论文标题
进化游戏理论中的手性边缘模式：岩纸剪辑器的Kagome网络
Chiral edge modes in evolutionary game theory: a kagome network of rock-paper-scissors
论文作者
论文摘要
从理论上讲，我们在自然科学以外的系统中证明了手性边缘模式的实现。具体而言，我们阐明了岩纸仪（K-RPS）的Kagome网络具有人口密度的手性边缘模式，该模式受批量非客气拓扑的保护。手性边缘模式的出现通过数值求解Lotka-Volterra（LV）方程来证明。可以通过单个RPS循环的循环运动来直观地理解该数值结果，该循环运动类似于费米子的回旋子运动。此外，我们指出的是，线性化的LV方程在数学上等同于描述量子系统的Schrödinger方程。这种等效性使我们能够阐明K-RPS手性边缘模式的拓扑起源。收益矩阵的非零CHERN数量诱导了人口密度的手性边缘模式，这体现了进化游戏理论所描述的二维系统中的批量边缘对应关系。
We theoretically demonstrate the realization of a chiral edge mode in a system beyond natural science. Specifically, we elucidate that a kagome network of rock-paper-scissors (K-RPS) hosts a chiral edge mode of the population density which is protected by the non-trivial topology in the bulk. The emergence of the chiral edge mode is demonstrated by numerically solving the Lotka-Volterra (LV) equation. This numerical result can be intuitively understood in terms of cyclic motion of a single RPS cycle which is analogues to the cyclotron motion of fermions. Furthermore, we point out that a linearized LV equation is mathematically equivalent to the Schrödinger equation describing quantum systems. This equivalence allows us to clarify the topological origin of the chiral edge mode in the K-RPS; a non-zero Chern number of the payoff matrix induces the chiral edge mode of the population density, which exemplifies the bulk-edge correspondence in two-dimensional systems described by evolutionary game theory.
