Time-resolved simulation under a laser pulse

Develop a calculation that tracks the time resolution of the non-equilibrium dynamics under the influence of a laser pulse using the instantaneous-approximation theory developed in Section II.A.

Background

The paper develops an instantaneous approximation (IAP) for pump-driven correlated systems by separating the rapid relative-time decay of Green’s functions from their slower average-time evolution. In the FePS$_3$ application, the authors use a computationally economical implementation that evaluates the self-energy at a single population-inversion instant rather than propagating the local problem throughout the laser pulse.

The unresolved task is to use the more general IAP framework to follow the time-dependent evolution throughout the pulse. Such a calculation would provide genuinely time-resolved non-equilibrium Green’s functions and could improve the description of transient photoemission dynamics beyond the single-instant approximation used in the paper.