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We derive a general expression for the electron nonequilibrium (NE)distribution function in the context of steady state quantum transport througha two-terminal nanodevice with interaction. The central idea for the use of NEdistributions for open quantum systems is that both the NE and many-body (MB)effects are taken into account in the statistics of the finite size systemconnected to reservoirs. We develop an alternative scheme to calculate the NEsteady state properties of such systems. The method, using NE distribution andspectral functions, presents several advantages, and is equivalent toconventional steady-state NE Green's functions (NEGF) calculations when thesame level of approximation for the MB interaction is used. The advantages ofour method resides in the fact that the NE distribution and spectral functionshave better analytic behaviour for numerical calculations. Furthermore ourapproach offer the possibility of introducing further approximations, not onlyat the level of the MB interaction as in NEGF, but also at the level of thefunctional form used for the NE distributions. For the single level model withelectron-phonon coupling we have considered, such approximations provide a goodrepresentation of the exact results, for either the NE distributions themselvesor the transport properties. We also derive the formal extensions of our methodfor systems consisting of several electronic levels and several vibrationmodes.

Nonequilibrium distribution functions for quantum transport: universality and approximation for the steady state regime