Non-equilibrium steady-states for interacting open systems: exact results

TL;DR

This paper proves the existence of exact steady-state transport regimes in interacting mesoscopic systems coupled to reservoirs, providing formulas for steady-state currents and analyzing initial state independence.

Contribution

It introduces an exact time-dependent scattering approach applicable to both partitioned and partition-free scenarios, deriving formulas for steady-state currents and first-order interaction corrections.

Findings

Steady-state transport exists under certain conditions in interacting systems.

Steady-state quantities are independent of initial sample states.

First-order interaction corrections recover mean-field results.

Abstract

Under certain conditions we prove the existence of a steady-state transport regime for interacting mesoscopic systems coupled to reservoirs (leads). The partitioning and partition-free scenarios are treated on an equal footing. Our time-dependent scattering approach is {\it exact} and proves, among other things the independence of the steady-state quantities from the initial state of the sample. Closed formulas for the steady-state current amenable for perturbative calculations w.r.t. the interaction strength are also derived. In the partitioning case we calculate the first order correction and recover the mean-field (Hartree-Fock) results.