Perturbation theory for the one-dimensional trapping reaction

TL;DR

This paper develops a perturbation series to analyze the survival probability of a particle among multiple diffusing traps in one dimension, revealing how initial trap asymmetry influences the persistence exponent.

Contribution

It introduces a perturbation approach to approximate the survival probability for more than two traps, providing new insights into the effects of trap asymmetry.

Findings

Persistence exponent depends on initial trap asymmetry

Second-order perturbation calculation performed

Method extends understanding of trapping reactions in 1D

Abstract

We consider the survival probability of a particle in the presence of a finite number of diffusing traps in one dimension. Since the general solution for this quantity is not known when the number of traps is greater than two, we devise a perturbation series expansion in the diffusion constant of the particle. We calculate the persistence exponent associated with the particle's survival probability to second order and find that it is characterised by the asymmetry in the number of traps initially positioned on each side of the particle.