| Abstract |
The energy of sunlight absorbed by an antenna chlorophyll inside a thylakoid disc in chloroplast is known to migrate to the reaction center in the form of an exciton. At normal temperature both the mechanisms of resonance transfer and exciton hopping contribute comparably. The finite-temperature theory of excitons in a molecular aggregate is translated in the language of solid state physics as the treatment of the exciton in a thermal bath of phonons. For the sake of simplicity, the exciton-phonon interaction can be viewed as linear in lattice displacements with higher-order terms neglected. In the interaction picture, the effects of the thermal bath on the dynamics of the exciton can be incorporated into a time-dependent effective potential that involves terms arising from the fluctuation of the medium coordinates from their equilibrium values. The probability of site-to-site exciton transfer is written as a correlation function whose evolution in time can be determined by the cumulant expansion technique. The exciton clothed by phonons can be defined in a natural way. This procedure leads to coarse-graining, and the correlation function for the coarse-grained exciton is defined in terms of the dressed states and the dressed operators. The zeroth-order term in the cumulant expansion corresponds to the resonance transfer of the dressed exciton while the second- and the higher-order terms lead to an expression for the probability of hopping. The transfer probabilities for a clothed exciton is derived under the Debye approximation for a cubic lattice. These expressions can be used to determine the nearest-neighbour transfer probabilities in a reasonably realistic model of the thylakoid disc which in turn can be used for a numerical simulation of excitons dynamics. The model aggregate can be spatially and orientationally disordered. So the transfer probabilities at different sites in different directions are all different which is in sharp contrast with the so-called random walk model. In an earlier computer experiment we have shown that if all the excitons are considered to be created simultaneously, physical processes occurring at widely varying time scales (like exciton creation, exciton transfer, exciton decay by fluorescence, exciton trapping, phonon dynamics and electron transfers) are found to be time-wise self-consistent with one another. In this work we view exciton generation as a continuous process and derive a few analytical results. An algorithm for a very realistic numerical simulation of exciton generation and its utilization in chloroplast is also presented. |
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