Anomalous diffusion among two-dimensional scatterers

In this study, we introduce a new model to study the particle diffusion among 2D scatterers. Different from previous models, the potential between the particle and scatterers consists of an attractive interaction as well as a repulsive one. The geometric arrangement of the scatterers has important effects on the diffusion behavior. In the case of periodic scatterers, the low-energy particles may show superdiffusive motion while the high-energy ones diffuse normally. In the case of random scatterers, the global subdiffusive motion may be observed in an energy region slightly above the localization threshold. The subdiffusion phenomenon is explored for the first time in Hamiltonian systems with deterministic scatterers. The mechanism of the observed diffusion behavior is linked to the stickiness effect of chaotic Hamiltonian systems.