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

TL;DR

This paper investigates how initial correlations in low-dimensional quantum systems influence steady-state electrical currents, revealing that history and interaction quench processes significantly affect transport properties.

Contribution

It provides an analytic framework showing the impact of initial correlations on steady-state currents in Luttinger liquids and introduces a universal formula accounting for interaction quench histories.

Findings

Initial correlations persist in steady-state currents.

Steady-state current depends on the history of interaction quenches.

Universal formula for steady-state current derived for arbitrary quenches.

Abstract

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.