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We study how time- and angle-resolved photoemission (tr-ARPES) reveals thedynamics of BCS-type, s-wave superconducting systems with time-varying orderparameters. Approximate methods are discussed, based on previous approaches toeither optical conductivity or quantum dot transport, in order to enablecomputationally efficient prediction of photoemission spectra. One use of suchpredictions is to enable extraction of the underlying order parameter dynamicsfrom experimental data, which is topical given the rapidly growing use oftr-ARPES in studying unconventional superconductivity. The methods consideredmodel the two-time lesser Green's functions with an approximated lesserself-energy that describes relaxation by coupling of the system to two types ofbaths. The approach primarily used here also takes into consideration therelaxation of the excited states into equilibrium by explicitly including thelevel-broadening of the retarded and advanced Green's functions. We presentequilibrium and non-equilibrium calculations of tr-ARPES spectrum from ourmodel and discuss the signatures of different types of superconductingdynamics.

Efficient Prediction of Time- and Angle-Resolved Photoemission Spectroscopy Measurements on a Non-Equilibrium BCS Superconductor