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We discuss the formal relationship between the real-time Keldysh andimaginary-time theory for nonequilibrium in quantum dot systems. The latter canbe reformulated using the recently proposed Matsubara voltage approach. Weestablish general conditions for correct analytic continuation procedure onphysical observables, and apply the technique to the calculation of staticquantities in steady-state non-equilibrium for a quantum dot subject to afinite bias voltage and external magnetic field. Limitations of the Matsubaravoltage approach are also pointed out.

Imaginary-time quantum many-body theory out of equilibrium I: Formal equivalence to Keldysh real-time theory and calculation of static properties