Filling of the one-dimensional lattice by k-mers proceeds via fast power-law-like kinetics

During the filling of a one-dimensional lattice by k-site-long hard particles, we find that after initial jamming a power-law-like decay of the density of interparticle gaps occurs, described by a much larger exponent than that expected from mean-field theory. We show that this effect dominates post-jamming filling for large k and should be observable, e.g., during the binding of proteins along a long, stretched DNA molecule.