On the self-consistent Landauer-B\"uttiker formalism

TL;DR

This paper establishes conditions under which a mesoscopic open system with non-linear interactions reaches a unique steady state, and demonstrates that the steady current can be described by Landauer-B"uttiker formulas, linking non-linear and weakly interacting cases.

Contribution

It provides a rigorous framework for the convergence to a self-consistent steady state in non-linear mesoscopic systems and connects it to established Landauer-B"uttiker formulas.

Findings

Steady states are independent of initial conditions under certain conditions.

Steady charge currents follow Landauer-B"uttiker-like formulas.

Connection established between non-linear and weakly interacting systems.

Abstract

We provide sufficient conditions such that the time evolution of a mesoscopic tight-binding open system with a local Hartree-Fock non-linearity converges to a self-consistent non-equilibrium steady state, which is independent of the initial condition from the "small sample". We also show that the steady charge current intensities are given by Landauer-B\"uttiker-like formulas, and make the connection with the case of weakly self-interacting many-body systems.