Passage Times for Polymer Translocation Pulled through a Narrow Pore

We study the passage times of a translocating polymer of length $N$ in three dimensions, while it is pulled through a narrow pore with a constant force $F$ applied to one end of the polymer. At small to moderate forces, satisfying the condition $FN^{\nu}/k_BT\lesssim1$, where $\nu\approx0.588$ is the Flory exponent for the polymer, we find that $\tau_N$, the mean time the polymer takes to leave the pore, scales as $N^{2+\nu}$ independent of $F$, in agreement with our earlier result for F=0. At strong forces, i.e., for $FN^{\nu}/k_BT\gg1$, the behaviour of the passage time crosses over to $\tau_N\sim N^2/F$. We show here that these behaviours stem from the polymer dynamics at the immediate vicinity of the pore -- in particular, the memory effects in the polymer chain tension imbalance across the pore.