  We investigate theoretically the phenomenon of exchange narrowing in the
absorption spectrum of a chain of monomers, which are coupled via resonant
dipole-dipole interaction. The individual (uncoupled) monomers exhibit a broad
absorption line shape due to the coupling to an environment consisting of a
continuum of vibrational modes. Upon increasing the interaction between the
monomers, the absorption spectrum of the chain narrows. For a non-Markovian
environment with a Lorentzian spectral density, we find a narrowing of the peak
width (full width at half maximum (FWHM)) by a factor 1/N, where N is the
number of monomers. This is much stronger than the usual 1/sqrt{N} narrowing.
Furthermore it turns out that for a Markovian environment no exchange narrowing
at all occurs. The relation of different measures of the width (FWHM, standard
deviation) is discussed.
