Current-constraining variational approaches to quantum transport

TL;DR

This paper explores variational methods for quantum transport that directly construct non-equilibrium steady states from statistical principles, highlighting limitations of current-constrained approaches in capturing electrostatic potential drops.

Contribution

It analyzes existing current-constrained variational theories and demonstrates their inability to produce realistic electrostatic potential drops in quantum transport.

Findings

Current-constrained theories yield zero electrostatic potential drop.

Such theories require incoherent scattering states to match time-evolved states.

Limitations highlight the need for alternative variational approaches.

Abstract

Presently, the main methods for describing a non-equilibrium charge-transporting steady state are based on time-evolving it from the initial zero-current situation. An alternative class of theories would give the statistical non-equilibrium density operator from principles of statistical mechanics, in a spirit close to Gibbs ensembles for equilibrium systems, leading to a variational principle for the non-equilibrium steady state. We discuss the existing attempts to achieve this using the maximum entropy principle based on constraining the average current. We show that the current-constrained theories result in a zero induced drop in electrostatic potential, so that such ensembles cannot correspond to the time-evolved density matrix, unless left- and right-going scattering states are mutually incoherent.