Open Quantum Systems


Lecture details

The lecture will be given by Professor Schoeller.


  • quantum mechanics and statistical mechanics
  • second quantization + Wick theorem
  • suitable for students in the first Master semester


This lecture gives an introduction to the microscopic description of the dynamics of small quantum systems coupled to several reservoirs. Based on the knowledge of elementary statistical mechanics (where large quantum systems in equilibrium are coupled weakly to one reservoir), this lecture will cover a full microscopic formalism including the following aspects:

  • microscopic description of charge, energy and spin exchange between a quantum system and a reservoir
  • Liouville operator formalism to set up formally exact kinetic equations to describe the time evolution of the density matrix into a stationary state (physics of irreversibility)
  • quantum field theory in Liouville space to develop a diagrammatic formalism in the reservoir-system interaction
  • the effect of several reservoirs with different chemical potentials and/or temperatures (stationary currents)
  • the effect of strong system-reservoir interaction (quantum fluctuations at zero temperature)
  • the effect of strong Coulomb interactions on the quantum system (Coulomb blockade)
  • the combination of Liouville formalism with renormalization group methods in nonequilibrium (real-time RG)
  • application to elementary models: Kondo model, interacting resonant level model, spin boson model

Related lecture:

There is a parallel lecture on Greens Functions in Nonequilibrium , where quantum Boltzmann equations are discussed. This lecture requires some more knowledge about many-body theory as introduced in "Quantum theory of condensed matter I"

Subsequent lecture:

There will be a another lecture on "Open Quantum Systems" in the summer semester by Prof. Maarten Wegewijs applying the formalism to many other models relevant for mesoscopic and molecular systems.

For more details, please refer to the university calendar.

Time Room Start
Wed. 10am - 12.30pm 4263 (26 C 401) 15.10.2014 (15 dates)