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We propose a systematic approach to the non-equilibrium dynamics of stronglyinteracting many-body quantum systems, building upon the standard perturbativeexpansion in the Coulomb interaction. High order series are derived from theKeldysh version of determinantal diagrammatic Quantum Monte Carlo, and thereconstruction beyond the weak coupling regime of physical quantities isobtained by considering them as analytic functions of a complex-valuedinteraction $U$. Our advances rely on two crucial ingredients: i) a conformalchange of variable, based on the approximate location of the singularities ofthese functions in the complex $U$-plane; ii) a Bayesian inference technique,that takes into account additional known non-perturbative relations, in orderto control the amplification of noise occurring at large $U$. This generalmethodology is applied to the strongly correlated Anderson quantum impuritymodel, and is thoroughly tested both in- and out-of-equilibrium. In thesituation of a finite voltage bias, our method is able to extend previousstudies, by bridging with the regime of unitary conductance, and by dealingwith energy offsets from particle-hole symmetry. We also confirm the existenceof a voltage splitting of the impurity density of states, and find that it istied to a non-trivial behavior of the non-equilibrium distribution function.Beyond impurity problems, our approach could be directly applied toHubbard-like models, as well as other types of expansions.

Reconstructing non-equilibrium regimes of quantum many-body systems from the analytical structure of perturbative expansions