NON-EQUILIBRIUM PHYSICS WS 18/19
Lectures: Mon,Wed 12:00-14:00 D6-135 Tutorials: Fri 14:00-16:00 U2-232 Instructor: Jun.-Prof. Dr. Soeren Schlichting (sschlichting AT physik.uni-bielefeld.de) Tutor: Dennis Schroeder (dennis 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``
Topics include:
- Thermodynamics of irreversible processes - Statistical description of non-eq. systems - Kinetic theory - Weak wave turbulence - Stochastic processes - Linear repsonse theoryCourse materials and exercise sheets will become available below over the course of the semester.
Course evaluation for Lectures and Tutorials .
Exercise sheets:
Course materials:
Week 1 -- Thermodynamics of irreversible processes: Equilibrium thermodynamics (reminder), Description of irreversible processes, Local equilibrium, Entropy production in discrete & continuous systems Notes from Oct 8th and Notes from Oct 10th
Week 2 -- Thermodynamics of irreversible processes: Linear irreversible proccesses, Simple transport phenomena, Curie and Onsager relations Notes from Oct 15th
Week 3 -- Thermodynamics of irreversible processes: Coupled transport phenomena, Dynamics of simple fluids, Navier-Stokes equation Notes from Oct 22th and Notes from Oct 24th
Week 4 -- Thermodynamics of irreversible processes: Simple problems in fluid dynamics -- Statistical description of non-equilibrium systems: Description of classical & quantum systems Notes from Oct 22th and Notes from Oct 24th
Week 5 -- Statistical description of non-equilibrium systems: Wigner-Weyl formalism Notes from Nov 5th and Nov 7th
Some additional LaTeX Notes on Wigner-Weyl formalismWeek 6 -- Statistical description of non-equilibrium systems: Non-equilibrium path integral, reduced phase-space distributions Notes from Nov 12th and Notes from Nov 14th
Some additional LaTeX Notes on non-equilibrium path integralWeek 7 -- Statistical description of non-equilibrium systems: BBGKY Hierarchy, Boltzmann equation Notes from Nov 19th and Notes from Nov 21st
Week 8 -- Kinetic theory/Boltzmann equation: Balance equations, Statistical entropy, H-Theorem Notes from Nov 26th and Notes from Nov 28th
Week 9 -- Kinetic theory/Boltzmann equation: Equilibrium solutions, Hilbert expansion, Relaxation Time Approximation Notes from Dec 3rd and Notes from Dec 5th
Week 10 -- Kinetic theory/Boltzmann equation: Calculation of transport coefficients, Hydrodynamic limit Notes from Dec 10th and Notes from Dec 12th
Week 11 -- Kinetic theory/Boltzmann equation: Hydrodynamic limit Notes from Dec 17th -- Wave turbulence: Stationary turbulence, Richardson cascade, Kolmogorov-Zhakarov spectra Notes from Dec 19th 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 12 -- Stationary turbulence: Kolmogorov-Zhakarov spectra, Energy cascade, Decaying turbulence Notes from Jan 7th and Notes from Jan 9th See also textbook S. Nazarenko; Wave turbulence (Chapter 9)
Week 13 -- Stochastic processes: Brownian motion, Fluctuation Dissipation relations Notes from Jan14th and Jan 16th
Week 14 -- Stochastic processes: Kramers-Moyal expansion, Fokker-Planck equations Notes from Jan 21st and Notes from Jan 23rd
Week 15 -- Linear response theory: Derivation of Kubo formula, Fluctuation Dissipation relations Notes from Jan 28th and Jan30th
