长程定向逾渗中的双稳态和时间晶体
Bistability and time crystals in long-ranged directed percolation
摘要：
随机过程支配着科学中各种各样的现实系统的时间演化。利用概率元胞自动机给出了马尔可夫图中含噪多粒子系统的最小描述，并引入了空间维数的概念.在这里，我们提出了一个简单的元胞自动机与幂律相互作用，产生了一个长期的定向渗流，其长期的行为不仅是由系统动力学，但也由初始条件的一个连续相。在存在的周期性调制的更新规则，我们发现，系统响应的周期大于调制的指数（在系统大小）长的时间。这种离散时间平移对称性的基础动力学的破坏是通过补偿噪声引起的缺陷的长程相互作用的自校正机制实现的。因此，我们的工作提供了一个坚实的例子，一个经典的离散时间晶体相的物质和铺平了道路，为研究新的非平衡相在未开发的领域的“Floquet概率元胞自动机”。
英文摘要：
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'.
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