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Research Highlights

Time crystals in long-range classical noisy systems

Andrea Pizzi, Andreas Nunnenkamp, and Johannes Knolle.

A team of current and former TCM researchers showed how long-range interactions can be leveraged to realize a classical discrete time crystal.

Classical discrete time crystal with period doubling in directed percolation with long-range and periodically modulated update rules.

Stochastic processes are ubiquitous throughout the sciences. A minimal description of noisy classical many-body dynamics is provided by probabilistic cellular automata, in which the state of the system is encoded in a sequence of bits and its evolution in discrete time determined by simple (but stochastic) update rules. Due to their noisy nature these systems are generally characterized by a quick ‘loss of memory’ of their past, as captured by a finite correlation time. The authors show that this paradigm breaks down if the range of the interactions in the system is sufficiently long. The result is a novel bistable phase of directed percolation which, in the presence of a periodic modulation of the update rules, turns into a classical discrete time crystal. The latter is a non-equilibrium phase of matter which breaks the discrete time translational symmetry of the update rules. Thus, the system maintains an infinite autocorrelation time.

This research paves the way for the study of novel dynamical behaviours in the unexplored field of driven probabilistic cellular automata. As a timely example, the team has also investigated the ramifications of these phenomena in the context of social networks, where they recently linked them to the timely phenomenon of biennial epidemics (see the article in Physical Review Research).

Pizzi, A., Nunnenkamp, A., and Knolle, J., "Bistability and time crystals in long-ranged directed percolation." Nature Communications 12.1 (2021): 1-8.

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