Mapping of strongly correlated steady-state nonequilibrium to an effective equilibrium

TL;DR

This paper introduces a method to map steady-state nonequilibrium problems onto an effective equilibrium framework, enabling the use of equilibrium many-body techniques to analyze electron transport phenomena.

Contribution

It develops a theoretical mapping that simplifies nonequilibrium problems into an equilibrium form, validated through an example with the Anderson impurity model and a proposed self-consistent algorithm.

Findings

Successfully derived the bias operator Y for the Anderson model

Obtained Kondo conductance and inelastic transport results

Proposed a self-consistent mapping algorithm for general nonequilibrium systems

Abstract

By mapping steady-state nonequilibrium to an effective equilibrium, we formulate nonequilibrium problems within an equilibrium picture where we can apply existing equilibrium many-body techniques to steady-state electron transport problems. We study the analytic properties of many-body scattering states, reduce the boundary condition operator in a simple form and prove that this mapping is equivalent to the correct linear-response theory. In an example of infinite-U Anderson impurity model, we approximately solve for the scattering state creation operators, based on which we derive the bias operator Y to construct the nonequilibrium ensemble in the form of the Boltzmann factor exp(-beta(H-Y)). The resulting Hamiltonian is solved by the non-crossing approximation. We obtain the Kondo anomaly conductance at zero bias, inelastic transport via the charge excitation on the quantum dot and significant inelastic current background over a wide range of bias. Finally, we propose a self-consistent algorithm of mapping general steady-state nonequilibrium.