The Keldysh action of a multi-terminal time-dependent scatterer

TL;DR

This paper derives a compact expression for the Keldysh action of a multi-terminal, time-dependent quantum scatterer, facilitating advanced analysis in quantum transport, including Full Counting Statistics and Fermi Edge Singularity.

Contribution

It provides a general, simplified form of the Keldysh action for multi-channel, time-dependent scatterers, extending the theoretical tools for quantum transport analysis.

Findings

Derived a compact form of the Keldysh action involving the scattering matrix and Green functions.

Presented special cases applicable to reservoirs with well-defined filling factors and two-reservoir connections.

Demonstrated applications in Full Counting Statistics and Fermi Edge Singularity analysis.

Abstract

We present a derivation of the Keldysh action of a general multi-channel time-dependent scatterer in the context of the Landauer-B\"uttiker approach. The action is a convenient building block in the theory of quantum transport. This action is shown to take a compact form that only involves the scattering matrix and reservoir Green functions. We derive two special cases of the general result, one valid when reservoirs are characterized by well-defined filling factors, the other when the scatterer connects two reservoirs. We illustrate its use by considering Full Counting Statistics and the Fermi Edge Singularity.