Exact Asymptotics for One-Dimensional Diffusion with Mobile Traps
Statistical Mechanics
2009-11-07 v3
Abstract
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 rho. We show that the asymptotic behavior of the survival probability, P(t), is given by P(t) ~ exp[-4 rho(Dt/pi)^{1/2}], 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' for an arbitrary finite number of traps.
Cite
@article{arxiv.cond-mat/0205381,
title = {Exact Asymptotics for One-Dimensional Diffusion with Mobile Traps},
author = {Alan J. Bray and Richard A. Blythe},
journal= {arXiv preprint arXiv:cond-mat/0205381},
year = {2009}
}
Comments
Minor revisions; new results for d>1