Single-File Diffusion in an Interval: First Passage Properties

TL;DR

This paper studies the long-term survival probability of a tagged particle in single-file diffusion within a finite interval under various boundary and initial conditions, revealing different asymptotic behaviors.

Contribution

It provides a comprehensive analysis of first passage properties in single-file diffusion with diverse boundary conditions and initial configurations, including random interval lengths.

Findings

Different asymptotic behaviors for survival probability depending on boundary conditions.

Initial concentration influences decay similarly to trap density in random intervals.

Analysis of survival probability in single-file diffusion with mixed boundary types.

Abstract

We investigate the long-time behavior of the survival probability of a tagged particle in a single-file diffusion in a finite interval. The boundary conditions are of two types: 1) one boundary is absorbing the second is reflecting, 2) both boundaries are absorbing. For each type of the boundary conditions we consider two types of initial conditions: a) initial number of particles N is given, b) initial concentration of particles is given (N is random). In all four cases the tagged-particle survival probability exhibits different asymptotic behavior. When the both boundaries are absorbing we also consider a case of a random interval length (single-file diffusion on a line with randomly distributed traps). In the latter setting, the initial concentration of particles has the same effect on the asymptotic decay of the survival probability as the concentration of traps.