Topological band theory of thermal diffusion and rock-paper-scissors games

While topological edge modes are originally reported for electronic systems, it has tuned out that their platforms may extend beyond quantum systems[1]. Searching new platforms of topological physics is considered to be significant as it may provide new insights and may result in invention of new devices[2]. In this paper, we report the emergence of topological edge modes in classical diffusion systems[3] and systems described by the evolutionary game theory[4,5,6]. Specifically, we elucidate the emergence of topological edge modes by discretizing diffusion equation in one and two dimensions[3]. In addition, by analyzing the payoff matrix of rock-paper-scissors cycles, we demonstrate the emergence of chiral edge modes[5]. If time allows, we also discuss non-Hermitian topological phenomena[6].