Calculating exact propagators in single-file systems via the reflection principle

The dynamics of tagged particles in diffusive single-file systems (one-dimensional systems where the particles are not able to pass each other) is investigated. The presented approach, based on the reflection principle, yields exact propagators for quite a general class of systems. Examples are considered explicitly and compared both with results of computer simulations and, in one case, with the asymptotic behavior known from the literature. Practical implications of the results to the interpretation of data from scattering experiments and to the application of single files for the controlled release of particles are discussed.