  We present a method for investigating the steady-state transport properties
of one-dimensional correlated quantum systems. Using a procedure based on our
analysis of finite-size effects in a related classical model (LC line) we show
that stationary currents can be obtained from transient currents in finite
systems driven out of equilibrium. The non-equilibrium dynamics of correlated
quantum systems is calculated using the time-evolving block decimation method.
To demonstrate our method we determine the full I-V characteristic of the
spinless fermion model with nearest-neighbour hopping t_H and interaction V_H
using two different setups to generate currents (turning on/off a potential
bias). Our numerical results agree with exact results for non-interacting
fermions (V_H=0). For interacting fermions we find that in the linear regime eV
<< 4t_H the current I is independent from the setup and our numerical data
agree with the predictions of the Luttinger liquid theory combined with the
Bethe Ansatz solution. For larger potentials V the steady-state current depends
on the current-generating setup and as V increases we find a negative
differential conductance with one setup while the currents saturate at finite
values in the other one. Both effects are due to finite renormalized
bandwidths.
