  We theoretically study the efficiency of energy harvesting in linear exciton
chains with an energy bias, where the initial excitation is taking place at the
high-energy end of the chain and the energy is harvested (trapped) at the other
end. The efficiency is characterized by means of the average time for the
exciton to be trapped after the initial excitation. The exciton transport is
treated as the intraband energy relaxation over the states obtained by
numerically diagonalizing the Frenkel Hamiltonian that corresponds to the
biased chain. The relevant intraband scattering rates are obtained from a
linear exciton-phonon interaction. Numerical solution of the Pauli master
equation that describes the relaxation and trapping processes, reveals a
complicated interplay of factors that determine the overall harvesting
efficiency. Specifically, if the trapping step is slower than or comparable to
the intraband relaxation, this efficiency shows a nonmonotonic dependence on
the bias: it first increases when introducing a bias, reaches a maximum at an
optimal bias value, and then decreases again because of dynamic (Bloch)
localization of the exciton states. Effects of on-site (diagonal) disorder,
leading to Anderson localization, are addressed as well.
