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

Abstract

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