Advanced Topics in Statistical Physics

- Thermodynamics and Dynamical Statistics -

Lecture

Thomas Gasenzer

Friday, 9:15-11:00, gHS Pw 12 [LSF]

Content - Prerequisites - Literature

Content:
  • 1. Stochastic Processes
    - Elements of probability theory - Introduction to stochastic dynamics - Markov chains - Master equation - Detailed balance - Brownian Motion and dissipation - Langevin equation - Fokker-Planck equation
    Notes
  • 2. From reversible dynamics to irreversibility
    - Liouville dynamics in phase space - Ergodic theorem - KAM theorem for coupled nonlinear harmonic oscillators - Quantum density operator and Wigner function - BBGKY hierarchy
    Notes
  • 3. Hydrodynamic processes
    - Hydrodynamic equations - Dynamic equilibrium fluctuations and near-equilibrium transport - Onsager's Reciprocity Relations - Linear response theory, Kubo formalism - Causality and Kramers-Kronig relations - Fluctuation-dissipation theorem - Application: Power absorption
    Notes
  • 4. Transport Theory
    - Boltzmann equation - Boltzmann's H theorem - Maxwell-Boltzmann distribution - Linearized Boltzmann and Lorentz-Boltzmann equations - Diffusion equation and coefficient of self-diffusion
    Notes

Prerequisites:
  • Quantum Mechanics (Theoretical Physics III), Statistical Mechanics (Theor. Phys. IV)

Literature:
  • R. Balian, From Microphysics to Macrophysics Vol 1+2, Springer Verlag 2007.
  • B. Diu, C. Guthmann, D. Lederer, B. Roulet, Grundlagen der Statistischen Physik, de Gruyter, 1994.
  • K. Huang, Statistical Mechanics, Wiley, 1987 (ISBN 0-471-81518-7).
  • L. D. Landau, E. M. Lifshitz, Lehrbuch der theoretischen Physik, Statistische Physik, Teil 1+2; Statistical Physics part I+II, Pergamon Press, 1980 (ISBN 0-7506-3372-7).
  • R.L. Libov, Kinetic Theory, Prentice Hall, 1990.
  • L. Mandel, E. Wolf, Optical Coherence and Quantum Optics, CUP, Cambridge, 2008 (ISBN 0-521-41711-2).
  • L.E. Reichl, A Modern Course in Statistical Physics, Wiley Interscience, 2nd edition 1998 (ISBN 0-471-59520-9).
  • F. Reif, Fundamentals of Statistical and Thermal Physics McGraw-Hill (1965).
  • F. Schwabl Statistische Mechanik Springer-Verlag, 2000 (ISBN 3-540-31095-2).
  • M. Toda, R. Kubo, N. Saito, Statistical Physics, Equilibrium Statistical Mechanics, Springer Verlag, 2nd edition 1992 (ISBN 3-540-53662-0).