Exact analytical description of tracer exchange and particle conversion in single-file systems

Abstract

The finite single-file system (diffusion in one dimension where the mutual passage of particles is inhibited) with particle exchange at the margins and an attractive nearest-neighbor particle-particle interaction is investigated. As the central quantity, the residence time distribution is introduced and related to experimentally observable quantities concerning tracer exchange and conversion. Exact equations determining these quantities are derived. The numerical solution yields the dependence of these quantities on the system parameters. In addition, the correlations in the single-file system are considered.