纠缠引发的网络分叉的出现
Emergence of Network Bifurcation Triggered by Entanglement
摘要：
在许多非线性系统中，如等离子体振荡、玻色子凝聚、化学反应，甚至捕食者-被捕食者振荡，其粗粒度动力学都是由一个包含反对称跃迁的方程所控制，称为反对称Lotka-Volterra（ALV）方程。在这项工作中，我们证明了一个新的分歧机制的ALV方程，其中的平衡态可以急剧改变翻转的稳定性的一对不动点。作为一个应用，我们研究了演化网络中的分岔机制，发现分岔点可以通过微观量子纠缠来定量确定.平衡态可以从一种全球人口凝聚状态转变为另一种支持同质网络全球合作的状态。换句话说，我们的结果表明，存在一类多体系统，其中的宏观性质是不变的与一定量的微观纠缠，但它们可以突然改变，一旦纠缠超过一个临界值。此外，我们提供的数值证据表明，分叉的出现对网络拓扑结构的变化是强大的，临界值与我们的理论预测吻合得很好。这些结果表明，分叉机制可能是普遍存在于许多物理系统，除了进化网络。
英文摘要：
In many non-linear systems, such as plasma oscillation, boson condensation, chemical reaction, and even predatory-prey oscillation, the coarse-grained dynamics are governed by an equation containing anti-symmetric transitions, known as the anti-symmetric Lotka-Volterra (ALV) equations. In this work, we prove the existence of a novel bifurcation mechanism for the ALV equations, where the equilibrium state can be drastically changed by flipping the stability of a pair of fixed points. As an application, we focus on the implications of the bifurcation mechanism for evolutionary networks; we found that the bifurcation point can be determined quantitatively by the microscopic quantum entanglement. The equilibrium state can be critically changed from one type of global demographic condensation to another state that supports global cooperation for homogeneous networks. In other words, our results indicate that there exist a class of many-body systems where the macroscopic properties are invariant with a certain amount of microscopic entanglement, but they can be changed abruptly once the entanglement exceeds a critical value. Furthermore, we provide numerical evidence showing that the emergence of bifurcation is robust against the change of the network topologies, and the critical values are in good agreement with our theoretical prediction. These results show that the bifurcation mechanism could be ubiquitous in many physical systems, in addition to evolutionary networks.
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