Anomalous Dynamics of Unbiased Polymer Translocation through a Narrow Pore

We consider a polymer of length $N$ translocating through a narrow pore in the absence of external fields. Characterization of its purportedly anomalous dynamics has so far remained incomplete. We show that the polymer dynamics is anomalous until the Rouse time $\tau_{R}\sim N^{1+2\nu}$, with a mean square displacement through the pore consistent with $t^{(1+\nu)/(1+2\nu)}$, with $\nu\approx0.588$ the Flory exponent. This is shown to be directly related to a decay in time of the excess monomer density near the pore as $t^{-(1+\nu)/(1+2\nu)}\exp(-t/\tau_{R})$. Beyond the Rouse time translocation becomes diffusive. In consequence of this, the dwell-time $\tau_{d}$, the time a translocating polymer typically spends within the pore, scales as $N^{2+\nu}$, in contrast to previous claims.