Year: 2002
Type: article
Abstract: We consider a diffusing particle, with diffusion constant ${D}^{\ensuremath{'}}$, moving in one dimension in an infinite sea of noninteracting mobile traps with diffusion constant $D$ and density $\ensuremath{\rho}$. We show that the asymptotic behavior of the survival probability, $P(t)$, satisfies $\underset{t\ensuremath{\rightarrow}\ensuremath{\infty}}{lim}[\ensuremath{-}\mathrm{ln}P(t)]/\sqrt{{\ensuremath{\rho}}^{2}Dt}=4/\sqrt{\ensuremath{\pi}}$, independent of ${D}^{\ensuremath{'}}$. 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 ${D}^{\ensuremath{'}}/D$ for an arbitrary finite number of traps.
Source: Physical Review Letters
Authors: Alan J. Bray, Richard A. Blythe
Institution: University of Manchester
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2031300295