Time-resolved photoemission spectroscopy provides a unique and direct way to explore the real-time nonequilibrium dynamics of electrons and holes. The formal theory of spectral function evolution requires inclusion of electronic correlations and dissipation, which are challenging due to the associated long simulation timescales which translate to a high computational cost. Recent methodological developments, namely, the real-time Dyson expansion, as well as theoretical developments of many-body perturbation theory for dissipative systems, have allowed for the study of driven-dissipative interacting quantum systems. In this work, we implement the hitherto unrealized study of driven dynamically correlated systems and utilize these methods and perturbative expansions. We illustrate the combined formalism on a prototypical two-band semiconductor model with long-range density-density Coulomb interactions. We show that the intraband thermalization of conduction band electrons induces nontrivial time-dependent changes in the system's band structure and a time-evolving band-gap renormalization (with a reduction by up to 8.4%). We show that the qualitative features are preserved for a variety of parameters, discuss the corresponding spectral dynamics, and provide an outlook on the introduced simulation framework, which enables treating electron-electron scattering and dissipation effects on equal footing.

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• Dissipative dynamics
• Electronic structure
• Open quantum systems
• Green's function methods
• Many-body techniques