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The present review is devoted to our recent studies on the excitonic motionin photosynthetic systems. In photosynthesis, the light photon is absorbed tocreate an exciton in the antenna complex of the photosynthetic pigments. Thisexciton then migrates along the chain-biomolecules, like FMO complex, to thereaction centre where it initiates the chemical reactions leading to biomassgeneration. Recently, it has been experimentally observed that the excitonmotion is highly quantum mechanical in nature i.e., it involve long time ($\sim600$ femto sec) quantum coherence effects. Traditional semiclassical theorieslike Forrester's and second Born master equations cannot be applied. We pointout why the 2nd Born non-Markovian master equation and its Markovian limit(also called the Redfield master equation) cannot be used to explain theobserved long coherences. Briefly, the reason is that these approaches areperturbative in nature and in real light harvesting systems various couplings(system-system and system-bath) are of the similar order of magnitude. Variousnew approaches are being developed to go beyond the above two limitingtheories. The present review is not a review in the usual sense of the word aswe summarize our own approaches and only refer to the literature for the otherones. A brief introduction to the sophisticated 2D photon echo spectroscopy isalso given at the end with an emphasis on the underlying physics of themultidimensional echo spectroscopies.

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