2005/01/01 by Andrea Pizzi, Andreas Nunnenkamp, Johannes Knolle +4 · 1 citation
Chemistry · Computer Science · Mathematics · Physics and Astronomy · #Astronomy #Astrophysics #Astrophysics and Star Formation Studies #Bistability #Brown dwarf #Cellular Automata and Applications #Cellular automaton #Directed percolation #Low Mass #Modulation (music) #Molecular Spectroscopy and Structure #Molecular cloud #Percolation (cognitive psychology) #Phase (matter) #Physics #Population #Probabilistic logic #Quantum many-body systems #Spectroscopy and Laser Applications #Stars #Stochastic cellular automaton #Stochastic processes and statistical mechanics #Translation (biology) #cond-mat.stat-mech #quant-ph
paper · pdf · doi:10.1038/s41467-021-21259-4
published as Nature Communications, 12.1, 1-8 (2021) · 9+3 pages, 4+2 figures
openalex publication_date 2005/01/01 · openalex created_date 2016/06/24 · arxiv created 2021/02/24 · arxiv updated 2021/02/25 · openalex updated_date 2026/06/23
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.