  Single file diffusion (SFD) exhibits anomalously slow collective transport
when particles are able to immobilize by binding and unbinding to the
one-dimensional channel within which the particles diffuse. We have explored
this system for short pore-like channels using a symmetric exclusion process
(SEP) with fully stochastic dynamics. We find that for shorter channels, a
non-Fickian regime emerges for slow binding kinetics. In this regime the
average flux $\langle \Phi \rangle \sim 1/L^3$, where $L$ is the channel length
in units of the particle size. We find that a two-state model describes this
behavior well for sufficiently slow binding rates, where the binding rates
determine the switching time between high-flux bursts of directed transport and
low-flux leaky states. Each high-flux burst is Fickian with $\langle \Phi
\rangle \sim 1/L$. Longer systems are more often in a low flux state, leading
to the non-Fickian behavior.
