Exact Asymptotics for One-Dimensional Diffusion with Mobile Traps

We consider a diffusing particle, with diffusion constant D^', moving in one dimension in an infinite sea of noninteracting mobile traps with diffusion constant D and density ρ. We show that the asymptotic behavior of the survival probability, $P(t)$, satisfies t→∞lim[-lnP(t)]/√ρ²Dt=4/√π, independent of D^'. The result comes from obtaining upper and lower bounds on $P(t)$, and showing that they coincide asymptotically. We also obtain exact results for $P(t)$ to first order in D^'/D for an arbitrary finite number of traps.