Master

2041 | **Field Theory of Non-Equilibrium Systems**

Dienstag 10:00 bis 11.30, Seminarraum 0.03 Neubau

Übung Donnerstag 14.00 bis 15.30, Konferenzraum 0.01 Neubau (begins April 27, runs every second week)

Primary Areas of Specialization: ThSol (specialized course)

Tutor:

Federico Tonielli

The course gives an introduction to various aspects of the field theory of non- equilibrium many-body systems, a young and rapidly evolving area of research. A modern functional integral formulation opens up the powerful toolbox of quantum field theory to non-equilibrium situations, such as the efficient use of collective degrees of freedom or the renormalization group. We develop the theoretical concepts needed to work in this field, and apply them to concrete and prominent physical situations.

Lecture notes and exercises

**Contents:**

**• Classical dynamical systems: **

- Techniques: Langevin equations, Martin-Siggia-Rose functional integral, Fokker Planck equations.

- Applications: rare fluctuations, activation problems, dynamical phase transitions: directed percolation (wetting transition), stochastic surface dynamics (Kardar-Parisi-Zhang equation).

**• Quantum dynamical systems:**

- Techniques: Quantum Master equations, Keldysh functional integral.

- Applications: experimental platforms (exciton polariton systems, microcavity arrays), fate of Kosterlitz-Thouless physics in driven open quantum systems, dynamical symmetries, dissipative quantum state engineering, driven closed (Floquet) quantum systems.

**Requirements: **

Statistical mechanics, quantum mechanics, quantum field theory is helpful but not mandatory (can be attended simultaneously).

*Literature:*

*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
J. Zinn-Justin, Quantum Field Theory and Critical Phenomena
L. Sieberer, M. Buchhold, S. Diehl, Keldysh Field Theory for Driven Open Quantum Systems, Rep. Prog. Phys. 79, 096001 (2016), arxiv:1512.00637*