  We present simulation data for the motion of a polymer chain through a
regular lattice of impenetrable obstacles (Evans-Edwards model). Chain lengths
range from N=20 to N=640, and time up to $10^{7}$ Monte Carlo steps. For $N
\geq 160$ we for the central segment find clear $t^{1/4}$-behavior as an
intermediate asymptote. The also expected $t^{1/2}$-range is not yet developed.
For the end segment also the $t^{1/4}$-behavior is not reached. All these data
compare well to our recent analytical evaluation of the reptation model, which
shows that for shorter times $(t \alt 10^{4})$ the discreteness of the
elementary motion cannot be neglected, whereas for longer times and short
chains $(N \alt 100)$ tube renewal plays an essential role also for the central
segment. Due to the very broad crossover behavior both the diffusion
coefficient and the reptation time within the range of our simulation do not
reach the asymptotic power laws predicted by reptation theory. We present
results for the center-of-mass motion, showing the expected intermediate
$t^{1/2}$-behavior, but again only for very long chains. In addition we show
results for the motion of the central segment relative to the center of mass,
where in some intermediate range we see the expected increase of the effective
power beyond the $t^{1/4}$-law, before saturation sets in. Analysis and
simulations agree on defining a new set of criteria as characteristic for
reptation of finite chains.
