Short-Range Coherence in the Energy Transfer of Photosynthetic Light-Harvesting Systems

Abstract

We employ a simple model for the electronic excitations and the exciton-vibration coupling characterizing the B850 ring of the light-harvesting complex in photosynthetic bacteria to investigate the possibility of coherence in the energy transfer within the system. The structure of the equilibrium density matrix is studied using the path integral formulation of quantum statistical mechanics. The calculated mean coherence length is computed from the average root-mean-square deviation of closed imaginary time paths that are sampled via a Monte Carlo procedure. This procedure allows simultaneous examination of the effects of thermal averaging and dynamic and static disorder in a single calculation. The mean coherence length is found to be about two to three chlorophyll monomers at room temperature. The principal factor responsible for this localization is thermal averaging, although static and dynamic disorder further destabilize extended states. At low temperatures the circular arrangement of the pigments favors coherence with respect to the situation in a linear aggregate. Visual inspection of typical paths offers an intuitive picture of the extent of coherent energy delocalization in biological antenna systems.