  We evaluate the non-equilibrium single particle Green's functions in the
steady state of the interacting resonant level model (IRLM) under the effect of
an applied bias voltage. Employing the so-called auxiliary master equation
approach, we present accurate nonperturbative results for the non-equilibrium
spectral and effective distribution functions, as well as for the
current-voltage characteristics. We find a drastic change of these spectral
properties between the regimes of low and high bias voltages and discuss the
relation of these changes to the negative differential conductance (NDC), a
prominent feature in the non-equilibrium IRLM. The anomalous evolution of the
distribution function next to the impurity shown by our calculations suggests a
mechanism whereby the impurity gets effectively decoupled from the leads at
voltages where the NDC sets in, in agreement with previous renormalization
group approaches. This scenario is qualitatively confirmed by a Hartree-Fock
treatment of the model.
