Current-constraining variational approaches to quantum transport

P. Bokes, H. Mera, and R. W. Godby
Phys. Rev. B 72, 165425 – Published 25 October 2005

Abstract

Presently, the main methods for describing a nonequilibrium 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 nonequilibrium density operator from principles of statistical mechanics, in a spirit close to Gibbs ensembles for equilibrium systems, leading to a variational principle for the nonequilibrium 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.

  • Received 18 July 2005

DOI:https://doi.org/10.1103/PhysRevB.72.165425

©2005 American Physical Society

Authors & Affiliations

P. Bokes1,*, H. Mera2, and R. W. Godby2

  • 1Department of Physics, Faculty of Electrical Engineering and Information Technology, Slovak University of Technology, Ilkovičova 3, 841 04 Bratislava, Slovak Republic
  • 2Department of Physics, University of York, Heslington, York YO10 5DD, United Kingdom

  • *Electronic address: Peter.Bokes@stuba.sk

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Issue

Vol. 72, Iss. 16 — 15 October 2005

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