  We suggest a new method of studying coherence in finite level systems coupled
to the environment and use it for the Hamiltonian that has been used to
describe the light-harvesting pigment-protein complex. The method works with
the adiabatic states and transforms the Hamiltonian to a form in which the
terms responsible for decoherence and population relaxation are separated out.
Decoherence is then accounted for non-perturbatively, and population relaxation
using a Markovian master equation. Analytical results can be obtained for the
seven level system and the calculations are very simple for systems with more
levels. We apply the treatment to the seven level system and the results are in
excellent agreement with the exact numerical results of Nalbach et al. (P.
Nalbach, D. Braun, and M. Thorwart, Physical Review E, 84, 041926 (2011)). Our
approach is able to account for decoherence and population relaxation
separately. It is found that decoherence only causes damping of oscillations,
and does not lead to transfer to the reaction centre. Population relaxation is
necessary for efficient transfer to the reaction centre, in agreement with
earlier findings. Our results show that the transformation to the adiabatic
basis followed by a Redfield type of approach leads to results in good
agreement with exact simulation.
