  Despite several different measures of efficiency that are applicable to the
photosynthetic systems, a precise degree of efficiency of these systems is not
completely determined. Introducing an efficient model for the dynamics of
light-harvesting complexes in biological environments is a major purpose in
investigating such systems. Here, we investigate the effect of macroscopic
quantum behavior of a system of two pigments on the transport phenomena in this
system model which interacts with an oscillating environment. We use the
second-order perturbation theory to calculate the time-dependent population of
excitonic states of a two-dimensional Hamiltonian using a non-master equation
approach. Our results demonstrate that the quantum efficiency is robust with
respect to the macroscopicity parameter h solely, but the ratio of
macroscopicity over the pigment-pigment interaction energy can be considered as
a parameter that may control the energy transfer efficiency at a given time.
So, the dynamical behavior and the quantum efficiency of the supposed
photosynthetic system may be influenced by a change in the macroscopic behavior
of the system.
