Applying voltage sources to a Luttinger liquid with arbitrary transmission

TL;DR

This paper extends the Landauer approach to include strong correlations in quantum wires with arbitrary backscattering, providing an exact solution at a specific interaction strength.

Contribution

It introduces a method to incorporate external voltage sources into the Luttinger liquid model with arbitrary backscatterers, advancing theoretical understanding of correlated quantum transport.

Findings

Exact solution for transport at g=1/2 with arbitrary backscattering

Radiative boundary conditions derived for voltage sources in Luttinger liquids

Generalization of Landauer approach to strongly correlated systems

Abstract

The Landauer approach to transport in mesoscopic conductors has been generalized to allow for strong electronic correlations in a single-channel quantum wire. We describe in detail how to account for external voltage sources in adiabatic contact with a quantum wire containing a backscatterer of arbitrary strength. Assuming that the quantum wire is in the Luttinger liquid state, voltage sources lead to radiative boundary conditions applied to the displacement field employed in the bosonization scheme. We present the exact solution of the transport problem for arbitrary backscattering strength at the special Coulomb interaction parameter g=1/2.