Interacting excitons in organic and semiconductor systems; the nonlinear exciton equations

Summary form only given. A unified description of nonlinear optical spectroscopies of molecular aggregates (starting with the Frenkel-Heitler-London Hamiltonian) and semiconductors (starting with the two-band model) is developed using the nonlinear exciton equations (NEE). The equations follow explicitly the complete set of dynamical (one-, two-, and three-point) exciton variables relevant for the third-order response. Effects of nuclear motions are incorporated through relaxation superoperators calculated perturbatively in exciton-phonon coupling. A Green function expression for the third order response is derived by solving the (NEE) using a new truncation scheme based on factorizing the three-point relaxation kernels. These results set the stage for designing multidimensional spectroscopies of excitons and analyzing them using coherence-transfer pathways.