Transition from single-file to two-dimensional diffusion of interacting particles in a quasi-one-dimensional channel

Diffusive properties of a monodisperse system of interacting particles confined to a \textit{quasi}-one-dimensional (Q1D) channel are studied using molecular dynamics (MD) simulations. We calculate numerically the mean-squared displacement (MSD) and investigate the influence of the width of the channel (or the strength of the confinement potential) on diffusion in finite-size channels of different shapes (i.e., straight and circular). The transition from single-file diffusion (SFD) to the two-dimensional diffusion regime is investigated. This transition (regarding the calculation of the scaling exponent ($\alpha$) of the MSD $<\Delta x^{2}(t)>$ $\propto t^{\alpha}$) as a function of the width of the channel, is shown to change depending on the channel's confinement profile. In particular the transition can be either smooth (i.e., for a parabolic confinement potential) or rather sharp/stepwise (i.e., for a hard-wall potential), as distinct from infinite channels where this transition is abrupt. This result can be explained by qualitatively different distributions of the particle density for the different confinement potentials.