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Abstract
We introduce a method for obtaining analytic approximations to the evolution of Markovian open quantum systems. It is based on resumming a generalized Dyson series in a way that ensures optimal convergence even in the absence of a small parameter. The power of this approach is demonstrated by two benchmark examples: the spatial detection of a free particle and the Landau-Zener problem in the presence of dephasing. The derived approximations are asymptotically exact and exhibit errors on the per mill level over the entire parameter range.
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