Analysis of energy transfer in quantum networks using kinetic network approximations

Abstract

Coherent energy transfer in pigment-protein complexes has been studied by mapping the quantum network to a kinetic network. This gives an analytic way to find parameter values for optimal transfer efficiency. In the case of the Fenna-Matthews-Olson (FMO) complex, the comparison of quantum and kinetic network evolution shows that dephasing-assisted energy transfer is driven by the two-site coherent interaction, and not system-wide coherence. Using the Schur complement, we find a new kinetic network that gives a closer approximation to the quantum network by including all multi-site coherence contributions. Our new network approximation can be expanded as a series with contributions representing different numbers of coherently interacting sites. For both kinetic networks we study the system relaxation time, the time it takes for the excitation to spread throughout the complex. We make mathematically rigorous estimates of the relaxation time when comparing kinetic and quantum network. Numerical simulations comparing the coherent model and the two kinetic network models, confirm our bounds, and show that the relative error of the new kinetic network approximation is several orders of magnitude smaller. Keywords: exciton transfer, quantum efficiency, kinetic networks, FMO, coherent energy transfer, quantum networks, Schur complement.