A dynamic scattering approach for a gated interacting wire

TL;DR

This paper introduces a dynamic scattering method for analyzing conductance in gated interacting wires, providing a new way to compute both dc and ac conductance matrices in correlated one-dimensional systems.

Contribution

It develops a novel scattering approach that encodes adiabatic contacts via time-dependent boundary conditions, enabling exact conductance calculations for interacting wires.

Findings

DC conductance equals e^2/h for models with conserved charges.

Explicit computation of AC conductance matrix for the Tomonaga-Luttinger model.

The approach respects charge conservation and applies to arbitrary gated wires.

Abstract

A new scattering approach for correlated one-dimensional systems is developed. The adiabatic contact to charge reservoirs is encoded in time-dependent boundary conditions. The conductance matrix for an arbitrary gated wire, respecting charge conservation, is expressed through a dynamic scattering matrix. It is shown that the dc conductance is equal to e^2/h for any model with conserved total left- and right-moving charges. The ac conductance matrix is explicitly computated for the interacting Tomonaga-Luttinger model.