  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.

Soft Condensed Matter;Statistical Mechanics