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Noise-assisted quantum electron transfer in photosynthetic complexes

Electron transfer (ET) between primary electron donors and acceptors is modeled in the photosystem II reaction center (RC). Our model includes (i) two discrete energy levels associated with donor and acceptor, interacting through a dipole-type matrix element and (ii) two continuum manifolds of electron energy levels ("sinks"), which interact directly with the donor and acceptor. Namely, two discrete energy levels of the donor and acceptor are embedded in their independent sinks through the corresponding interaction matrix elements. We also introduce classical (external) noise which acts simultaneously on the donor and acceptor (collective interaction). We derive a closed system of integro-differential equations which describes the non-Markovian quantum dynamics of the ET. A region of parameters is found in which the ET dynamics can be simplified, and described by coupled ordinary differential equations. Using these simplified equations, both sharp and flat redox potentials are analyzed. We analytically and numerically obtain the characteristic parameters that optimize the ET rates and efficiency in this system.