  We demonstrate the remnant presence of {\em initial} correlations in the {\em
steady-state} electrical current flowing between low-dimensional interacting
leads. The leads are described as Luttinger liquids and electrons can tunnel
via a quantum point-contact. We derive an analytic result for the
time-dependent current and show that ground-state correlations have a large
impact on the relaxation and long-time behavior. In particular, the I-V
characteristic cannot be reproduced by quenching the interaction in time. We
further present a universal formula of the steady-state current $j_{S}$ for an
arbitrary sequence of interaction quenches. It is established that $j_{S}$ is
history dependent provided that the switching process is non-smooth.
