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, where P(s,t) is the probability of finding the carrier at s at time t if it slnrtcd at S, at t = O in a spccific configuration of randomly distributed sites. Equivalently, the process of configuration averaging defines a self-energy operator 2 for a coherent medium [14]. The descriptions are sinlply related by fs,sl = u$(s-sr,u) [l $(u)]-I and therefore a selfconsistent calculation of 5 [8,14] can be used to determine a $(s,t). [$(s,u), ~ ( L I ) are the Laplace transform (LT) of $(s,t) and $(t) r zs +(s,t), respectively.] The CTRW approach is particularly fruitful for trapping or recombination problems. Specifically, there have been a .lumber of cases in the RW literature [15,16] which demonstrate that under certain conditions various transport proverties (including diffusion) on lattices depend onlv on the densitv of "defects" and not on thew spatial arrangements. l'he conditions include low defect concentration and spatial dimension d22. We will further demonstrate this fact by the two approaches to the problem taken in this note. An exact solution for
can be obtained for a general &(s.t) and a periodic distribution of traps [l71 of concentration c = n-3, where n is the distance between traps in units of the lattice constant. The traps are taken to be absorbing sites and the zeroth and the time derivative of the first spatial moment of
determine n(t) and TP, respectively. The details of this derivation will be given elsewhere. We further specialize the result to the case where $(U) --l-bua (O 2 transit times. In the limit of low concentration the sum in Eq. (2) can be replaced by an integral and ( T ~ ) ~ = (0.77)bf1w, W = f" d 3 ~ [lA(K, o)]-I (3)