Survival probability of a subdiffusive particle in a d-dimensional sea of mobile traps.
We investigate the long-time behavior of the survival probability P(t) of a mobile particle in d-dimensional continuous Euclidean media doped with noninteracting mobile traps. The particle is strictly subdiffusive, implying that its mean-square displacement grows as tgamma' with 0<gamma'<1. Initially, the traps are scattered randomly and their subsequent mean-square displacement grows as tgamma with 0<gamma<or=1. Instantaneous annihilation of the particle takes place upon contact with any of the traps. The solution to this problem is obtained by deriving lower and upper asymptotic bounds of the survival probability and showing that they converge to one another for long times, thereby unambiguously determining the long-time decay of P(t). For d>or=2 we find that at late times the survival probability is that of the pure target problem (the problem where the particle remains immobile) in agreement with previous studies for the d=1 case. These decay laws remain invariant over the whole gamma range as opposed to the dynamical crossover observed for the case of a purely diffusive particle (gamma'=1) where, for gamma<2/(2+d) , the survival probability becomes that of the so-called trapping problem (the problem where the particle moves in a sea of static traps). This behavior implies that for sufficiently low values of gamma(gamma<2/(2+d)) the survival probability becomes singular in the limit gamma'-->1: trappinglike for gamma'=1 and targetlike for any gamma'<1.
Borrego
R
R
Departamento de Física, Universidad de Extremadura, E-06071 Badajoz, Spain.
Abad
E
E
Yuste
Santos B
SB
D003198:Computer Simulation; D004058:Diffusion; D008956:Models, Chemical; D015233:Models, Statistical; D010316:Particle Size