Energy relaxation and transfer in excitonic trimer

Two models describing exciton relaxation and transfer (the Redfield model in the secular approximation and Čápekʹs model) are compared for a simple example—a symmetric trimer coupled to a phonon bath. Energy transfer within the trimer occurs via resonance interactions and coupling between the trimer and the bath occurs via modulation of the monomer energies by phonons. Two initial conditions are adopted: (1) one of higher eigenstates of the trimer is initially occupied and (2) one local site of the trimer is initially occupied. The diagonal exciton density matrix elements in the representation of eigenstates are found to be the same for both models, but this is not so for the off-diagonal density matrix elements. Only if the off-diagonal density matrix elements vanish initially (initial condition (1)), they then vanish at arbitrary times in both models. If the initial excitation is local, the off-diagonal matrix elements essentially differ.