Short Time Behavior in De Gennes' Reptation Model

To establish a standard for the distinction of reptation from other modes of polymer diffusion, we analytically and numerically study the displacement of the central bead of a chain diffusing through an ordered obstacle array for times $t < O(N^2)$. Our theory and simulations agree quantitatively and show that the second moment approaches the $t^{1/4}$ often viewed as signature of reptation only after a very long transient and only for long chains (N > 100). Our analytically solvable model furthermore predicts a very short transient for the fourth moment. This is verified by computer experiment.