  The non-hermitian quantum dynamics of excitonic energy transfer in
photosynthetic systems is investigated using a dissipative two-level dimer
model. The approach is based on the Green's function formalism which permits
consideration of decoherence and intersite transfer processes on comparable
terms. The results indicate a combination of coherent and incoherent behavior
at higher temperatures with the possibility of exceptional points occurring at
the coherent-incoherent crossover regime at critical temperatures. When each
dimer site is coupled equally to the environmental sources of dissipation, the
excitonic wavepacket evolves with time with a coherent component, which can be
attributed to the indistinguishability of the sources of dissipation. The time
evolution characteristics of the B850 Bchls dimer system is analysed using
typical parameter estimates in photosynthetic systems, and the quantum
brachistochrone passage times are obtained for a range of parameters.
