Quantum versus Population Dynamics over Cayley Graphs

Abstract: 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.