Analysis of energy transfer in quantum networks using kinetic network approximations

TL;DR

This paper develops improved kinetic network models to approximate quantum energy transfer in pigment-protein complexes, providing more accurate predictions of transfer efficiency and relaxation times compared to previous models.

Contribution

It introduces a new kinetic network approximation using the Schur complement that better captures multi-site coherence effects in quantum networks.

Findings

The new kinetic network closely matches quantum network dynamics.

Dephasing-assisted transfer is driven by two-site coherence, not system-wide coherence.

The approximation error is several orders of magnitude smaller than previous models.

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.