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We develop a stochastic model to describe the spectral line shapes in the presence of a non-stationary and co-evolving background population of excitations. Starting from a field theory description for interacting bosonic excitons, we derive a reduced model in which the optically bright excitons are coupled to an incoherent background via scattering mediated by their screened Coulomb coupling. The Heisenberg equations of motion for the bright excitons are then driven by an auxiliary stochastic background population variable characterized by an Ornstein-Uhlenbeck process. The model is applied to interpret the evolution of 2D line shape observed in 2D metal-halide perovskite derivatives. We further generalize the stochastic approach by including the exchange coupling to the bath, and show its distinct spectral signatures. The mathematical limits are provided on determining the background density of states from an Anderson-Kubo like spectrum. Host: Andrei Piryatinski |