  While the dynamics of polymer chains in equilibrium media is well understood
by now, the polymer dynamics in active non-equilibrium environments can be very
different. Here we study the dynamics of polymers in a viscous medium
containing self-propelled particles in two dimensions by using Brownian
dynamics simulations. We find that the polymer center of mass exhibits a
superdiffusive motion at short to intermediate times and the motion turns
normal at long times, but with a greatly enhanced diffusivity. Interestingly,
the long time diffusivity shows a non-monotonic behavior as a function of the
chain length and stiffness. We analyze how the polymer conformation and the
accumulation of the self-propelled particles, and therefore the directed motion
of the polymer, are correlated. At the point of maximal polymer diffusivity,
the polymer has preferentially bent conformations maintained by the balance
between the chain elasticity and the propelling force generated by the active
particles. We also consider the barrier crossing dynamics of actively-driven
polymers in a double-well potential. The barrier crossing times are
demonstrated to have a peculiar non-monotonic dependence, related to that of
the diffusivity. This effect can be potentially utilized for sorting of
polymers from solutions in \textit{in vitro} experiments.
