Jamming and dynamics in Confined Quasi-One Dimensional Systems

Geometrically confining particles to a quasi-one dimensional arrangement so that they can only interact with their nearest neighbours simplifies the way the particles can pack to the extent that we can calculate the distribution of jammed packings exactly, making them ideal systems for exploring the connection between jamming and dynamics. We study the mean squared displacement (MSD) of a system of two dimensional hard discs subject to inertial motion and confined to a single file by two hard lines. At low densities the MSD of the discs increases linearly with time, consistent with the Einstein relation for normal diffusion. However, at high densities the system exhibits anomalous diffusion, where the MSD is proportional to $t^{1/2}$. We show how this dynamic transition is related to the nature and distribution of jammed structures. We also use this simple system to examine the role of dynamic heterogeneity in the motion of dense confined fluids.