  We study the nature of the energy transfer process within a pair of coupled
two-level systems (donor and acceptor) subject to interactions with the
surrounding environment. Going beyond a standard weak-coupling approach, we
derive a master equation within the polaron representation that allows for
investigation of both weak and strong system-bath couplings, as well as
reliable interpolation between these two limits. With this theory, we are then
able to explore both coherent and incoherent regimes of energy transfer within
the donor-acceptor pair. We elucidate how the degree of correlation in the
donor and acceptor fluctuations, the donor-acceptor energy mismatch, and the
range of the environment frequency distribution impact upon the energy transfer
dynamics. In the resonant case (no energy mismatch) we describe in detail how a
crossover from coherent to incoherent transfer dynamics occurs with increasing
temperature [A. Nazir, Phys. Rev. Lett. 103, 146404 (2009)], and we also
explore how fluctuation correlations are able to protect coherence in the
energy transfer process. We show that a strict crossover criterion is harder to
define when off-resonance, though we find qualitatively similar population
dynamics to the resonant case with increasing temperature, while the amplitude
of coherent population oscillations also becomes suppressed with growing site
energy mismatch.
