Nonequilibrium Kubo Formula of Finite Conductor Connected to Reservoirs based on Keldysh Formalism

TL;DR

This paper derives a generalized Kubo formula for finite conductors in nonequilibrium steady states using Keldysh formalism, connecting density matrix structure to observable transport properties.

Contribution

It demonstrates that the Keldysh formalism yields a MacLennan-Zubarev form of the density matrix, enabling a nonequilibrium generalization of the Kubo formula and related transport relations.

Findings

Derivation of a nonequilibrium Kubo formula for finite conductors.

Proposal of a shot noise formula in nonequilibrium conditions.

Establishment of a nonequilibrium identity linking conductance, noise, and shot noise.

Abstract

We show that the density matrix for a finite conductor attached to reservoirs obtained by Keldysh formalism is of MacLennan-Zubarev form. On the basis of the fact that the density matrix is the invariant part proposed by Zubarev, it is shown that Keldysh formalism may describe the irreversible processes and steady-state feature of the system. An important consequence of the MacLennan-Zubarev form of the density matrix is a generalization of the Kubo formula in a nonequilibrium case. On the basis of the result, we propose the formula of shot noise and a nonequilibrium identity between differential conductance, noise power and shot noise as a generalized Nyquist-Johnson relation.