Open system dynamics in linear-time beyond the wide-band limit

Nonequilibrium heat transport in quantum systems coupled to wide-band embeddings provides a striking example of the limitations of the generalized Kadanoff-Baym ansatz (GKBA), while solving the full two-time Kadanoff-Baym equations remains computationally prohibitive. To address this challenge, we propose an iterated solution to the reconstruction problem, resulting in a time-linear evolution scheme involving 14 correlators for systems with narrow-band embeddings. This approach eliminates GKBA-related artifacts and resolves convergence issues associated with the wide-band limit. Furthermore, it enables the calculation of energy- and time-resolved currents, facilitating the modeling of heat flows in quantum systems and energy- and time-resolved photoemission experiments, all at significantly reduced computational cost.