论文标题
量子与人口动态在cayley图上
Quantum versus Population Dynamics over Cayley Graphs
论文作者
论文摘要
考虑一个图形，其顶点是由相同对象填充的，以及一种算法，用于放置在每个顶点上的对象数的时间进化。可以使用简单且廉价的实验室设置观察和研究这些对象的离散动力学。这种种群动力学与在同一图上跳跃的粒子的量子动力学之间存在许多相似之处。在这项工作中，我们表明原始图的特定装饰可以在人群模型和量子动力学之间进行精确映射。因此，图形上的人口动态是另一个可以模拟量子效应的经典平台。几个示例用于证明这一主张。
Consider a graph whose vertices are populated by identical objects, together with an algorithm for the time-evolution of the number of objects placed at each of the vertices. The discrete dynamics of these objects can be observed and studied using simple and inexpensive laboratory settings. There are many similarities but also many differences between such population dynamics and the quantum dynamics of a particle hopping on the same graph. In this work, we show that a specific decoration of the original graph enables an exact mapping between the models of population and quantum dynamics. As such, population dynamics over graphs is yet another classical platform that can simulate quantum effects. Several examples are used to demonstrate this claim.
