41467-021-21259-4
dc.identifier.other21259
dc.identifier.urihttps://www.repository.cam.ac.uk/handle/1810/317729
dc.descriptionFunder: Royal Society; doi: https://doi.org/10.13039/501100000288
dc.description.abstractStochastic processes govern the time evolution of a huge variety of realistic systems throughout the sciences. A minimal description of noisy many-particle systems within a Markovian picture and with a notion of spatial dimension is given by probabilistic cellular automata, which typically feature time-independent and short-ranged update rules. Here, we propose a simple cellular automaton with power-law interactions that gives rise to a bistable phase of long-ranged directed percolation whose long-time behaviour is not only dictated by the system dynamics, but also by the initial conditions. In the presence of a periodic modulation of the update rules, we find that the system responds with a period larger than that of the modulation for an exponentially (in system size) long time. This breaking of discrete time translation symmetry of the underlying dynamics is enabled by a self-correcting mechanism of the long-ranged interactions which compensates noise-induced imperfections. Our work thus provides a firm example of a classical discrete time crystal phase of matter and paves the way for the study of novel non-equilibrium phases in the unexplored field of driven probabilistic cellular automata.
dc.languageen
dc.publisherSpringer Science and Business Media LLC
dc.rightsAttribution 4.0 International (CC BY 4.0)
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.subjectArticle
dc.subject/639/766/119
dc.subject/639/766/530
dc.subjectarticle
dc.titleBistability and time crystals in long-ranged directed percolation.
dc.typeArticle
dc.date.updated2021-02-16T16:18:06Z
prism.issueIdentifier1
prism.publicationNameNat Commun
prism.volume12
dc.identifier.doi10.17863/CAM.64843
dcterms.dateAccepted2021-01-19
rioxxterms.versionofrecord10.1038/s41467-021-21259-4
rioxxterms.versionVoR
rioxxterms.licenseref.urihttp://creativecommons.org/licenses/by/4.0/
dc.contributor.orcidPizzi, Andrea [0000-0002-6714-7360]
dc.contributor.orcidNunnenkamp, Andreas [0000-0003-2390-7636]
dc.contributor.orcidKnolle, Johannes [0000-0002-0956-2419]
dc.identifier.eissn2041-1723
dc.publisher.urlhttp://dx.doi.org/10.1038/s41467-021-21259-4
pubs.funder-project-idRoyal Society (RGF/EA/180038)
pubs.funder-project-idRoyal Society (URF\R\191001)
cam.issuedOnline2021-02-16


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Attribution 4.0 International (CC BY 4.0)
Except where otherwise noted, this item's licence is described as Attribution 4.0 International (CC BY 4.0)