Landauer Conductance and Nonequilibrium Noise of One-Dimensional Interacting Electron Systems

TL;DR

This paper calculates the conductance and noise in one-dimensional interacting electron systems, showing conductance remains unrenormalized by interactions and no low-frequency noise occurs, applicable to both Fermi liquids and Luttinger liquids.

Contribution

It introduces a direct ratio-based method to evaluate conductance in interacting systems, differing from traditional Kubo formula approaches, and demonstrates the invariance of conductance under electron-electron interactions.

Findings

Conductance is not renormalized by electron-electron interactions.

No low-frequency nonequilibrium noise is observed in these systems.

Method applies to both Fermi liquids and Tomonaga-Luttinger liquids.

Abstract

The conductance of one-dimensional interacting electron systems is calculated in a manner similar to Landauer's argument for non-interacting systems. Unlike in previous studies in which the Kubo formula was used, the conductance is directly evaluated as the ratio of current $J$ to the chemical potential difference $\Delta \mu$ between right-going and left-going particles. It is shown that both $J$ and $\Delta \mu$ are renormalized by electron-electron (e-e) interactions, but their ratio, the conductance, is not renormalized at all if the e-e interactions are the only scattering mechanism. It is also shown that nonequilibrium current fluctuation at low frequency is absent in such a case. These conclusions are drawn for both Fermi liquids (in which quasi-particles are accompanied with the backflow) and Tomonaga-Luttinger liquids.