Short time behavior in de Gennes' reptation model

To establish a standard for the distinction of reptation fi om 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) power law (often viewed as a 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.