Conductance of a quantum wire: Landauer's approach versus Kubo formula

TL;DR

This paper compares Landauer's and Kubo's approaches to electron transport in a one-dimensional quantum wire, showing conductance is unaffected by interactions when reservoirs set boundary conditions, and revisiting the Kubo formula in Luttinger liquids.

Contribution

It demonstrates that both Landauer's and Kubo's methods yield consistent conductance results under proper boundary conditions and clarifies the intrinsic conductance in Luttinger liquids.

Findings

Perfect transmission in a quantum wire regardless of interactions.

Conductance is not renormalized by interactions with reservoirs.

Intrinsic conductance in Luttinger liquids depends on interaction parameters.

Abstract

The transport in a pure one-dimensional quantum wire is investigated for any range of interactions. First, the wire is connected to measuring leads. The transmission of an incident electron is found to be perfect, and the conductance is not renormalized by the interactions. Either Landauer's approach or Kubo formula can be used as long as the reservoirs impose the boundary conditions. Second, the Kubo formula as a response to the local field is reconsidered in a generic Luttinger liquid: the ``intrinsic'' conductance thus obtained is determined by the same combination of interaction parameters as that which renormalizes the current.