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Advanced Statistical Physics: Many-body systems out of equilibrium

Alex Tsyplyatyev, WS 2022/2023

Lectures: 3 hours per week, Tuesdays 14:00-16:00 and Thursdays 12:00-13:00
Room: Phys 01.114 (Tuesdays and Thursdays)
First lecture: 18.10.2022
Last lecture: 09.02.2023 (15 weeks of lectures in total, 2 weeks of Christmas vacation 22.12.2022 - 06.01.2023)

Tutorials: 2 hours every second week on Fridays 12:00-14:00, 1 group
Tutor: Mr. Carlo Musolino
Room: Phys 2.116
First tutorial:  04.11.2022 (7 weeks of tutorials in total, dates are 04.11, 18.11, 02.12, 16.12, 13.01, 27.01, 10.02)

This course develops the theoretical methods for dealing with many-body systems out of equilibrium. The lecture consists of three major parts. The first part builds on top of the Thermodynamics and Statistical Physics course (VTH5). Here the basic notion of non-equilibrium statistical systems in classical mechanics is developed. The second part starts at the end of the Quantum Mechanics I course (VTH4). Here the dynamical tools for quantum mechanical systems within the framework of Hamiltonian formalism are developed. And in the third part of the course, the Green function technique is generalised to the non-equilibrium problems. The many-body theory course (VQMPT) is suggested for the last part but it is not strictly necessary, this lecture contains a complete introduction to the generic Green functions method.

Announcements

The tutorial classes start on Friday the 4th of November.

Lecture notes

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Complete lecture notes

Problem sheets

  1. Gaussian distribution, Central limiting theorem, Cauchy distribution
  2. Discrete Markov Process, Fourier transform of auto-correlation function, Diffusion coefficient of Brownian particle
  3. Nyquist theorem, Brownian motion and Wick's theorem for Gaussian random variables
  4. Continuous random walks and master equation
  5. BCS model and Heisenberg equations of motion
  6. Fourier transform of the Theta-function and Green functions of the non-interacting system
  7. Fermi liquid theory

Master solutions

  1. Gaussian distribution, Central limiting theorem, Cauchy distribution
  2. Discrete Markov Process, Fourier transform of auto-correlation function, Diffusion coefficient of Brownian particle
  3. Nyquist theorem, Brownian motion and Wick's theorem for Gaussian random variables
  4. Continuous random walks and master equation
  5. BCS model and Heisenberg equations of motion
  6. Fourier transform of the Theta-function and Green functions of the non-interacting system
  7. Fermi Liquid Theory

Content of the course
  1. Introduction: the problem of irreversibility and quantum dynamics
  2. Basic principles of statistics
  3. Langevin equation
  4. Fokker-Planck equation
  5. Quantum dissipation problem
  6. Dynamic phase diagram: non-stationary BCS theory
  7. Non-equilibrium Green functions
  8. Keldysh diagrammatic technique
  9. Quantum kinetic equation
Literature
  • R. Zwanzig, Nonequilibrium Statistical Mechanics, Oxford University Press, Oxford, 2001.
  • D. J. Thouless, The Quantum Mechanics of Many-Body Systems, Dover Publishing, 2014.
  • L. D. Landau, E. M. Lifshitz, Course of Theoretical Physics, Volume 10: Physical Kinetics, Pergamon Press, Exeter, 1981.