Scattering Theory of Efficient Quantum Transport across Finite Networks

We present a scattering theory for the efficient transmission of an excitation across a finite network with designed disorder. We show that the presence of randomly positioned networks sites allows to significantly accelerate the excitation transfer processes as compared to a dimer structure, if only the disordered Hamiltonians are constrained to be centrosymmetric, and to exhibit a dominant doublet in their spectrum. We identify the cause of this efficiency enhancement in the constructive interplay between disorder-induced fluctuations of the dominant doublet's splitting and the coupling strength between the input and output sites to the scattering channels. We find that the characteristic strength of these fluctuations together with the channel coupling fully control the transfer efficiency.