Exact Asymptotics for One-Dimensional Diffusion with Mobile Traps

Details Exact Asymptotics for One-Dimensional Diffusion with Mobile Traps Exact Asymptotics for One-Dimensional Diffusion with Mobile Traps

2002-05-17

arxiv.org/abs/cond-mat/0205381v3

Phys. Rev. Lett. 89, 150601 (2002)

Physics

Condensed Matter

Statistical Mechanics

Minor revisions; new results for d>1

Scientific paper

10.1103/PhysRevLett.89.150601

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.

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