基于量子规则的随机图生长
Growing Random Graphs with Quantum Rules
摘要：
随机图是研究复杂动态网络（如互联网、大脑或社会经济现象）的核心要素。生成随机图的新方法可以产生新的应用程序，并深入了解更成熟的技术。我们提出了两种变化的模型来生长随机图和树，基于连续时间量子行走的图形。在随机特征时间之后，测量步行者的位置，并将新节点附接到步行者倒塌的节点。这样的动力学系统让人想起量子力学中的自发坍缩理论。我们调查几个率的这种自发崩溃的个人量子步行者和两个非相互作用的步行者。我们推测（并报告一些数值证据），模型是无标度的。
英文摘要：
Random graphs are a central element of the study of complex dynamical networks such as the internet, the brain, or socioeconomic phenomena. New methods to generate random graphs can spawn new applications and give insights into more established techniques. We propose two variations of a model to grow random graphs and trees, based on continuous-time quantum walks on the graphs. After a random characteristic time, the position of the walker(s) is measured and new nodes are attached to the nodes where the walkers collapsed. Such dynamical systems are reminiscent of the class of spontaneous collapse theories in quantum mechanics. We investigate several rates of this spontaneous collapse for an individual quantum walker and for two non-interacting walkers. We conjecture (and report some numerical evidence) that the models are scale-free.
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