$(1 + 1)D$量子元胞自动机中的量子和经典时间关联
Quantum and classical temporal correlations in $(1 + 1)D$ Quantum Cellular Automata
摘要：
本文利用$(1 + 1)$维量子元胞自动机研究了具有非平衡稳态相变的量子系统在临界点附近纠缠和相干的演化。这种构造允许直接进入潜在的非平衡动力学的整个时空结构。它包含了经典轨迹的完整集合，也允许分析非传统的相关性，例如“现在”和“过去”之间时间方向上的纠缠。接近临界状态时，这些相关性的动力学--我们通过二阶Renyi熵来量化--在接近平稳性时显示出幂律行为。我们的分析是基于经典的非平衡系统的量子推广：Domany-Kinzel元胞自动机和Bagnoli-Boccara-Rechtman模型，我们提供了相关的熵的经典和量子分量的临界指数的估计。我们的研究表明，$(1 + 1)$ -维量子元胞自动机允许一个有趣的观点的经典和量子关联的性质在平衡系统。
英文摘要：
We employ $(1 + 1)$-dimensional quantum cellular automata to study the evolution of entanglement and coherence near criticality in quantum systems that display non-equilibrium steady-state phase transitions. This construction permits direct access to the entire space-time structure of the underlying non-equilibrium dynamics. It contains the full ensemble of classical trajectories and also allows for the analysis of unconventional correlations, such as entanglement in the time direction between the "present" and the "past". Close to criticality, the dynamics of these correlations - which we quantify through the second-order Renyi entropy - displays power-law behavior on its approach to stationarity. Our analysis is based on quantum generalizations of classical non-equilibrium systems: the Domany-Kinzel cellular automaton and the Bagnoli-Boccara-Rechtman model, for which we provide estimates for the critical exponents related to the classical and quantum components of the entropy. Our study shows that $(1 + 1)$-dimensional quantum cellular automata permit an intriguing perspective on the nature of classical and quantum correlations in out-of-equilibrium systems.
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