Statistische Physik im Nicht-Gleichgewicht
Non-Equilibrium Statistical Physics

I) Non-Equilibrium Dynamics of Classical Systems


1) Onsager Theory, Minimal Entropy Production
2) Boltzmann Equation, H-Theorem
3) Navier-Stokes Equation, Hydrodynamic Modes
4) Long-Time Tails, Fluctuating Hydrodynamics in 1D, KPZ-Equation  5) Turbulence, Kolmogorov Spectrum
6) Dynamical Scaling near Continuous Phase Transitions

II) Non-Equilibrium Dynamics of Quantum Systems

1) Linear Response, Relaxation and Ergodicity Breaking  2) Kibble-Zurek Dynamics
3) Lieb-Robinson bounds
4) Periodically Driven (Floquet) Systems
5) Anderson versus Many-Body Localization

The students will learn the basic methods of Non-Equlibrium Thermodynamics and Statistical Physics together with their applications in a wide range of problems, with an emphasis on examples from Condensed Matter and Many-Body Physics. Both classic topics (Boltzmann-Equation, Linear Response, Scaling and Turbulence) as well as topics of current interest are covered (Lieb-Robinson bounds, Floquet systems, Many-Body Localization). The course will thus prepare students for independent research projects.

The course is a continuation of the Lecture on Thermodynamics and Statistical Physics of the previous semester, which is a necessary requirement. In addition, a good knowledge of Quantum Mechanics and standard mathematical methods like Fourier-Transformation is assumed.

In the thematically structured lecture the learning content is presented. A proper understanding of the contents of the lecture will be verified through the weekly exercise classes. In particular, students are required to present the solution of the elementary parts of the exercise problems on the blackboard.

• R. Balian: From Microphysics to Macrophysics, Volume 2
• D. Forster: Hydrodynamic Fluctuations, Broken Symmetry and Correlation Functions
• Specific literature will be given for chapters I.4-6 and II.2-5

Es findet eine mündliche Prüfung von etwa 30 Minuten Dauer statt. Darin wird das Erreichen der im Abschnitt Lernergebnisse dargestellten Kompetenzen mindestens in der dort angegebenen Erkenntnisstufe exemplarisch durch Verständnisfragen und Beispielrechnungen überprüft.

Prüfungsaufgabe könnte beispielsweise sein:

• Write down the basic evolution equations in non-equilibrium thermodynamics (Onsager, Boltzmann)
• Sketch methods of their solution (relaxation time approximation, ...)
• Write down the definitions of linear response and correlation functions and their interrelations (Fluctuation-Dissipation Theorem, Kramers-Kronig relations)
• Write down scaling solutions for transport coefficients or for spectra far from equilibrium (Kolmogorov)
• Formulate the basic theorems for Floquet systems in terms of the quasi-energy spectrum