On the steady state correlation functions of open interacting systems

TL;DR

This paper proves the existence of steady state correlation functions in interacting fermionic mesoscopic systems and derives explicit formulas, connecting to Landauer-Buettiker and Hartree-Fock results.

Contribution

It establishes the existence of NESS in interacting systems under spectral assumptions and provides explicit formulas for correlation functions, including perturbative corrections.

Findings

Steady state exists under small interactions and spectral assumptions.

Explicit formulas for NESS correlation functions are derived.

First-order correction recovers Hartree-Fock results.

Abstract

We address the existence of steady state Green-Keldysh correlation functions of interacting fermions in mesoscopic systems for both the partitioning and partition-free scenarios. Under some spectral assumptions on the non-interacting model and for sufficiently small interaction strength, we show that the system evolves to a NESS which does not depend on the profile of the time-dependent coupling strength/bias. For the partitioned setting we also show that the steady state is independent of the initial state of the inner sample. Closed formulae for the NESS two-point correlation functions (Green-Keldysh functions), in the form of a convergent expansion, are derived. In the partitioning approach, we show that the 0th order term in the interaction strength of the charge current leads to the Landauer-Buettiker formula, while the 1st order correction contains the mean-field (Hartree-Fock) results.