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

Maicol A. Ochoa*, Michael Galperin, Mark A. Ratner

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


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 (US)
Article number455301
JournalJournal of Physics Condensed Matter
Issue number45
StatePublished - Nov 12 2014


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

ASJC Scopus subject areas

  • Materials Science(all)
  • Condensed Matter Physics


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