  Energy transfer within photosynthetic systems can display quantum effects
such as delocalized excitonic transport. Recently, direct evidence of
long-lived coherence has been experimentally demonstrated for the dynamics of
the Fenna-Matthews-Olson (FMO) protein complex [Engel et al., Nature 446, 782
(2007)]. However, the relevance of quantum dynamical processes to the exciton
transfer efficiency is to a large extent unknown. Here, we develop a
theoretical framework for studying the role of quantum interference effects in
energy transfer dynamics of molecular arrays interacting with a thermal bath
within the Lindblad formalism. To this end, we generalize continuous-time
quantum walks to non-unitary and temperature-dependent dynamics in Liouville
space derived from a microscopic Hamiltonian. Different physical effects of
coherence and decoherence processes are explored via a universal measure for
the energy transfer efficiency and its susceptibility. In particular, we
demonstrate that for the FMO complex an effective interplay between free
Hamiltonian and thermal fluctuations in the environment leads to a substantial
increase in energy transfer efficiency from about 70% to 99%.
