  The large deviation theory has recently been applied to open quantum systems
to uncover dynamical crossovers in the space of quantum trajectories associated
to Markovian evolutions. Such dynamical crossovers are characterized by
qualitative changes in the fluctuations of rare quantum jump trajectories, and
have been observed in the statistics of coherently driven quantum systems. In
this article we investigate the counting statistics of rare quantum
trajectories of an undriven system undergoing a pure relaxation process,
namely, Markovian exciton transport. We find that dynamical crossovers occur in
systems with a minimum of three interacting molecules, and are strongly
activated by exciton delocalization and interference. Our results illustrate
how quantum features of the underlying system Hamiltonian can influence the
statistical properties of energy transfer processes in a non-trivial manner.
