The Multimode Conductance Formula for a Closed Ring

TL;DR

This paper derives a classical multimode conductance formula for closed rings, generalizing the Landauer approach, using Kubo and master equation methods, with an example calculation for a waveguide-cavity system.

Contribution

It introduces a classical multimode conductance formula for closed rings, extending the Landauer framework through Kubo and master equation approaches.

Findings

Derived a generalized conductance formula for closed rings

Validated the formula with a waveguide-cavity example

Bridged scattering approach with classical formalism

Abstract

The multimode conductance of a {\em closed} ring is found within the framework of a scattering approach. The expression can be regarded as a generalization of the Landauer formula. The treatment is essentially {\em classical} because we assume short coherence time. Our starting point is the Kubo formalism, but we also use a master equation approach for the derivation. As an example we calculate the conductance of a multimode waveguide with an attached cavity.