Generic Mechanism of Optimal Energy Transfer Efficiency: A Scaling Theory of the Mean First Passage Time in Exciton Systems

An asymptotic scaling theory is presented using the conceptual basis of trapping-free subspace (i.e., orthogonal subspace) to establish the generic mechanism of optimal efficiency of excitation energy transfer (EET) in light-harvesting systems. Analogous to Kramers' turnover in classical rate theory, the enhanced efficiency in the weak damping limit and the suppressed efficiency in the strong damping limit define two asymptotic scaling regimes, which are interpolated to predict the functional form of optimal efficiency of the trapping-free subspace. In the presence of static disorder, the scaling law of transfer time with respect to dephasing rate changes from linear to square root, suggesting a weaker dependence on the environment. Though formulated in the context of EET, the analysis and conclusions apply in general to open quantum processes, including electron transfer, fluorescence emission, and heat conduction.