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Advanced Statistical Physics: Many-body systems out of equilibrium

Alex Tsyplyatyev, WS 2020/2021

Lectures: 3 hours per week
Room: Online via ZOOM on Tuesdays 13:15-15:00 and Thursdays 12:15-13:00
First week: 03.11.2020
Last week: 18.02.2021 (13 weeks of lectures in total, 3 weeks of Christmas vacation 19.12.2020 - 08.01.2021)

Tutorials: 2 hours every second week, 1 group
Tutor: Mr. Viktor Hahn/Mr. Roman Smit
Room: Online via ZOOM on Wednesdays 11:15-13:00
First tutorial:  18.11.2020 (6 weeks of tutorials in total, dates are 18.11, 02.12, 16.12, 20.01, 03.02, 17.02)

This course develops the theoretical methods for dealing with many-body systems in the direction of out-of-equilibrium dynamics. The lecture consists of three parts. The first part can be understood directly after the Thermodynamics and Statistical Physics course (VTH5). Here the basic notion of non-equilibrium statistical systems is developed. The second part can be followed after the Quantum Mechanics I course (VTH4). Here the quantum dynamical tools within the framework of Hamiltonian formalism are developed. And in the third (the largest) 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 is not necessary, all the relevant information about Green functions will be introduced in this lecture.

Announcements

Due to the current situation with coronavirus this course will be conducted online. To sign up you need to send an email to tsyplyatyev[at]itp.uni-frankfurt.de with the following information: your name, surname, Matrikelnummer, and contact email. You will receive access to all materials, including ZOOM link.

You can find the organisational details for this course here.

The tutorial classes start on Wednesday the 18th of November.

Lecture notes

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Complete lecture notes

Problem sheets

  1. Gaussian distribution, Central limiting theorem, Cauchy distribution (Smit)
  2. Discrete Markov process, Fourier transform of an auto-correlation function, Diffusion coefficient of a Brownian particle (Hahn)
  3. Nyquist theorem, Brownian particle in a constant gravitational field, Wick's theorem for Gaussian random variables (Smit)
  4. Master equation in matrix form, Continuous random walk (Hahn)
  5. Aderson's pseudo-spin formulation of the BCS model, Heisenberg equations for the Anderson's pseudo-spin operators (Smit)
  6. Fourier transform of the Theta-function, Green functions of the non-interacting system (Hahn)

Master solutions

  1. Gaussian distribution, Central limiting theorem, Cauchy distribution (Smit)
  2. Discrete Markov process, Fourier transform of an auto-correlation function, Diffusion coefficient of a Brownian particle (Hahn)
  3. Nyquist theorem, Brownian particle in a constant gravitational field, Wick's theorem for Gaussian random variables (Smit)
  4. Master equation in matrix form, Continuous random walk (Hahn)
  5. Aderson's pseudo-spin formulation of the BCS model, Heisenberg equations for the Anderson's pseudo-spin operators (Smit)
  6. Fourier transform of the Theta-function, Green functions of the non-interacting system (Hahn)

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.