  We use an off - lattice bead - spring model of a self - avoiding polymer
chain immersed in a 3-dimensional quenched random medium to study chain
dynamics by means of a Monte - Carlo (MC) simulation. The chain center of mass
mean-squared displacement as a function of time reveals two crossovers which
depend both on chain length $N$ and on the degree of Gaussian disorder
$\Delta$. The first one from normal to anomalous diffusion regime is found at
short time $\tau_1$ and observed to vanish rapidly as $\tau_1 \propto \Delta^{-
11}$ with growing disorder. The second crossover back to normal diffusion,
$\tau_2$, scales as $\tau_2 \propto N^{2\nu + 1} f(N^{2-3\nu}\Delta)$ with $f$
being some scaling function. The diffusion coefficient $D_N$ depends strongly
on disorder and drops dramatically at a {\em critical dispersion} $\Delta_{c}
\propto N^{-2 + 3\nu}$ of the disorder potential so that for $\Delta >
\Delta_c$ the chain center of mass is practically frozen.The time-dependent
Rouse modes correlation function $C_{p}(t)$ reveals a characteristic plateau at
$\Delta > \Delta_c$ which is the hallmark of a non - ergodic regime. These
findings agree well with our recent theoretical predictions.
