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Nonequilibrium superoperator GW equations.

Upendra Harbola1, Shaul Mukamel

  • 1Department of Chemistry, University of California, Irvine, California 92697-2025, USA. uharbola@uci.edu

The Journal of Chemical Physics
|February 8, 2006
PubMed
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This study generalizes Hedin's equations for many-electron systems to describe nonequilibrium open systems. A closed hierarchy of equations is derived for key Green's function components in Liouville space.

Area of Science:

  • Condensed Matter Physics
  • Quantum Many-Body Theory
  • Theoretical Chemistry

Background:

  • Hedin's equations provide a framework for calculating the one-particle equilibrium Green's function in many-electron systems.
  • Describing nonequilibrium open quantum systems presents significant theoretical challenges.
  • Existing methods often struggle to capture the complex dynamics of interacting electrons in open, non-equilibrium environments.

Purpose of the Study:

  • To generalize Hedin's equations to the realm of nonequilibrium open systems.
  • To develop a theoretical framework capable of describing the dynamics of interacting electrons beyond equilibrium.
  • To establish a closed hierarchy for fundamental quantities in nonequilibrium Green's function theory.

Main Methods:

  • Utilized two fields to independently control the bra and ket evolution of the density matrix.

Related Experiment Videos

  • Extended the formalism to Liouville space, representing quantities as Keldysh matrices.
  • Derived a closed hierarchy connecting the Green's function, self-energy, screened potential, polarization, and vertex function.

    • Main Results:

    • Successfully generalized Hedin's equations to nonequilibrium open systems.
    • Established a closed set of equations for the Green's function and related quantities.
    • Expressed all derived quantities as Keldysh matrices within the Liouville space formalism.

    Conclusions:

    • The developed formalism provides a powerful new tool for studying nonequilibrium phenomena in many-electron systems.
    • The closed hierarchy simplifies the theoretical treatment of complex open quantum systems.
    • This work lays the foundation for future investigations into dynamics beyond equilibrium in condensed matter and quantum chemistry.