Department of Physics

14756.2030 | Field Theory of Driven Open Quantum Matter (SoSe2023)

Prof. Dr. Sebastian Diehl
Priv. Doz. Dr. Michael Buchhold

Tuesday 12.00 - 13.30, SR 0.03 ITP
Thursday 10.00-11.30, SR 0.03 ITP (first on April 06, every second week)

Thursday 10.00-11.30, SR 0.03 ITP (every other second week)

Further details will be announced in the week before the semester starts.

Contact Tutorials:
Dr. Johannes Lang
Dr. Romain Daviet

Further information
Please register to the Slack workspace, which will serve as a communication platform, and where the exercises will be posted. To do so, please send an email to Thomas Müller (

Recent experimental developments in diverse areas -- ranging from cold atomic gases over light driven semiconductors to NISQ (noisy intermediate scale quantum) platforms -- move systems into the focus, which are located on the interface of quantum optics, condensed matter physics and statistical mechanics. They realize instances of driven open quantum matter: Coherent and driven-dissipative quantum dynamics occur on an equal footing, and they are operated in the thermodynamic limit.
In these lectures, we will develop the tools to understand such systems based on a field theory approach to the many-body Lindblad equation, which is particularly well suited to perform the transition from microscopic physics to macroscopic observables, thereby distilling universal aspects of such setups.

Topics include:
- Lindblad quantum master equation.
- Markovian Keldysh functional integral.
- Semiclassical limit, relation to Langevin equations.
- Equilibrium vs. non-equilibrium conditions, thermal symmetry.
- Universality in non-equilibrium stationary states: renormalization group framework, non-equilibrium criticality, exciton-polariton systems and the Kardar-Parisi-Zhang equation, fate of the Kosterlitz-Thouless phase out of equilibrium.
- Pure vs. mixed states of bosons and fermions: entropy pumps, preparation of pure states by dissipation, Markovian quantum criticality.
- Weak vs. strong symmetries: weak symmetries, symmetry breaking, and slow Goldstone modes; strong symmetries, conservation laws, and slow hydrodynamic modes.
- Strong and weak measurements in many-body systems, replica Keldysh field theory.

- A script will be available
- A. Kamenev, Field Theory of Non-Equilibrium Systems;
- U. C. Tauber, Field Theory Approaches to Non-Equilibrium Dynamics;
- A. Altland and B. Simons, Condensed Matter Field Theory;
- L. Sieberer, M. Buchhold, S. Diehl, Keldysh field theory for driven open quantum systems, Reports of Progress in Physics (2016).