Andrea Pizzi
Bistability and time crystals in long-ranged directed percolation
Pizzi, Andrea; Nunnenkamp, Andreas; Knolle, Johannes
Authors
Andreas Nunnenkamp
Johannes Knolle
Abstract
Stochastic 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 'Floquet probabilistic cellular automata'.
Citation
Pizzi, A., Nunnenkamp, A., & Knolle, J. (2021). Bistability and time crystals in long-ranged directed percolation. Nature Communications, 12, Article 1061. https://doi.org/10.1038/s41467-021-21259-4
Journal Article Type | Article |
---|---|
Acceptance Date | Jan 19, 2021 |
Online Publication Date | Feb 16, 2021 |
Publication Date | Feb 16, 2021 |
Deposit Date | Jan 28, 2021 |
Publicly Available Date | Feb 19, 2021 |
Journal | Nature Communications |
Electronic ISSN | 2041-1723 |
Publisher | Nature Publishing Group |
Peer Reviewed | Peer Reviewed |
Volume | 12 |
Article Number | 1061 |
DOI | https://doi.org/10.1038/s41467-021-21259-4 |
Public URL | https://nottingham-repository.worktribe.com/output/5247197 |
Publisher URL | https://www.nature.com/articles/s41467-021-21259-4 |
Files
PCA DTC
(1.5 Mb)
PDF
Publisher Licence URL
https://creativecommons.org/licenses/by/4.0/
Downloadable Citations
About Repository@Nottingham
Administrator e-mail: discovery-access-systems@nottingham.ac.uk
This application uses the following open-source libraries:
SheetJS Community Edition
Apache License Version 2.0 (http://www.apache.org/licenses/)
PDF.js
Apache License Version 2.0 (http://www.apache.org/licenses/)
Font Awesome
SIL OFL 1.1 (http://scripts.sil.org/OFL)
MIT License (http://opensource.org/licenses/mit-license.html)
CC BY 3.0 ( http://creativecommons.org/licenses/by/3.0/)
Powered by Worktribe © 2024
Advanced Search