NON-EQUILIBRIUM PHYSICS WS 20/21
Lectures: Mon 10:00-12:00; Wed 12:00-14:00 (ONLINE) Tutorials: Mon 12:00-14:00 (ONLINE) Instructor: Jun.-Prof. Dr. Soeren Schlichting (sschlichting AT physik.uni-bielefeld.de) Tutor: Ismail Soudi (isma AT physik.uni-bielefeld.de)
This graduate (M.Sc.) level course provides an introduction to non-equilibrium statistical physics, based on the book of N. Pottier on ``Nonequilibrium Statistical Physics`` and the lecture notes of Prof. Dr. Nicolas Borghini available on his webpage .
.Due to the COVID-19 situation, lectures will be recorded and uploaded on a weekly basis. Notes from the lectures will be posted on this website. Weekly discussion sessions and tutorials will be held via ZOOM; the respective link will we provided to registered participants via E-Mail. Questions regarding the lectures and tutorials can also be posted in the EKVV Lernraum Forum and shall be addressed during the weekly discussions (lectures) or answered directly in the Forum (tutorials).
Topics include:
- Thermodynamics of irreversible processes - Statistical description of non-eq. systems - Kinetic theory - Weak wave turbulence - Stochastic processes - Linear repsonse theoryEvaluation of > Lectures and Tutorials
Exercise sheets:
Exercise Sheet 1 -- Nov 2nd and Solution
Exercise Sheet 2 -- Nov 9th and Solution
Exercise Sheet 3 -- Nov 16th and Solution
Exercise Sheet 4 -- Nov 23rd and Solution
Exercise Sheet 5 -- Nov 30th and Solution
Exercise Sheet 6 -- Dec 7th and Solution
Exercise Sheet 7 -- Dec 14th and Solution
Exercise Sheet 8 -- Dec 21st and Solution
Exercise Sheet 9 -- Jan 4th and Solution
Exercise Sheet 10 -- Jan 11th and Solution
Exercise Sheet 11 -- Jan 18th and Solution
Course materials:
Introductory remarks Notes from Introduction
Week 1 -- Thermodynamics of irreversible processes: Equilibrium thermodynamics (reminder), Description of irreversible processes, Local equilibrium, Entropy production in discrete & continuous systems Notes from Lecture 1 and Notes from Lecture 2
Week 2 -- Thermodynamics of irreversible processes: Linear irreversible proccesses, Simple transport phenomena, Curie and Onsager relations Notes from Lecture 3 and Notes from Lecture 4
Week 3 -- Thermodynamics of irreversible processes: Hydrodynamics, Navier-Stokes equation Notes from Lecture 5 and Notes from Lecture 6
Week 4 -- Thermodynamics of irreversible processes: Simple problems in Hydrodynamics Notes from Lecture 7 -- Statistical description of non-equilibrium systems: Classical systems Notes from Lecture 8
Week 5 -- Statistical description of non-equilibrium systems: Quantum systems, Wigner-Weyl formalism, Reduced distributions, BBGKY Hierarchy Notes from Lecture 9 and Notes from Lecture 10 Some additional LaTeX Notes on Wigner-Weyl formalism
Week 6 -- Statistical description of non-equilibrium systems: Vlasov equatiom, Scales in BBGKY Hierarchy Notes from Lecture 11 -- Kinetic theory: Boltzmann equation, Heuristic derivation Notes from Lecture 12
Week 7 -- Kinetic therory: Boltzmann equation from BBGYKY hierarchy, Balance equations Notes from Lecture 13 and Notes from Lecture 14
Week 8 -- Kinetic therory: Boltzmann entropy, H-Theorem, Equilibrium solutions, Hilbert expansion Notes from Lecture 15 and Notes from Lecture 16
Week 9 -- Kinetic therory: Calculation of transport coefficients Notes from Lecture 17 and Notes from Lecture 18
Week 10 -- Kinetic therory: Hydrodynamics from kinetic theory Notes from Lecture 19 -- Wave turbulence: Stationary turbulence, Richardson cascade, Kolmogorov-Zhakarov spectra Notes from Lecture 20 See also textbook V.E. Zakharov, V.S. L'vov and G. Falkovich; Kolmogorov Spectra of Turbulence I: Wave turbulence (Chapters 1,2,3)
Week 11 -- Wave turbulence: Energy flux along the cascade, Decaying turbulence Notes from Lecture 21 and Notes from Lecture 22
Week 12 -- Stochastic processes: Stochastic Differential Equations, Brownian Motion Notes from Lecture 23 and Notes from Lecture 24
Week 13 -- Stochastic processes: Markov Processes, Fokker-Planck Equation Notes from Lecture 25 and Notes from Lecture 26
Week 14 -- Linear response theory: Kubo relation, Equilibrium correlation functions Notes from Lecture 27 and Notes from Lecture 28
