A non-equilibrium equation-of-motion approach to quantum transport utilizing projection operators

Maicol A. Ochoa, Michael Galperin, Mark A Ratner

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

We consider a projection operator approach to the non-equilbrium Green function equation-of-motion (PO-NEGF EOM) method. The technique resolves problems of arbitrariness in truncation of an infinite chain of EOMs and prevents violation of symmetry relations resulting from the truncation (equivalence of left- and right-sided EOMs is shown and symmetry with respect to interchange of Fermi or Bose operators before truncation is preserved). The approach, originally developed by Tserkovnikov (1999 Theor. Math. Phys. 118 85) for equilibrium systems, is reformulated to be applicable to time-dependent non-equilibrium situations. We derive a canonical form of EOMs, thus explicitly demonstrating a proper result for the non-equilibrium atomic limit in junction problems. A simple practical scheme applicable to quantum transport simulations is formulated. We perform numerical simulations within simple models and compare results of the approach to other techniques and (where available) also to exact results.

Original languageEnglish
Article number455301
JournalJournal of Physics Condensed Matter
Volume26
Issue number45
DOIs
Publication statusPublished - Nov 12 2014

Fingerprint

Interchanges
Green's function
Equations of motion
Mathematical operators
equations of motion
projection
operators
Computer simulation
approximation
canonical forms
symmetry
equivalence
Green's functions
simulation

Keywords

  • Equation-of-motion
  • Green functions
  • Hubbard operators

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Materials Science(all)

Cite this

A non-equilibrium equation-of-motion approach to quantum transport utilizing projection operators. / Ochoa, Maicol A.; Galperin, Michael; Ratner, Mark A.

In: Journal of Physics Condensed Matter, Vol. 26, No. 45, 455301, 12.11.2014.

Research output: Contribution to journalArticle

@article{5fb91b084fc24e1e8e95b5c3baab8ef0,
title = "A non-equilibrium equation-of-motion approach to quantum transport utilizing projection operators",
abstract = "We consider a projection operator approach to the non-equilbrium Green function equation-of-motion (PO-NEGF EOM) method. The technique resolves problems of arbitrariness in truncation of an infinite chain of EOMs and prevents violation of symmetry relations resulting from the truncation (equivalence of left- and right-sided EOMs is shown and symmetry with respect to interchange of Fermi or Bose operators before truncation is preserved). The approach, originally developed by Tserkovnikov (1999 Theor. Math. Phys. 118 85) for equilibrium systems, is reformulated to be applicable to time-dependent non-equilibrium situations. We derive a canonical form of EOMs, thus explicitly demonstrating a proper result for the non-equilibrium atomic limit in junction problems. A simple practical scheme applicable to quantum transport simulations is formulated. We perform numerical simulations within simple models and compare results of the approach to other techniques and (where available) also to exact results.",
keywords = "Equation-of-motion, Green functions, Hubbard operators",
author = "Ochoa, {Maicol A.} and Michael Galperin and Ratner, {Mark A}",
year = "2014",
month = "11",
day = "12",
doi = "10.1088/0953-8984/26/45/455301",
language = "English",
volume = "26",
journal = "Journal of Physics Condensed Matter",
issn = "0953-8984",
publisher = "IOP Publishing Ltd.",
number = "45",

}

TY - JOUR

T1 - A non-equilibrium equation-of-motion approach to quantum transport utilizing projection operators

AU - Ochoa, Maicol A.

AU - Galperin, Michael

AU - Ratner, Mark A

PY - 2014/11/12

Y1 - 2014/11/12

N2 - We consider a projection operator approach to the non-equilbrium Green function equation-of-motion (PO-NEGF EOM) method. The technique resolves problems of arbitrariness in truncation of an infinite chain of EOMs and prevents violation of symmetry relations resulting from the truncation (equivalence of left- and right-sided EOMs is shown and symmetry with respect to interchange of Fermi or Bose operators before truncation is preserved). The approach, originally developed by Tserkovnikov (1999 Theor. Math. Phys. 118 85) for equilibrium systems, is reformulated to be applicable to time-dependent non-equilibrium situations. We derive a canonical form of EOMs, thus explicitly demonstrating a proper result for the non-equilibrium atomic limit in junction problems. A simple practical scheme applicable to quantum transport simulations is formulated. We perform numerical simulations within simple models and compare results of the approach to other techniques and (where available) also to exact results.

AB - We consider a projection operator approach to the non-equilbrium Green function equation-of-motion (PO-NEGF EOM) method. The technique resolves problems of arbitrariness in truncation of an infinite chain of EOMs and prevents violation of symmetry relations resulting from the truncation (equivalence of left- and right-sided EOMs is shown and symmetry with respect to interchange of Fermi or Bose operators before truncation is preserved). The approach, originally developed by Tserkovnikov (1999 Theor. Math. Phys. 118 85) for equilibrium systems, is reformulated to be applicable to time-dependent non-equilibrium situations. We derive a canonical form of EOMs, thus explicitly demonstrating a proper result for the non-equilibrium atomic limit in junction problems. A simple practical scheme applicable to quantum transport simulations is formulated. We perform numerical simulations within simple models and compare results of the approach to other techniques and (where available) also to exact results.

KW - Equation-of-motion

KW - Green functions

KW - Hubbard operators

UR - http://www.scopus.com/inward/record.url?scp=84908529814&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84908529814&partnerID=8YFLogxK

U2 - 10.1088/0953-8984/26/45/455301

DO - 10.1088/0953-8984/26/45/455301

M3 - Article

AN - SCOPUS:84908529814

VL - 26

JO - Journal of Physics Condensed Matter

JF - Journal of Physics Condensed Matter

SN - 0953-8984

IS - 45

M1 - 455301

ER -