A new microscopic approach to the optical transitions in quantum dots and quantum dot molecules, which accounts for both diagonal and nondiagonal exciton-phonon interaction, is developed. The cumulant expansion of the linear polarization is generalized to a multilevel system and is applied to calculation of the full time dependence of the polarization and the absorption spectrum. In particular, the broadening of zero-phonon lines is evaluated directly and discussed in terms of real and virtual phonon-assisted transitions. The influence of Coulomb interaction, tunneling, and structural asymmetry on the exciton dephasing in quantum dot molecules is analyzed.
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