Super-fermion representation of the Lindblad master equation for the electron transport problem

TL;DR

This paper introduces a super-fermion formalism to solve the Lindblad master equation for electron transport, transforming it into a many-body problem and applying it to a model system, achieving results consistent with established theories.

Contribution

The paper develops a novel super-fermion approach to represent and solve quantum kinetic equations for electron transport, including interacting systems, using non-Hermitian Liouvillian transformations.

Findings

Approach agrees with Landauer theory for non-interacting models.

Successfully models Coulomb blockade regime with Hartree-Fock approximation.

Transforms quantum kinetic equations into a many-body framework.

Abstract

We discuss the use of super-fermion formalism to represent and solve quantum kinetic equations for the electron transport problem. Starting with the Lindblad master equation for the molecule connected to two metal electrodes, we convert the problem of finding the nonequilibrium steady state to the many-body problem with non-Hermitian Liouvillian in super-Fock space. We transform the Liouvillian to the normal ordered form, introduce nonequilibrium quasiparticles by a set of canonical nonunitary transformations and develop general many-body theory for the electron transport through the interacting region. The approach is applied to the electron transport through a single level. We consider a minimal basis hydrogen atom attached to two metal leads in Coulomb blockade regime (out of equilibrium Anderson model) within the nonequilibrium Hartree-Fock approximation as an example of the system with electron interaction. Our approach agrees with exact results given by the Landauer theory for the considered models.