Lagrange multiplier based transport theory for quantum wires

TL;DR

This paper introduces a Lagrange multiplier approach to model electronic transport in quantum wires, providing a theoretical framework that aligns with the Landauer method for analyzing current flow in nanoscale systems.

Contribution

It presents a novel application of the Lagrange multiplier method to quantum wire transport, establishing equivalence with the Landauer approach within a tight-binding model.

Findings

Lagrange multiplier method successfully models quantum wire transport.

The approach is equivalent to the Landauer method in the considered model.

Provides a new theoretical framework for non-equilibrium steady states.

Abstract

We discuss how a Lagrange multiplier method of non-equilibrium steady state statistical mechanics can be applied to describe the electronic transport in a quantum wire. We describe a theoretical scheme using tight-binding model. The Hamiltonian of the wire is extended via a Lagrange multiplier to ``open'' the quantum system and to drive the current through it. Diagonalization of the extended Hamiltonian yields transport properties of the wire. We show that the Lagrange multiplier method is equivalent to the Landauer approach within the considered model.