  The excitonic absorption spectrum for a disordered quantum well in presence
of exciton-acoustic phonon interaction is treated beyond the Markov
approximation. Realistic disorder exciton states are taken from a microscopic
simulation, and the deformation potential interaction is implemented. The
exciton Green's function is solved with a self energy in second order Born
quality. The calculated spectra differ from a superposition of Lorentzian
lineshapes by enhanced inter-peak absorption. This is a manifestation of pure
dephasing which should be possible to measure in near-field experiments.
