Nonequilibrium perturbation theory in Liouville-Fock space for inelastic electron transport

TL;DR

This paper develops a nonequilibrium perturbation theory in Liouville-Fock space for inelastic electron transport through quantum dots, combining Lindblad equations with field theory to handle interactions.

Contribution

It introduces a novel perturbation framework in Liouville-Fock space that unifies Lindblad kinetic equations with non-Hermitian field theory for quantum transport.

Findings

Perturbation theory aligns with Keldysh Green's functions for large buffer zones.

Provides a new approach to treat electron-vibronic and electron-electron interactions.

Derives a Lindblad-type kinetic equation for embedded quantum dots.

Abstract

We use a superoperator representation of the quantum kinetic equation to develop nonequilibrium perturbation theory for an inelastic electron current through a quantum dot. We derive a Lindblad-type kinetic equation for an embedded quantum dot (i.e. a quantum dot connected to Lindblad dissipators through a buffer zone). The kinetic equation is converted to non-Hermitian field theory in Liouville-Fock space. The general nonequilibrium many-body perturbation theory is developed and applied to the quantum dot with electron-vibronic and electron-electron interactions. Our perturbation theory becomes equivalent to a Keldysh nonequilibrium Green's function perturbative treatment provided that the buffer zone is large enough to alleviate the problems associated with approximations of the Lindblad kinetic equation.