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In this paper we present a quantum stochastic model for spectroscopicline-shapes in the presence of a co-evolving and non-stationary backgroundpopulation of excitations. Starting from a field theory description forinteracting bosonic excitons, we derive a reduced model whereby opticalexcitons are coupled to an incoherent background via scattering as mediated bytheir screened Coulomb coupling. The Heisenberg equations of motion for theoptical excitons are then driven by an auxiliary stochastic populationvariable, which we take to be the solution of an Ornstein-Uhlenbeck process.It\^o's Lemma then allows us to easily construct and evaluate correlationfunctions and response functions. Focusing on the linear response, we compareour model to the classic Anderson-Kubo model. While similar in motivation,there are profound differences in the predicted lineshapes, notably in terms ofasymmetry, and variation with increasing background population.

Stochastic scattering theory for excitation induced dephasing: Comparison to the Anderson-Kubo lineshape