Single-File diffusion in a Box

We study diffusion of (fluorescently) tagged hard-core interacting particles of finite size in a finite one-dimensional system. We find an exact analytical expression for the tagged particle probability density using a coordinate Bethe-ansatz, from which the mean square displacement is calculated. The analysis show the existence of three regimes of drastically different behavior for short, intermediate and large times. The results show excellent agreement with stochastic simulations (Gillespie algorithm). The findings of the Letter holds promise for the development of novel bio-nano sensors.