A minimal model of quantized conductance in interacting ballistic quantum wires

TL;DR

This paper presents a minimal, boundary-condition-aware model for quantized conductance in finite interacting quantum wires, deriving a Drude-like expression for AC conductance considering spatially varying interactions.

Contribution

It introduces a simple equation-of-motion approach that incorporates different boundary conditions and derives a low-frequency conductance formula for interacting quantum wires.

Findings

Boundary conditions significantly affect conductance behavior.

Derived a Drude-type formula for AC conductance.

Clarified relation to other theoretical approaches.

Abstract

We review what we consider to be the minimal model of quantized conductance in a finite interacting quantum wire. Our approach utilizes the simplicity of the equation of motion description to both deal with general spatially dependent interactions and finite wire geometry. We emphasize the role of two different kinds of boundary conditions, one associated with local "chemical" equilibrium in the sense of Landauer, the other associated with screening in the proximity of the Fermi liquid metallic leads. The relation of our analysis to other approaches to this problem is clarified. We then use our formalism to derive a Drude type expression for the low frequency AC-conductance of the finite wire with general interaction profile.