Survival probability of a diffusing particle constrained by two moving, absorbing boundaries

TL;DR

This paper derives an exact asymptotic survival probability for a Brownian particle confined by two moving absorbing boundaries, with applications to trapping reactions involving evanescent traps.

Contribution

It provides a novel exact formula for the survival probability of a diffusing particle with moving boundaries, extending previous static boundary results.

Findings

Exact asymptotic survival probability formula derived

Results applicable to boundaries with different speeds

Application to trapping reactions with evanescent traps

Abstract

We calculate the exact asymptotic survival probability, Q, of a one-dimensional Brownian particle, initially located located at the point x in (-L,L), in the presence of two moving absorbing boundaries located at \pm(L+ct). The result is Q(y,\lambda) = \sum_{n=-\infty}^\infty (-1)^n \cosh(ny) \exp(-n^2\lambda), where y=cx/D, \lambda = cL/D and D is the diffusion constant of the particle. The results may be extended to the case where the absorbing boundaries have different speeds. As an application, we compute the asymptotic survival probability for the trapping reaction A + B -> B, for evanescent traps with a long decay time.