Green's Functions in Nonequilibrium


Lecture details

The lecture will be given by Professor Schoeller.


  • elementary knowledge about many-body theory of quantum systems, see e.g. the lecture on "Quantum theory of condensed matter I" given in the first Master semester
  • 2. quantization, field operators, Wick theorem, definition and properties of Greens- and correlation functions in equilibrium, Matsubara formalism, linear response theory, electrons, phonons, random impurities
  • suitable for students in the third Master semester


This lecture contains an introduction to nonequilibrium Greens functions (Keldysh formalism):

  • Introduction to real time Greens functions
  • diagrammatic expansion, Feynman diagrams, path integral formalism
  • derivation of Dyson equation
  • derivation of quantum Boltzmann equations: gradient expansion, quasiparticle approximation, quasiclassical approximation
  • application to random impurities, electron-phonon interaction, electron-electron interaction
  • Fermi liquid theory
  • derivation of linearized quantum Boltzmann equations, calculation of conductivity
  • application to mesoscopic systems

Related Lecture:

Parallel to this lecture there is a lecture on Open quantum systems, where n onequilibrium properties of small quantum systems coupled to a dissipative environment are discussed based on the Liouville operator formalism.

Subsequent Lecture:

In the next summer semester there will be a continuation of this lecture by Dr. Severin Jakobs combining Keldysh formalism with functional renormalization group methods and applying the formalism to one- and zero-dimensional electronic systems coupled to reservoirs.

For more details please refer to the university calendar.

Time Room Starts
Tues. 10am - 12.30pm 4263 (26 C 401) 20.10.2014 (14 dates)