Time-dependent Landauer-B\"uttiker formula for transient dynamics

TL;DR

This paper derives an exact, analytical time-dependent Landauer-Büttiker formula for noninteracting quantum junctions, enabling direct calculation of transient electron densities and currents without numerical time propagation.

Contribution

It provides the first analytical solution to the Kadanoff-Baym equations for arbitrary noninteracting junctions, incorporating initial equilibrium states via an imaginary track.

Findings

Analytic expressions for time-dependent densities and currents

No numerical time propagation needed for transient analysis

Applicable to systems with multiple noninteracting leads

Abstract

We solve analytically the Kadanoff-Baym equations for a noninteracting junction connected to an arbitrary number of noninteracting wide-band terminals. The initial equilibrium state is properly described by the addition of an imaginary track to the time contour. From the solution we obtain the time-dependent electron densities and currents within the junction. The final results are analytic expressions as a function of time, and therefore no time propagation is needed - either in transient or in steady-state regimes. We further present and discuss some applications of the obtained formulae.