Revisiting the transient cage effect: Roughness characterization for diffusion of hard-core particles in quasi-one-dimensional channels

Ballistic diffusion in one dimension displays non-trivial diffusive behavior, with normal diffusion at intermediate time scales related to the cage effect constraining particle diffusion. When particles diffuse in a quasi-one-dimensional channel, overtaking leads to transient cages that practically wash out the normal diffusion regime. In this study, we investigate the ballistic diffusion of particles with two distinct sizes and hard-core interactions within quasi-one-dimensional channels. The dynamics of the system are characterized by the global roughness, which provides clear information about the growing correlations within the system, and the usual mean-square displacement. Diffusion of smaller particles shifts from ballistic-like diffusion characteristics, signaled by saturation of the global roughness, to quasi-two-dimensional diffusion features where the global roughness grows linearly. Interestingly, our findings reveal a double saturation regime in the global roughness of larger particles as the channel width increases, signaling the time scale of smaller particles overtaking. The global roughness thus provides important insights into the interplay between particle size and spatial constraints in confined diffusion processes.