Single-File System with Absorbing Boundary: Tracer Dynamics and First-Passage Properties

Abstract

In this paper, we review the tagged particle dynamics in a semi-infinite system with an absorbing boundary. The emphasis is on an interplay between the hard-core interparticle interaction and the absorption process. The exact probability density function for the position of a tagged particle is derived by means of probabilistic arguments. First, the initially homogeneous system with constant density of particles is studied. In this setting, the dynamics of the tracer conditioned on nonabsorption becomes subdiffusive, the generalized diffusion coefficient being different from that reported for the system without absorbing boundary. Second, the case when the initial number of particles is finite is discussed. In this case, in the long time limit the tracer diffusion is normal and the hard-core interaction manifests itself through the renormalization of the tracer diffusion coefficient. The Gaussian distribution derived for infinite single-file systems is, in the present semi-infinite setting, replaced by the Rayleigh distribution. Special Issue Comments: This article presents results on the dynamics of a tagged particle in open systems, where the number of particles is not conserved in time. This article is related to the Special Issue articles about advanced statistical properties in single file dynamics,1 the calculation of correlations,2 files with force3 and the zig-zag patterns in files.4