  We pioneerly investigate the non-equilibrium transport near a quantum phase
transition in a generic and relatively simple case model, the dissipative
resonant level model, that has many ramifications in nanosystems. We formulate
a rigorous mapping and apply a controlled frequency-dependent renormalization
group approach to compute the non-equilibrium current in the presence of a
finite bias voltage V. For V -> 0, we find that the conductance has its
well-known equilibrium form, while it displays a distinct non-equilibrium
profile at finite voltage.
