Landauer transport as a quasisteady state on finite chains under unitary quantum dynamics

TL;DR

This paper demonstrates how Landauer transport emerges as a quasi-steady-state in finite quantum chains under unitary dynamics, with implications for cold atom experiments and a connection to the Kubo formula.

Contribution

It shows the emergence of Landauer transport in finite disordered chains from quantum dynamics, linking initial conditions, transient behavior, and the Kubo formula.

Findings

Large leads produce a uniform quasi-steady-state current matching Landauer's prediction.

Transient regimes last proportional to the disordered sample length.

Finite-size oscillations depend on initial conditions and lead size.

Abstract

In this paper, we study the emergence of a Landauer transport regime from the quantum-mechanical dynamics of free electrons in a disordered tight-binding chain, which is coupled to finite leads with open boundaries. Both partitioned and partition-free initial conditions are analyzed and seen to give rise, for large enough leads, to the same spatially uniform quasi-steady-state current, which agrees with the Landauer value. The quasi-steady-state regime is preceded by a transient regime, which last for a time proportional to the length of the disordered sample, and followed by recursions, after a time that is proportional to the lead size. These theoretical predictions may be of interest to future experiments on transport of fermionic ultra-cold atoms across optical lattices. We also observe finite-size current oscillations, superimposed on the quasi-steady-state, whose behavior depends crucially on the conditions initially imposed on the system. Finally, we show how a time-resolved Kubo formula is able to reproduce this Landauer transport regime, as the leads grow bigger.