  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.
