论文标题
可逆的蜂窝自动机中的太空状动力学
Space-like dynamics in a reversible cellular automaton
论文作者
论文摘要
在本文中，我们研究了规则54可逆细胞自动机中的空间演变，这是确定性相互作用晶格气体的范式示例。我们表明，自动机的时间配置的空间翻译是根据局部确定性图给出的，其支持较小，但比时间演化的支持大。因此，该模型是时空双重可逆细胞自动机的一个示例，即其双重偶（通常不同）可逆细胞自动机。我们对结果提供了两个等效的解释；第一个依赖于准颗粒的动力学，并遵循对所有相关时间配置的详尽检查，而第二个则依赖于基于动力学电路表示的纯代数考虑。此外，我们使用局部空间演化图的属性来提供位于同一空间坐标处的局部可观察物的多时间相关函数的矩阵乘积表示的替代推导。
In this paper we study the space evolution in the Rule 54 reversible cellular automaton, which is a paradigmatic example of a deterministic interacting lattice gas. We show that the spatial translation of time configurations of the automaton is given in terms of local deterministic maps with the support that is small but bigger than that of the time evolution. The model is thus an example of space-time dual reversible cellular automaton, i.e. its dual is also (in general different) reversible cellular automaton. We provide two equivalent interpretations of the result; the first one relies on the dynamics of quasi-particles and follows from an exhaustive check of all the relevant time configurations, while the second one relies on purely algebraic considerations based on the circuit representation of the dynamics. Additionally, we use the properties of the local space evolution maps to provide an alternative derivation of the matrix product representation of multi-time correlation functions of local observables positioned at the same spatial coordinate.
