Expansion of time-convolutionless non-Markovian quantum master equations: A case study using the Fano–Anderson model

We explore the performance of the time-convolutionless (TCL) projection operator technique using the Fano-Anderson model as a test case. Comparing the exact TCL master equation with an expansion in powers of the strength of the system-environment coupling, we analyze the transient dynamics as well as the steady-state behavior. For a Lorentzian spectral density, we demonstrate that the dimensionless expansion parameter corresponds to the ratio of the environmental correlation time to the relaxati