Extrapolation of the long time behavior of a quasithermal field driven quantum system

We study the relaxation of an isolated interacting heavy-light Fermi-Fermi mixture after it is placed under the influence of an artificial constant electric field. In the regime where the dynamics of the system are characterized by a monotonic evolution through quasi-thermal states and respects the fluctuation dissipation theorem throughout its relaxation, we use the monotonic increase of the effective temperature to infer the two-time self-energy and extrapolate it at long times. This allows us to calculate, in the Dynamical Mean Field Theory framework, momentum dependent quantities at longer times than would otherwise be accessible. Such an approach makes it possible to observe the real-time approach to the steady state with a very low computational cost.