  We develop a theory of the linear optical spectrum of excitons in quantum dot
molecules, including the effect of exciton-phonon coupling beyond the Markov
limit. The model reproduces the general trend of the zero-phonon line
broadening as a function of interdot distance, that were recently measured. The
unexpectedly broad linewidths and their large variation are explained in terms
of both the non-Markov nature of the coupling and of the matching of the phonon
wavelength to the interdot distance.
