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Steady-state observables, such as occupation numbers and currents, arecrucial experimental signatures in open quantum systems. Thetime-convolutionless (TCL) master equation, which is both exact and time-local,is an ideal candidate for the perturbative computation of such observables. Wedevelop a diagrammatic approach to evaluate the steady-state TCL generatorbased on operators rather than superoperators. We obtain the steady-stateoccupation numbers, extend our formulation to the calculation of currents, andprovide a simple physical interpretation of the diagrams. We further benchmarkour method on a single non-interacting level coupled to Fermi reservoirs, wherewe recover the exact expansion to next-to-leading order. The low number ofdiagrams appearing in our formulation makes the extension to higher ordersaccessible. Combined, these properties make the steady-statetime-convolutionless master equation an effective tool for the calculation ofsteady-state properties in open quantum systems.

Open quantum systems beyond Fermi's golden rule: Diagrammatic expansion of the steady-state time-convolutionless master equation