In a recent paper, Bray and Blythe have shown that the survival probability $P_A\mathrm{}\left(t\right)\mathrm{}$ of an A particle diffusing with a diffusion coefficient $D_A$ in a one-dimensional system with diffusive traps B is independent of $D_A$ in the asymptotic limit $\overrightarrow{t}\infty$ and coincides with the survival probability of an immobile target in the presence of diffusive traps. Here, we show that this remarkable behavior has a more general range of validity and holds for systems of an arbitrary dimension d, integer or fractal, provided that the traps are “compactly exploring” the space, i.e., the “fractal” dimension $d_w$ of traps’ trajectories is greater than d. For the marginal case when $d_w=d,$ as exemplified here by conventional diffusion in two-dimensional systems, the decay form is determined up to a numerical factor in the characteristic decay time.

• Received 17 June 2002

DOI:https://doi.org/10.1103/PhysRevE.66.060101