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 0or=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.