  We study a linear chain of oscillators with inhomogeneity in their
interactions with phonon bath. In a previous work on the Markovian master
equation of the system, we investigated a model in which the difference in the
site-phonon coupling between adjacent oscillators is the same throughout the
chain. Here we look into another model in which the oscillators are coupled to
the phonon bath with alternating strength at successive sites. Whereas in the
first model all exciton modes are connected, in the second model they are
coupled in pairs that are not connected to each other. Owing to this special
structure in the coupling, the excitation numbers of different modes can be
solved exactly in the steady state. In the first model, the minima of the
excitation profile in the site basis occur at the edges of the chain, whereas
in the second model the maxima occur at the edges. The energy transfer
efficiency in the first model is affected by the source power whereas in the
second model the efficiency is independent of it. A distinct feature in the
second model is that a sink placed at the middle of the chain is able to
distinguish between chains with even and odd number of sites. The energy
transfer efficiency in a chain with even number of sites is higher than a chain
with odd number of sites. Therefore, it reveals the discrete nature of the
chain. In the limit of very long chain when the discreteness of the chain is
less evident, the efficiencies approach each other.
