Absorption spectra of quantum aggregates interacting via long-range forces

We present a simple formula by which the shape of the absorption spectrum of an aggregate of quantum "monomers" (cold atoms, molecules, quantum dots, nanoparticles, etc.) interacting via dipole-dipole forces can be calculated from the averaged spectrum of the quantum monomer itself. Spectral broadening, due to a wide variety of causes, is included explicitly so that the formula is applicable not only to the idealization of a discrete spectrum but also to the practical situation of a continuously broadened spectrum. In simple cases, analytic results are obtained showing the strong dependence of the aggregate spectrum on the precise nature of the broadening of the quantum monomer spectrum. The formula is compared with results of exact diagonalization of model aggregate Hamiltonians and with experiment.