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Quantum effects in biology: master equation studies of exciton motion in photosynthetic systems

The present review is devoted to our recent studies on the excitonic motion in photosynthetic systems. In photosynthesis, the light photon is absorbed to create an exciton in the antenna complex of the photosynthetic pigments. This exciton then migrates along the chain-biomolecules, like FMO complex, to the reaction centre where it initiates the chemical reactions leading to biomass generation. Recently, it has been experimentally observed that the exciton motion is highly quantum mechanical in nature i.e., it involve long time ($\sim 600$ femto sec) quantum coherence effects. Traditional semiclassical theories like Forrester's and second Born master equations cannot be applied. We point out why the 2nd Born non-Markovian master equation and its Markovian limit (also called the Redfield master equation) cannot be used to explain the observed long coherences. Briefly, the reason is that these approaches are perturbative in nature and in real light harvesting systems various couplings (system-system and system-bath) are of the similar order of magnitude. Various new approaches are being developed to go beyond the above two limiting theories. The present review is not a review in the usual sense of the word as we summarize our own approaches and only refer to the literature for the other ones. A brief introduction to the sophisticated 2D photon echo spectroscopy is also given at the end with an emphasis on the underlying physics of the multidimensional echo spectroscopies.