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Bistability and time crystals in long-ranged directed percolation

Author

Listed:
  • Andrea Pizzi

    (University of Cambridge)

  • Andreas Nunnenkamp

    (University of Nottingham)

  • Johannes Knolle

    (Technische Universität München
    Munich Center for Quantum Science and Technology (MCQST)
    Imperial College London)

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 driven probabilistic cellular automata.

Suggested Citation

  • Andrea Pizzi & Andreas Nunnenkamp & Johannes Knolle, 2021. "Bistability and time crystals in long-ranged directed percolation," Nature Communications, Nature, vol. 12(1), pages 1-8, December.
  • Handle: RePEc:nat:natcom:v:12:y:2021:i:1:d:10.1038_s41467-021-21259-4
    DOI: 10.1038/s41467-021-21259-4
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    Cited by:

    1. Bang Liu & Li-Hua Zhang & Qi-Feng Wang & Yu Ma & Tian-Yu Han & Jun Zhang & Zheng-Yuan Zhang & Shi-Yao Shao & Qing Li & Han-Chao Chen & Bao-Sen Shi & Dong-Sheng Ding, 2024. "Higher-order and fractional discrete time crystals in Floquet-driven Rydberg atoms," Nature Communications, Nature, vol. 15(1), pages 1-8, December.

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