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Here a small interacting sample, coupled to several non‐interacting leads is considered. Initially, the system is at thermal equilibrium. At some instant  t  0  the system is set into the so‐called partition‐free transport scenario by turning on a bias on the leads. Using the theory of Volterra operators we rigorously formulate a Dyson equation for the retarded Green's function and we establish a closed formula for the associated proper interaction self‐energy.

A Dyson Equation for Non‐Equilibrium Green's Functions in the Partition‐Free Setting