  We review our recent quantum stochastic model for spectroscopic lineshapes in
the presence of a co-evolving and non-stationary background population of
excitations. Starting from a field theory description for interacting bosonic
excitons, we derive a reduced model whereby optical excitons are coupled to an
incoherent background via scattering as mediated by their screened Coulomb
coupling. The Heisenberg equations of motion for the optical excitons are then
driven by an auxiliary stochastic population variable, which we take to be the
solution of an Ornstein-Uhlenbeck process. Here we discuss an overview of the
theoretical techniques we have developed as applied to predicting coherent
non-linear spectroscopic signals. We show how direct (Coulomb) and exchange
coupling to the bath give rise to distinct spectral signatures and discuss
mathematical limits on inverting spectral signatures to extract the background
density of states.
