A review of modeling interacting transient phenomena with non-equilibrium Green functions

Mark R. Hirsbrunner, Timothy M. Philip, Bora Basa, Youngseok Kim, Moon Jip Park, Matthew J. Gilbert

Research output: Contribution to journalReview articlepeer-review


As experimental probes have matured to observe ultrafast transient and high frequency responses of materials and devices, so to have the theoretical methods to numerically and analytically simulate time- and frequency-resolved transport. In this review article, we discuss recent progress in the development of the time-dependent and frequency-dependent non-equilibrium Green function (NEGF) technique. We begin with an overview of the theoretical underpinnings of the underlying Kadanoff-Baym equations and derive the fundamental NEGF equations in the time and frequency domains. We discuss how these methods have been applied to a variety of condensed matter systems such as molecular electronics, nanoscale transistors, and superconductors. In addition, we survey the application of NEGF in fields beyond condensed matter, where it has been used to study thermalization in ultra-cold atoms and to understand leptogenesis in the early universe. Throughout, we pay special attention to the challenges of incorporating contacts and interactions, as the NEGF method is uniquely capable of accounting for such features.

Original languageEnglish (US)
Article number046001
JournalReports on Progress in Physics
Issue number4
StatePublished - Mar 5 2019


  • frequency-dependent transport
  • non-equilibrium Green functions (NEGF)
  • quantum transport
  • time-dependent transport

ASJC Scopus subject areas

  • Physics and Astronomy(all)


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