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arXiv · 2010.09838

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

Michael Sven Ferguson·Oded Zilberberg·Gianni Blatter
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Abstract

Steady-state observables, such as occupation numbers and currents, are crucial experimental signatures in open quantum systems. The time-convolutionless (TCL) master equation, which is both exact and time-local, is an ideal candidate for the perturbative computation of such observables. We develop a diagrammatic approach to evaluate the steady-state TCL generator based on operators rather than superoperators. We obtain the steady-state occupation numbers, extend our formulation to the calculation of currents, and provide a simple physical interpretation of the diagrams. We further benchmark our method on a single non-interacting level coupled to Fermi reservoirs, where we recover the exact expansion to next-to-leading order. The low number of diagrams appearing in our formulation makes the extension to higher orders accessible. Combined, these properties make the steady-state time-convolutionless master equation an effective tool for the calculation of steady-state properties in open quantum systems.

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Michael Sven Ferguson, Oded Zilberberg, Gianni Blatter. 2020-10-19. Open quantum systems beyond Fermi's golden rule: Diagrammatic expansion of the steady-state time-convolutionless master equation. https://doi.org/10.1103/physrevresearch.3.023127

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