Correlation induced memory effects in the transport properties of low dimensional systems

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.