  Inspired by the works of [F. Caruso, New J. Phys. 16, 055015 (2014)] and [T.
Scholak et al, J. Phys. B: At. Mol. Opt. Phys. 44 184012 (2011)], which state
that for a large class of complex noisy networks, the optimal efficiency of
quantum transport is universally obtained by mixing coherent (Hamiltonian) and
incoherent (noisy) parts where the contribution of the coherent part is
strictly more than incoherent one, we examine the effect of oscillatory
deformations on two simple prototypes in order to study their effects on the
efficiency of coherent and incoherent energy transport. The prototypes are
interchangeable to each other only by a simple phase modulation, such that the
dynamics for the first type is only coherent, while for the second one the
coherent evolution is completely suppressed and the evolution of the system is
only incoherent (noisy). In this regard, it is shown that there exist a special
deformation by which the efficiency of incoherent transport becomes better than
the coherent one. This result suggests that in the noisy networks with
collective harmonic motions, the optimality of transport can be occurred in
such a way that the contribution of incoherent term is more than the coherent
one.
