  Incoherent exciton dynamics in one-dimensional perfect lattices with traps at
sites arranged according to aperiodic deterministic sequences is studied. We
focus our attention on Thue-Morse and Fibonacci systems as canonical examples
of self-similar aperiodic systems. Excitons progressively extend over the
lattice on increasing time and, in this sense, they act as a probe of the
particular arrangements of traps in each system considered. The analysis of the
characteristic features of their time decay indicates that exciton dynamics in
self-similar aperiodic arrangements of traps is quite close to that observed in
periodic ones, but differs significatively from that corresponding to random
lattices. We also report on characteristic features of exciton motion
suggesting that Fibonacci and Thue-Morse orderings might be clearly observed by
appropriate experimental measurements. In the conclusions we comment on the
implications of our work on the way towards a unified theory of the orderings
of matter.
