Excitations in one-dimensional lattices with traps: Exact results and simulations

We study motion and capture of incoherent excitons in one-dimensional lattices with randomly placed, perfectly absorbing traps. Large-scale numerical simulations of both the master equation and the random walk version of the problem disagree with the result for the survival fraction obtained long ago by Movaghar et al. [J. Stat. Phys. 27 (1982) 473]. We carry out exact calculations for this problem and find that the disagreement can be traced back to rare-event contributions to the analytical result which cannot be seen in simulations, We conclude that for practical purposes, i.e., for averages taken over any finite number of realizations, the only asymptotics observable is the one we have found in our simulations.