Excitation Energy Transfer in a Classical Analogue of Photosynthetic Antennae

We formulate a classical pure dephasing system-bath interaction model in a full correspondence to the well-studied quantum model of natural light-harvesting antennae. The equations of motion of our classical model not only represent the correct classical analogy to the quantum description of excitonic systems, but they also have exactly the same functional form. We demonstrate derivation of classical dissipation and relaxation tensor in second order perturbation theory. We find that the only difference between the classical and quantum descriptions is in the interpretation of the state and in certain limitations imposed on the parameters of the model by classical physics. The effects of delocalization, transfer pathway interference, and the transition from coherent to diffusive transfer can be found already in the classical realm. The only qualitatively new effect occurring in quantum systems is the preference for a downhill energy transfer and the resulting possibility of trapping the energy in the lowest energy state.