Polymer translocation across a corrugated channel: Fick-Jacobs approximation extended beyond the mean first passage time

Polymer translocation across a corrugated channel is a paradigmatic stochastic process encountered in diverse systems. The instance of time when a polymer first arrives to some prescribed location defines an important characteristic time scale for various phenomena, which are triggered or controlled by such an event. Here we discuss the translocation dynamics of a Gaussian polymer in a periodically-corrugated channel using an appropriately generalized Fick-Jacobs approach. Our main aim is to probe an effective broadness of the first passage time distribution (FPTD), by determining the so-called coefficient of variation $\gamma$ of the FPTD, defined as the ratio of the standard deviation versus the mean first passage time (MFPT). We present a systematic analysis of $\gamma$ as a function of a variety of system's parameters. We show that $\gamma$ never significantly drops below 1 and, in fact, can attain very large values, implying that the MFPT alone cannot characterize the first-passage statistics of the translocation process exhaustively well.