Time-convolutionless master equation: Perturbative expansions to arbitrary order and application to quantum dots

Abstract

The time-convolutionless quantum master equation is an exact description of the nonequilibrium dynamics of open quantum systems, with the advantage of being local in time. We derive a perturbative expansion to arbitrary order in the system-reservoir coupling for its generator, which contains significantly fewer terms than the ordered-cumulant expansion. We show that the derived expansion also admits a simple recursive formulation. The derived series is then used to describe the nonequilibrium dynamics of a quantum dot, including coherences. We find a relation between the generator and a generalization of the $T$-matrix. Even though the $T$-matrix rate equations are plagued by divergences, we show that these cancel order by order in the generator of the time-convolutionless master equation. This generalizes previous work on the time-convolutionless Pauli master equation, which does not include coherences, and lays the ground for possible numerical evaluations and analytical resummations.

14 pages

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Cited by in corpus (5)

• Open quantum systems beyond Fermi's golden rule: Diagrammatic expansion of the steady-state time-convolutionless master equation
• Time-convolutionless master equations for composite open quantum systems
• Extracting Dynamical Maps of Non-Markovian Open Quantum Systems
• On time-dependent projectors and on generalization of thermodynamical approach to open quantum systems
• Superoperator master equations for depolarizing dynamics