  We derive a general formula for the non-Markovian fluorescence spectrum of a
multi-level system interacting with a bosonic environment. To this end, we
apply linear-response theory to describe the dynamics of a detector monitoring
the emission spectrum of a general multi-level system. The resultant emission
lineshape function is directly related to the two-time correlation of system
observables, which we derive using Nakajima-Zwanzig Generalized Master Equation
without assuming a Markov approximation.
