  We investigate random walks on a lattice with imperfect traps. In one
dimension, we perturbatively compute the survival probability by reducing the
problem to a particle diffusing on a closed ring containing just one single
trap. Numerical simulations reveal this solution, which is exact in the limit
of perfect traps, to be remarkably robust with respect to a significant
lowering of the trapping probability. We demonstrate that for randomly
distributed traps, the long-time asymptotics of our result recovers the known
stretched exponential decay. We also study an anisotropic three-dimensional
version of our model, where for sufficiently large transverse diffusion the
system is described by the mean-field kinetics. We discuss possible
applications of some of our findings to the decay of excitons in semiconducting
organic polymer materials, and emphasize the crucial influence of the spatial
trap distribution on the kinetics.
